%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWW259+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 00:29:16 EDT 2022
% Result : Theorem 12.21s 12.43s
% Output : CNFRefutation 12.28s
% Verified :
% SZS Type : ERROR: Analysing output (Cycle in a tree)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X85,X86,X8,X77] :
( ( class_RealVector_Oreal__normed__vector(X77)
& class_Orderings_Oord(X8) )
=> ( ! [X81] :
( c_Orderings_Oord__class_Oless__eq(X8,X86,X81)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X77,c_Groups_Ominus__class_Ominus(X77,hAPP(X85,X86),hAPP(X85,X81))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
=> ! [X81] :
( c_Orderings_Oord__class_Oless__eq(X8,X86,X81)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X77,hAPP(X85,X81)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X77,hAPP(X85,X86)))) ) ) ),
file('<stdin>',fact_lemmaCauchy) ).
fof(c_0_1,axiom,
! [X46] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X46)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X46)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
file('<stdin>',fact_mrmq__eq) ).
fof(c_0_2,axiom,
? [X71,X82] :
( X82 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& X71 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X76] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X76),X71),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))
& ! [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X55) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X55),X71)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X82,X76)),X55))) ) ),
file('<stdin>',fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096) ).
fof(c_0_3,axiom,
! [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X55) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X55),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X55))),
file('<stdin>',fact_kas_I4_J) ).
fof(c_0_4,axiom,
! [X7,X39,X8] :
( class_Rings_Oidom(X8)
=> ( X39 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Nat_OSuc(c_Polynomial_Oorder(X8,X7,X39))),X39) ) ),
file('<stdin>',fact_order__2) ).
fof(c_0_5,axiom,
! [X7,X39,X8] :
( class_Rings_Oidom(X8)
=> ( X39 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Polynomial_Oorder(X8,X7,X39)),X39)
& ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Nat_OSuc(c_Polynomial_Oorder(X8,X7,X39))),X39) ) ) ),
file('<stdin>',fact_order) ).
fof(c_0_6,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> ? [X47] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X47)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('<stdin>',fact_calculation) ).
fof(c_0_7,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
file('<stdin>',fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096) ).
fof(c_0_8,axiom,
! [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X55)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
file('<stdin>',fact_qr) ).
fof(c_0_9,axiom,
! [X1,X2,X8,X77] :
( class_Orderings_Oord(X77)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X77),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X77,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('<stdin>',fact_le__fun__def) ).
fof(c_0_10,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
file('<stdin>',fact_inv0) ).
fof(c_0_11,axiom,
! [X24,X7,X11,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X9,X7)),c_Groups_Ominus__class_Ominus(X8,X11,X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X9,X7)),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ominus__class_Ominus(X8,X11,X24))) ),
file('<stdin>',fact_mult_Oprod__diff__prod) ).
fof(c_0_12,axiom,
~ ! [X3,X62] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X62),
file('<stdin>',fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096) ).
fof(c_0_13,axiom,
! [X39,X27,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X27),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Polynomial_Osynthetic__div(X8,X39,X27)),c_Polynomial_OpCons(X8,hAPP(c_Polynomial_Opoly(X8,X39),X27),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))) = X39 ),
file('<stdin>',fact_synthetic__div__correct_H) ).
fof(c_0_14,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X26,X25)),X51),X33),X45) ) ),
file('<stdin>',fact_le__add__iff1) ).
fof(c_0_15,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45))
<=> c_Orderings_Oord__class_Oless__eq(X8,X33,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X25,X26)),X51),X45)) ) ),
file('<stdin>',fact_le__add__iff2) ).
fof(c_0_16,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45))
<=> c_Orderings_Oord__class_Oless(X8,X33,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X25,X26)),X51),X45)) ) ),
file('<stdin>',fact_less__add__iff2) ).
fof(c_0_17,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X26,X25)),X51),X33),X45) ) ),
file('<stdin>',fact_less__add__iff1) ).
fof(c_0_18,axiom,
! [X16,X36,X74,X57,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X57)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X57,X56)),X74),X36),X16) ) ),
file('<stdin>',fact_nat__less__add__iff1) ).
fof(c_0_19,axiom,
! [X16,X36,X74,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X57)),X74),X16)) ) ),
file('<stdin>',fact_nat__less__add__iff2) ).
fof(c_0_20,axiom,
! [X16,X36,X74,X57,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X57)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X57,X56)),X74),X36),X16) ) ),
file('<stdin>',fact_nat__le__add__iff1) ).
fof(c_0_21,axiom,
! [X16,X36,X74,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X57)),X74),X16)) ) ),
file('<stdin>',fact_nat__le__add__iff2) ).
fof(c_0_22,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
file('<stdin>',fact_th01) ).
fof(c_0_23,axiom,
! [X39,X7,X8] :
( class_Rings_Oidom(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Polynomial_Oorder(X8,X7,X39)),X39) ),
file('<stdin>',fact_order__1) ).
fof(c_0_24,axiom,
! [X6,X24] :
( X24 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X55] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X24),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X55),X6)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('<stdin>',fact_reduce__poly__simple) ).
fof(c_0_25,axiom,
! [X40,X27,X24,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Oplus__class_Oplus(X8,X27,X40))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X7,X27)),c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X24,X40)))) ),
file('<stdin>',fact_norm__diff__triangle__ineq) ).
fof(c_0_26,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24)) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),c_Groups_Ominus__class_Ominus(X8,X7,X24))),c_Rings_Oinverse__class_Oinverse(X8,X24))) ) ) ),
file('<stdin>',fact_Deriv_Oinverse__diff__inverse) ).
fof(c_0_27,axiom,
! [X6,X17,X10,X18,X49] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49,X18)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X10),X17),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X10),X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X49)),X10),X17),X6) ),
file('<stdin>',fact_nat__diff__add__eq1) ).
fof(c_0_28,axiom,
! [X6,X17,X10,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X10),X17),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X10),X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X18)),X10),X6)) ),
file('<stdin>',fact_nat__diff__add__eq2) ).
fof(c_0_29,axiom,
! [X9,X39,X6,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_Omonom(X8,c_Groups_Oone__class_Oone(X8),X6)),X39)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6)),hAPP(c_Polynomial_Opoly(X8,X39),X9)) ),
file('<stdin>',fact_poly__replicate__append) ).
fof(c_0_30,axiom,
? [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),X55) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096) ).
fof(c_0_31,axiom,
! [X83,X84,X45,X8] :
( ( class_Rings_Ocomm__ring(X8)
& class_Rings_Odvd(X8) )
=> ( c_Rings_Odvd__class_Odvd(X8,X45,X84)
=> ! [X3,X71] :
( c_Rings_Odvd__class_Odvd(X8,X45,c_Groups_Oplus__class_Oplus(X8,X3,X83))
<=> c_Rings_Odvd__class_Odvd(X8,X45,c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X71),X84)),X83)) ) ) ),
file('<stdin>',fact_inf__period_I3_J) ).
fof(c_0_32,axiom,
! [X83,X84,X45,X8] :
( ( class_Rings_Ocomm__ring(X8)
& class_Rings_Odvd(X8) )
=> ( c_Rings_Odvd__class_Odvd(X8,X45,X84)
=> ! [X3,X71] :
( c_Rings_Odvd__class_Odvd(X8,X45,c_Groups_Oplus__class_Oplus(X8,X3,X83))
<=> c_Rings_Odvd__class_Odvd(X8,X45,c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X71),X84)),X83)) ) ) ),
file('<stdin>',fact_inf__period_I4_J) ).
fof(c_0_33,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
file('<stdin>',fact_rnc) ).
fof(c_0_34,axiom,
! [X78,X79,X32,X14,X38,X24] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X38),X14) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X32)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X32)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,X79) ) ) ) ) ) ),
file('<stdin>',fact_zdiv__mono2__lemma) ).
fof(c_0_35,axiom,
! [X78,X79,X32,X14,X38,X24] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X38),X14) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X14,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X32)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,X38) ) ) ) ) ) ),
file('<stdin>',fact_zdiv__mono2__neg__lemma) ).
fof(c_0_36,axiom,
! [X33,X83,X15,X45,X26] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X26,X45)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X83))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X45)),X83)) ) ),
file('<stdin>',fact_zdvd__period) ).
fof(c_0_37,axiom,
! [X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ? [X87] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X87)
& ! [X82,X88] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X82),X88)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X82)),c_RealVector_Onorm__class_Onorm(X8,X88))),X87)) ) ),
file('<stdin>',fact_mult_Opos__bounded) ).
fof(c_0_38,axiom,
! [X24,X7,X8] :
( class_Fields_Ofield(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)),c_Rings_Oinverse__class_Oinverse(X8,X7))),c_Rings_Oinverse__class_Oinverse(X8,X24)) ) ) ),
file('<stdin>',fact_inverse__add) ).
fof(c_0_39,axiom,
! [X14,X38,X78,X79,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X79),X78),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X38),X14))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X24)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X14,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,X38) ) ) ) ),
file('<stdin>',fact_unique__quotient__lemma) ).
fof(c_0_40,axiom,
! [X14,X38,X78,X79,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X79),X78),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X38),X14))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,X14)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,X78)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,X79) ) ) ) ),
file('<stdin>',fact_unique__quotient__lemma__neg) ).
fof(c_0_41,axiom,
! [X16,X36,X74,X57,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X57)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X57,X56)),X74),X36) = X16 ) ),
file('<stdin>',fact_nat__eq__add__iff1) ).
fof(c_0_42,axiom,
! [X16,X36,X74,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16)
<=> X36 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X57)),X74),X16) ) ),
file('<stdin>',fact_nat__eq__add__iff2) ).
fof(c_0_43,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oring(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45)
<=> X33 = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X25,X26)),X51),X45) ) ),
file('<stdin>',fact_eq__add__iff2) ).
fof(c_0_44,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oring(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45)
<=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X26,X25)),X51),X33) = X45 ) ),
file('<stdin>',fact_eq__add__iff1) ).
fof(c_0_45,axiom,
! [X23] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X23) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X23,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X23,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X23,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X23,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('<stdin>',fact_unimodular__reduce__norm) ).
fof(c_0_46,axiom,
! [X24,X7,X11,X9,X8] :
( class_Rings_Oring(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),c_Groups_Ominus__class_Ominus(X8,X11,X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X9,X7)),X24)) ),
file('<stdin>',fact_mult__diff__mult) ).
fof(c_0_47,axiom,
! [X27,X24,X28,X7,X8] :
( class_Rings_Osemiring(X8)
=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X28),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X28),X27)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)),X28),X27) ),
file('<stdin>',fact_combine__common__factor) ).
fof(c_0_48,axiom,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('<stdin>',fact__0961_A_L_Aw_A_094_Ak_A_K_Aa_A_N_A1_A_061_A0_A_N_A1_096) ).
fof(c_0_49,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),c_Groups_Ominus__class_Ominus(X8,X24,X7))),c_Rings_Oinverse__class_Oinverse(X8,X24)) ) ) ),
file('<stdin>',fact_division__ring__inverse__diff) ).
fof(c_0_50,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),c_Groups_Oplus__class_Oplus(X8,X7,X24))),c_Rings_Oinverse__class_Oinverse(X8,X24)) ) ) ),
file('<stdin>',fact_division__ring__inverse__add) ).
fof(c_0_51,axiom,
! [X75,X10,X11,X7,X9,X8] :
( class_Rings_Olinordered__semiring__1__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X7)
=> ( c_Orderings_Oord__class_Oless(X8,X11,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X75)
=> ( c_Groups_Oplus__class_Oplus(X8,X10,X75) = c_Groups_Oone__class_Oone(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X75),X11)),X7) ) ) ) ) ) ),
file('<stdin>',fact_convex__bound__lt) ).
fof(c_0_52,axiom,
! [X75,X10,X11,X7,X9,X8] :
( class_Rings_Olinordered__semiring__1(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X75)
=> ( c_Groups_Oplus__class_Oplus(X8,X10,X75) = c_Groups_Oone__class_Oone(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X75),X11)),X7) ) ) ) ) ) ),
file('<stdin>',fact_convex__bound__le) ).
fof(c_0_53,axiom,
! [X64,X52,X8] :
( ( class_Rings_Odvd(X8)
& class_Rings_Osemiring__0(X8) )
=> ( ? [X3] : hBOOL(hAPP(X52,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X64),X3)))
<=> ? [X3] :
( c_Rings_Odvd__class_Odvd(X8,X64,c_Groups_Oplus__class_Oplus(X8,X3,c_Groups_Ozero__class_Ozero(X8)))
& hBOOL(hAPP(X52,X3)) ) ) ),
file('<stdin>',fact_unity__coeff__ex) ).
fof(c_0_54,axiom,
! [X48,X49,X10,X18] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X10),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X10),X48)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X49)),X10),X48),
file('<stdin>',fact_left__add__mult__distrib) ).
fof(c_0_55,axiom,
! [X10,X11,X12,X9] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X10))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X9)),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X12)),X10)) ) ) ),
file('<stdin>',fact_real__mult__inverse__cancel) ).
fof(c_0_56,axiom,
! [X11,X6,X39,X8] :
( class_Groups_Omonoid__mult(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X6),X39)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X39))),X11) ) ),
file('<stdin>',fact_lemma__realpow__diff) ).
fof(c_0_57,axiom,
! [X35,X15,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X35),X35)))
<=> ( X15 != c_Groups_Ozero__class_Ozero(X8)
| X35 != c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('<stdin>',fact_sum__squares__gt__zero__iff) ).
fof(c_0_58,axiom,
! [X41,X42,X44,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),X41)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(c_0_59,axiom,
! [X35,X15,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X35),X35)),c_Groups_Ozero__class_Ozero(X8))
<=> ( X15 = c_Groups_Ozero__class_Ozero(X8)
& X35 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('<stdin>',fact_sum__squares__le__zero__iff) ).
fof(c_0_60,axiom,
! [X11,X9,X8] :
( class_Rings_Olinordered__ring(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X11)),c_Groups_Ozero__class_Ozero(X8)) ),
file('<stdin>',fact_not__sum__squares__lt__zero) ).
fof(c_0_61,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('<stdin>',fact_r01) ).
fof(c_0_62,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,X7,X39)),X38) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X38),c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38))) ),
file('<stdin>',fact_mult__pCons__left) ).
fof(c_0_63,axiom,
! [X33,X63,X8] :
( class_Rings_Oidom(X8)
=> ( hAPP(c_Polynomial_Opoly(X8,X63),X33) = c_Groups_Ozero__class_Ozero(X8)
<=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X33),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))),X63) ) ),
file('<stdin>',fact_poly__eq__0__iff__dvd) ).
fof(c_0_64,axiom,
! [X10,X11,X12,X9] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X10))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X12))) ) ) ),
file('<stdin>',fact_real__mult__inverse__cancel2) ).
fof(c_0_65,axiom,
! [X9,X6,X8] :
( class_Groups_Omonoid__mult(X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6) ) ),
file('<stdin>',fact_realpow__minus__mult) ).
fof(c_0_66,axiom,
! [X63,X33,X8] :
( class_Rings_Oidom(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X33,c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))),X63)
<=> hAPP(c_Polynomial_Opoly(X8,X63),c_Groups_Ouminus__class_Ouminus(X8,X33)) = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_dvd__iff__poly__eq__0) ).
fof(c_0_67,axiom,
! [X37,X15,X35,X46,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X46),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X37)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X46),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X35))
<=> ( X46 = X15
| X35 = X37 ) ) ),
file('<stdin>',fact_crossproduct__eq) ).
fof(c_0_68,axiom,
! [X45,X33,X25,X26,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( ( X26 != X25
& X33 != X45 )
<=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X45)) != c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X33)) ) ),
file('<stdin>',fact_crossproduct__noteq) ).
fof(c_0_69,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
file('<stdin>',fact_th02) ).
fof(c_0_70,axiom,
! [X16,X26,X59,X60,X8] : hAPP(hAPP(c_Power_Opower_Opower(X8,X60,X59),X26),c_Nat_OSuc(X16)) = hAPP(hAPP(X59,X26),hAPP(hAPP(c_Power_Opower_Opower(X8,X60,X59),X26),X16)),
file('<stdin>',fact_power_Opower_Opower__Suc) ).
fof(c_0_71,axiom,
! [X38,X7,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),c_Polynomial_OpCons(X8,X7,X38)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38))) ),
file('<stdin>',fact_mult__pCons__right) ).
fof(c_0_72,axiom,
! [X6,X7,X8] :
( class_Rings_Oring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8))),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ),
file('<stdin>',fact_power__minus) ).
fof(c_0_73,axiom,
! [X78,X79,X32] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X32)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('<stdin>',fact_q__neg__lemma) ).
fof(c_0_74,axiom,
! [X78,X79,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X32)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X32)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79) ) ) ),
file('<stdin>',fact_q__pos__lemma) ).
fof(c_0_75,axiom,
! [X11,X9,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X9,X11)),c_Groups_Oplus__class_Oplus(X8,X9,X11)) ),
file('<stdin>',fact_realpow__two__diff) ).
fof(c_0_76,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Opcompose(X8,c_Polynomial_OpCons(X8,X7,X39),X38) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X38),c_Polynomial_Opcompose(X8,X39,X38))) ),
file('<stdin>',fact_pcompose__pCons) ).
fof(c_0_77,axiom,
! [X41,X42,X44,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X42)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X44),X41)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(c_0_78,axiom,
! [X41,X42,X44,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41))) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(c_0_79,axiom,
! [X7,X24] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X24,X7)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X24)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7)),
file('<stdin>',fact_complex__mod__triangle__ineq2) ).
fof(c_0_80,axiom,
! [X23,X22] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X22),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X22,X23)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X23))),
file('<stdin>',fact_complex__mod__triangle__sub) ).
fof(c_0_81,axiom,
! [X14,X38,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,X38)),X14) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X38),X14)) ),
file('<stdin>',fact_mult__poly__add__left) ).
fof(c_0_82,axiom,
! [X25,X26,X52] :
( hBOOL(hAPP(X52,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X25)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
& ~ hBOOL(hAPP(X52,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X58] :
( X26 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X58)
& ~ hBOOL(hAPP(X52,X58)) ) ) ),
file('<stdin>',fact_nat__diff__split__asm) ).
fof(c_0_83,axiom,
! [X25,X26,X52] :
( hBOOL(hAPP(X52,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X25)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
=> hBOOL(hAPP(X52,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X58] :
( X26 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X58)
=> hBOOL(hAPP(X52,X58)) ) ) ),
file('<stdin>',fact_nat__diff__split) ).
fof(c_0_84,axiom,
! [X6,X24,X17,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_Omonom(X8,X7,X17)),c_Polynomial_Omonom(X8,X24,X6)) = c_Polynomial_Omonom(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)) ),
file('<stdin>',fact_mult__monom) ).
fof(c_0_85,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ) ),
file('<stdin>',fact_power__Suc__less) ).
fof(c_0_86,axiom,
! [X37] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X37),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('<stdin>',fact_odd__less__0) ).
fof(c_0_87,axiom,
! [X13,X11,X14,X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X9),X14)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X11),X13)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oplus__class_Oplus(X8,X9,X11)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,X13)) ) ) ),
file('<stdin>',fact_norm__add__less) ).
fof(c_0_88,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
file('<stdin>',fact_kas_I3_J) ).
fof(c_0_89,axiom,
! [X9,X38,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Polynomial_Opoly(X8,X39),X9)),hAPP(c_Polynomial_Opoly(X8,X38),X9)) ),
file('<stdin>',fact_poly__mult) ).
fof(c_0_90,axiom,
! [X6,X17] :
( ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X6)) ) ),
file('<stdin>',fact_mult__eq__if) ).
fof(c_0_91,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X16)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X50),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X50))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ) ) ),
file('<stdin>',fact_less__diff__iff) ).
fof(c_0_92,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X16)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X50),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X50))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ) ) ),
file('<stdin>',fact_le__diff__iff) ).
fof(c_0_93,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
file('<stdin>',fact_mult__le__less__imp__less) ).
fof(c_0_94,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
file('<stdin>',fact_mult__less__le__imp__less) ).
fof(c_0_95,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
file('<stdin>',fact_mult__strict__mono_H) ).
fof(c_0_96,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
file('<stdin>',fact_mult__strict__mono) ).
fof(c_0_97,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
file('<stdin>',fact_mult__mono) ).
fof(c_0_98,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
file('<stdin>',fact_mult__mono_H) ).
fof(c_0_99,axiom,
! [X13,X11,X14,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X9),X14)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X11),X13)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X13)) ) ) ),
file('<stdin>',fact_norm__mult__less) ).
fof(c_0_100,axiom,
! [X27,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,c_Polynomial_Osmult(X8,X27,c_Polynomial_Osynthetic__div(X8,X39,X27))) = c_Polynomial_OpCons(X8,hAPP(c_Polynomial_Opoly(X8,X39),X27),c_Polynomial_Osynthetic__div(X8,X39,X27)) ),
file('<stdin>',fact_synthetic__div__correct) ).
fof(c_0_101,axiom,
! [X38,X11,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11)),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X38)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),X38)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(c_0_102,axiom,
! [X6,X24,X7,X8] :
( class_Groups_Ocomm__monoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),X6)) ),
file('<stdin>',fact_power__mult__distrib) ).
fof(c_0_103,axiom,
! [X24,X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),c_Nat_OSuc(X6)))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X24) ) ) ),
file('<stdin>',fact_power__le__imp__le__base) ).
fof(c_0_104,axiom,
! [X11,X9,X8] :
( class_Rings_Olinordered__ring(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X11))) ),
file('<stdin>',fact_sum__squares__ge__zero) ).
fof(c_0_105,axiom,
! [X36,X16,X50] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X50,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X36)))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X50,X16) ),
file('<stdin>',fact_zdvd__reduce) ).
fof(c_0_106,axiom,
! [X9,X8] :
( class_Rings_Oring__1(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X9),c_Groups_Oone__class_Oone(X8)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X9,c_Groups_Oone__class_Oone(X8))),c_Groups_Ominus__class_Ominus(X8,X9,c_Groups_Oone__class_Oone(X8))) ),
file('<stdin>',fact_real__squared__diff__one__factored) ).
fof(c_0_107,axiom,
! [X9,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_OpCons(X8,X7,X39)),X9) = c_Groups_Oplus__class_Oplus(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),hAPP(c_Polynomial_Opoly(X8,X39),X9))) ),
file('<stdin>',fact_poly__pCons) ).
fof(c_0_108,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6))) ) ),
file('<stdin>',fact_power__less__power__Suc) ).
fof(c_0_109,axiom,
! [X24,X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),X6))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
file('<stdin>',fact_power__less__imp__less__base) ).
fof(c_0_110,axiom,
! [X24,X7,X27,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X24) ) ) ),
file('<stdin>',fact_mult__left__le__imp__le) ).
fof(c_0_111,axiom,
! [X24,X27,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X24) ) ) ),
file('<stdin>',fact_mult__right__le__imp__le) ).
fof(c_0_112,axiom,
! [X24,X7,X27,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
file('<stdin>',fact_mult__less__imp__less__left) ).
fof(c_0_113,axiom,
! [X24,X7,X27,X8] :
( class_Rings_Olinordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
file('<stdin>',fact_mult__left__less__imp__less) ).
fof(c_0_114,axiom,
! [X24,X27,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
file('<stdin>',fact_mult__less__imp__less__right) ).
fof(c_0_115,axiom,
! [X24,X27,X7,X8] :
( class_Rings_Olinordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
file('<stdin>',fact_mult__right__less__imp__less) ).
fof(c_0_116,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X33,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> c_Orderings_Oord__class_Oless__eq(X8,X25,X26) ) ) ),
file('<stdin>',fact_mult__le__cancel__left__neg) ).
fof(c_0_117,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X33)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,X25) ) ) ),
file('<stdin>',fact_mult__le__cancel__left__pos) ).
fof(c_0_118,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X33)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> c_Orderings_Oord__class_Oless(X8,X26,X25) ) ) ),
file('<stdin>',fact_mult__less__cancel__left__pos) ).
fof(c_0_119,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X33,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> c_Orderings_Oord__class_Oless(X8,X25,X26) ) ) ),
file('<stdin>',fact_mult__less__cancel__left__neg) ).
fof(c_0_120,axiom,
! [X6,X17,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ) ) ),
file('<stdin>',fact_power__le__imp__le__exp) ).
fof(c_0_121,axiom,
! [X35,X15,X25,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X25)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X25),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X25),X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X35) ) ) ),
file('<stdin>',fact_power__increasing__iff) ).
fof(c_0_122,axiom,
! [X35,X15,X25,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X25)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X25),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X25),X35))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X35) ) ) ),
file('<stdin>',fact_power__strict__increasing__iff) ).
fof(c_0_123,axiom,
! [X6,X17,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ) ) ),
file('<stdin>',fact_power__less__imp__less__exp) ).
fof(c_0_124,axiom,
! [X38,X24,X39,X7,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X7,X39),c_Polynomial_OpCons(X8,X24,X38)) = c_Polynomial_OpCons(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,X38)) ),
file('<stdin>',fact_add__pCons) ).
fof(c_0_125,axiom,
! [X38,X24,X39,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X7,X39),c_Polynomial_OpCons(X8,X24,X38)) = c_Polynomial_OpCons(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X39,X38)) ),
file('<stdin>',fact_diff__pCons) ).
fof(c_0_126,axiom,
! [X9,X6,X39,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),X39),X6)),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Polynomial_Opoly(X8,X39),X9)),X6) ),
file('<stdin>',fact_poly__power) ).
fof(c_0_127,axiom,
! [X40,X24,X27,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24),c_Groups_Ominus__class_Ominus(X8,X27,X40)) ),
file('<stdin>',fact_Deriv_Oadd__diff__add) ).
fof(c_0_128,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Oplus__class_Oplus(X8,X27,X40)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(c_0_129,axiom,
! [X7,X34,X6,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X34)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X34),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ) ) ),
file('<stdin>',fact_power__decreasing) ).
fof(c_0_130,axiom,
! [X7,X34,X6,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X34)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X34),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ) ) ),
file('<stdin>',fact_power__strict__decreasing) ).
fof(c_0_131,axiom,
! [X6,X24,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),X6)) ) ) ) ),
file('<stdin>',fact_power__strict__mono) ).
fof(c_0_132,axiom,
! [X25,X33,X26,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X33))
<=> ( ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X33)
& c_Orderings_Oord__class_Oless(X8,X26,X25) )
| ( c_Orderings_Oord__class_Oless(X8,X33,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless(X8,X25,X26) ) ) ) ),
file('<stdin>',fact_mult__less__cancel__right__disj) ).
fof(c_0_133,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> ( ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X33)
& c_Orderings_Oord__class_Oless(X8,X26,X25) )
| ( c_Orderings_Oord__class_Oless(X8,X33,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless(X8,X25,X26) ) ) ) ),
file('<stdin>',fact_mult__less__cancel__left__disj) ).
fof(c_0_134,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ? [X87] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X87)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X3)),X87)) ) ),
file('<stdin>',fact_mult__right_Opos__bounded) ).
fof(c_0_135,axiom,
! [X11,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ? [X87] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X87)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X3),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X3)),X87)) ) ),
file('<stdin>',fact_mult__left_Opos__bounded) ).
fof(c_0_136,axiom,
! [X11,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9)),c_RealVector_Onorm__class_Onorm(X8,X11))) ),
file('<stdin>',fact_norm__mult__ineq) ).
fof(c_0_137,axiom,
! [X24,X30,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X7,X30)),X24) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X24)) ),
file('<stdin>',fact_mult_Odiff__left) ).
fof(c_0_138,axiom,
! [X29,X11,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X9,X11)),X29) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X29)) ),
file('<stdin>',fact_mult__left_Odiff) ).
fof(c_0_139,axiom,
! [X24,X17,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)),X17) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(c_0_140,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)),X27) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(c_0_141,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)),X27) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ),
file('<stdin>',fact_comm__semiring__class_Odistrib) ).
fof(c_0_142,axiom,
! [X24,X30,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X30)),X24) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X24)) ),
file('<stdin>',fact_mult_Oadd__left) ).
fof(c_0_143,axiom,
! [X29,X11,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X9,X11)),X29) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X29)) ),
file('<stdin>',fact_mult__left_Oadd) ).
fof(c_0_144,axiom,
! [X38,X39,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X39)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X38)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X38)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(c_0_145,axiom,
! [X6,X17,X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ),
file('<stdin>',fact_power__add) ).
fof(c_0_146,axiom,
! [X42,X44,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),X42) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X42)),X44) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(c_0_147,axiom,
! [X17,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X48),c_Nat_OSuc(X49)) ),
file('<stdin>',fact_diff__Suc__diff__eq1) ).
fof(c_0_148,axiom,
! [X17,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48)),X17) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X49),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X17)) ),
file('<stdin>',fact_diff__Suc__diff__eq2) ).
fof(c_0_149,axiom,
! [X40,X27,X24,X7,X14,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( X14 != c_Groups_Ozero__class_Ozero(X8)
=> ( ( X7 = X24
& X27 != X40 )
=> c_Groups_Oplus__class_Oplus(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X14),X27)) != c_Groups_Oplus__class_Oplus(X8,X24,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X14),X40)) ) ) ),
file('<stdin>',fact_add__scale__eq__noteq) ).
fof(c_0_150,axiom,
! [X6,X17,X18] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X17),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X6))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X18)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ) ),
file('<stdin>',fact_power__dvd__imp__le) ).
fof(c_0_151,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X6))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X6) ) ),
file('<stdin>',fact_dvd__mult__cancel) ).
fof(c_0_152,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X16) ) ),
file('<stdin>',fact_nat__mult__dvd__cancel1) ).
fof(c_0_153,axiom,
! [X35,X15,X37] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X37)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X37),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X37),X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X35) ) ),
file('<stdin>',fact_real__mult__le__cancel__iff2) ).
fof(c_0_154,axiom,
! [X35,X15,X37] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X37)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X35),X37))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X35) ) ),
file('<stdin>',fact_real__mult__le__cancel__iff1) ).
fof(c_0_155,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ) ),
file('<stdin>',fact_mult__le__cancel1) ).
fof(c_0_156,axiom,
! [X16,X50,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X50))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ) ),
file('<stdin>',fact_mult__le__cancel2) ).
fof(c_0_157,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ) ),
file('<stdin>',fact_nat__mult__le__cancel1) ).
fof(c_0_158,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ) ),
file('<stdin>',fact_nat__mult__less__cancel1) ).
fof(c_0_159,axiom,
! [X35,X15,X37] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X37)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X35),X37))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X35) ) ),
file('<stdin>',fact_real__mult__less__iff1) ).
fof(c_0_160,axiom,
! [X6,X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X17),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ) ),
file('<stdin>',fact_nat__power__less__imp__less) ).
fof(c_0_161,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),c_RealVector_Onorm__class_Onorm(X8,X24)),c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24))) ),
file('<stdin>',fact_norm__triangle__ineq2) ).
fof(c_0_162,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),c_RealVector_Onorm__class_Onorm(X8,X24)),c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24))) ),
file('<stdin>',fact_norm__diff__ineq) ).
fof(c_0_163,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),c_RealVector_Onorm__class_Onorm(X8,X24))) ),
file('<stdin>',fact_norm__triangle__ineq4) ).
fof(c_0_164,axiom,
! [X11,X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oplus__class_Oplus(X8,X9,X11)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X9),c_RealVector_Onorm__class_Onorm(X8,X11))) ),
file('<stdin>',fact_norm__triangle__ineq) ).
fof(c_0_165,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_Osmult(X8,X7,X39)),X38) = c_Polynomial_Osmult(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38)) ),
file('<stdin>',fact_mult__smult__left) ).
fof(c_0_166,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ),
file('<stdin>',fact_Suc__mult__less__cancel1) ).
fof(c_0_167,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ),
file('<stdin>',fact_Suc__mult__le__cancel1) ).
fof(c_0_168,axiom,
! [X9,X38,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,X38)),X9) = c_Groups_Oplus__class_Oplus(X8,hAPP(c_Polynomial_Opoly(X8,X39),X9),hAPP(c_Polynomial_Opoly(X8,X38),X9)) ),
file('<stdin>',fact_poly__add) ).
fof(c_0_169,axiom,
! [X9,X38,X39,X8] :
( class_Rings_Ocomm__ring(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X39,X38)),X9) = c_Groups_Ominus__class_Ominus(X8,hAPP(c_Polynomial_Opoly(X8,X39),X9),hAPP(c_Polynomial_Opoly(X8,X38),X9)) ),
file('<stdin>',fact_poly__diff) ).
fof(c_0_170,axiom,
! [X17,X24,X6,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17),X24) ) ) ),
file('<stdin>',fact_power__le__dvd) ).
fof(c_0_171,axiom,
! [X48,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),X17),X48) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
file('<stdin>',fact_int__power__div__base) ).
fof(c_0_172,axiom,
! [X57,X56,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X56)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X50))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X50),X56) ) ),
file('<stdin>',fact_le__diff__conv2) ).
fof(c_0_173,axiom,
! [X22,X20,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X21,X20)),X22) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X22)),
file('<stdin>',fact_zdiff__zmult__distrib) ).
fof(c_0_174,axiom,
! [X22,X20,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20)),X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X22)),
file('<stdin>',fact_zadd__zmult__distrib) ).
fof(c_0_175,axiom,
! [X48,X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)),X48) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X48)),
file('<stdin>',fact_diff__mult__distrib) ).
fof(c_0_176,axiom,
! [X48,X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)),X48) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X48)),
file('<stdin>',fact_add__mult__distrib) ).
fof(c_0_177,axiom,
! [X22,X20,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20)),X22) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),X22)),
file('<stdin>',fact_real__add__mult__distrib) ).
fof(c_0_178,axiom,
! [X6,X9,X8] :
( class_RealVector_Oreal__normed__algebra__1(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9)),X6)) ),
file('<stdin>',fact_norm__power__ineq) ).
fof(c_0_179,axiom,
! [X25,X33,X26,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X26,X33),c_Groups_Oplus__class_Oplus(X8,X25,X33))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,X25) ) ),
file('<stdin>',fact_add__le__cancel__right) ).
fof(c_0_180,axiom,
! [X25,X26,X33,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X33,X26),c_Groups_Oplus__class_Oplus(X8,X33,X25))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,X25) ) ),
file('<stdin>',fact_add__le__cancel__left) ).
fof(c_0_181,axiom,
! [X24,X27,X7,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X27))
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X24) ) ),
file('<stdin>',fact_add__le__imp__le__right) ).
fof(c_0_182,axiom,
! [X24,X7,X27,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X27,X7),c_Groups_Oplus__class_Oplus(X8,X27,X24))
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X24) ) ),
file('<stdin>',fact_add__le__imp__le__left) ).
fof(c_0_183,axiom,
! [X24,X7,X27,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X27,X7),c_Groups_Oplus__class_Oplus(X8,X27,X24))
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ),
file('<stdin>',fact_add__less__imp__less__left) ).
fof(c_0_184,axiom,
! [X24,X27,X7,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X27))
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ),
file('<stdin>',fact_add__less__imp__less__right) ).
fof(c_0_185,axiom,
! [X25,X26,X33,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X33,X26),c_Groups_Oplus__class_Oplus(X8,X33,X25))
<=> c_Orderings_Oord__class_Oless(X8,X26,X25) ) ),
file('<stdin>',fact_add__less__cancel__left) ).
fof(c_0_186,axiom,
! [X25,X33,X26,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X26,X33),c_Groups_Oplus__class_Oplus(X8,X25,X33))
<=> c_Orderings_Oord__class_Oless(X8,X26,X25) ) ),
file('<stdin>',fact_add__less__cancel__right) ).
fof(c_0_187,axiom,
! [X6,X17,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X6)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X48),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X48)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6) ) ),
file('<stdin>',fact_Nat_Odiff__diff__eq) ).
fof(c_0_188,axiom,
! [X25,X33,X26,X8] :
( class_Rings_Oidom(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X33))
<=> ( X33 = c_Groups_Ozero__class_Ozero(X8)
| c_Rings_Odvd__class_Odvd(X8,X26,X25) ) ) ),
file('<stdin>',fact_dvd__mult__cancel__right) ).
fof(c_0_189,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Oidom(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> ( X33 = c_Groups_Ozero__class_Ozero(X8)
| c_Rings_Odvd__class_Odvd(X8,X26,X25) ) ) ),
file('<stdin>',fact_dvd__mult__cancel__left) ).
fof(c_0_190,axiom,
! [X52,X16,X36] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
=> hBOOL(hAPP(hAPP(X52,X16),X36)) )
=> ( ( X36 = X16
=> hBOOL(hAPP(hAPP(X52,X16),X36)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X36)
=> hBOOL(hAPP(hAPP(X52,X16),X36)) )
=> hBOOL(hAPP(hAPP(X52,X16),X36)) ) ) ),
file('<stdin>',fact_nat__less__cases) ).
fof(c_0_191,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6))) ) ),
file('<stdin>',fact_power__gt1__lemma) ).
fof(c_0_192,axiom,
~ ! [X47] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X47),v_k____)),v_a____)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',fact__096_B_Bthesis_O_A_I_B_Bw_O_A1_A_L_Aw_A_094_Ak_A_K_Aa_A_061_A0_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(c_0_193,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',fact_w) ).
fof(c_0_194,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6))
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X6) ) ) ),
file('<stdin>',fact_dvd__diffD1) ).
fof(c_0_195,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6))
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X17) ) ) ),
file('<stdin>',fact_dvd__diffD) ).
fof(c_0_196,axiom,
! [X23,X11,X9] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X11)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X23)),
file('<stdin>',fact_zpower__zadd__distrib) ).
fof(c_0_197,axiom,
! [X7,X39,X27,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X27,X39),c_Polynomial_OpCons(X8,X7,X39)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> X39 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
file('<stdin>',fact_offset__poly__eq__0__lemma) ).
fof(c_0_198,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ),
file('<stdin>',fact_nat__add__left__cancel__le) ).
fof(c_0_199,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ),
file('<stdin>',fact_nat__add__left__cancel__less) ).
fof(c_0_200,axiom,
! [X38,X14,X7] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> ( X7 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7),X38))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('<stdin>',fact_self__quotient__aux2) ).
fof(c_0_201,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
file('<stdin>',fact_lgqr) ).
fof(c_0_202,axiom,
! [X38,X14,X7] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> ( X7 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7),X38))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X14,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X38) ) ) ),
file('<stdin>',fact_self__quotient__aux1) ).
fof(c_0_203,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X7,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,X38)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),c_Polynomial_Osmult(X8,X7,X38)) ),
file('<stdin>',fact_smult__add__right) ).
fof(c_0_204,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,X7,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X39,X38)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),c_Polynomial_Osmult(X8,X7,X38)) ),
file('<stdin>',fact_smult__diff__right) ).
fof(c_0_205,axiom,
! [X24,X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),X6)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> X7 = X24 ) ) ) ) ),
file('<stdin>',fact_power__eq__imp__eq__base) ).
fof(c_0_206,axiom,
! [X7,X17,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oone__class_Oone(X8))),X17) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(c_0_207,axiom,
! [X17,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X17),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oone__class_Oone(X8))),X17) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(c_0_208,axiom,
! [X11,X9,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X9),X9) ) ) ) ),
file('<stdin>',fact_mult__left__le__one__le) ).
fof(c_0_209,axiom,
! [X11,X9,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11),X9) ) ) ) ),
file('<stdin>',fact_mult__right__le__one__le) ).
fof(c_0_210,axiom,
! [X11,X9,X27,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),c_RealVector_Onorm__class_Onorm(X8,X11)))
=> X9 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('<stdin>',fact_norm__ratiotest__lemma) ).
fof(c_0_211,axiom,
! [X6,X24,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),X6)) ) ) ),
file('<stdin>',fact_power__mono) ).
fof(c_0_212,axiom,
! [X27,X7,X24,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
file('<stdin>',fact_mult__left__mono__neg) ).
fof(c_0_213,axiom,
! [X27,X7,X24,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ) ),
file('<stdin>',fact_mult__right__mono__neg) ).
fof(c_0_214,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Oordered__comm__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
file('<stdin>',fact_comm__mult__left__mono) ).
fof(c_0_215,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
file('<stdin>',fact_mult__left__mono) ).
fof(c_0_216,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ) ),
file('<stdin>',fact_mult__right__mono) ).
fof(c_0_217,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ) ),
file('<stdin>',fact_mult__strict__right__mono) ).
fof(c_0_218,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
file('<stdin>',fact_mult__strict__left__mono) ).
fof(c_0_219,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Olinordered__comm__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
file('<stdin>',fact_comm__mult__strict__left__mono) ).
fof(c_0_220,axiom,
! [X27,X7,X24,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X7)
=> ( c_Orderings_Oord__class_Oless(X8,X27,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ) ),
file('<stdin>',fact_mult__strict__right__mono__neg) ).
fof(c_0_221,axiom,
! [X27,X7,X24,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X7)
=> ( c_Orderings_Oord__class_Oless(X8,X27,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
file('<stdin>',fact_mult__strict__left__mono__neg) ).
fof(c_0_222,axiom,
! [X17,X6,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X17),X48)) ),
file('<stdin>',fact_le__add__diff) ).
fof(c_0_223,axiom,
! [X40,X27,X24,X7,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X27,X40)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) ) ) ),
file('<stdin>',fact_add__le__less__mono) ).
fof(c_0_224,axiom,
! [X40,X27,X24,X7,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X40)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) ) ) ),
file('<stdin>',fact_add__less__le__mono) ).
fof(c_0_225,axiom,
! [X40,X27,X24,X7,X8] :
( class_Groups_Oordered__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X40)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) ) ) ),
file('<stdin>',fact_add__mono) ).
fof(c_0_226,axiom,
! [X40,X27,X24,X7,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X27,X40)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) ) ) ),
file('<stdin>',fact_add__strict__mono) ).
fof(c_0_227,axiom,
! [X7,X34,X6,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X34)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X34)) ) ) ),
file('<stdin>',fact_power__increasing) ).
fof(c_0_228,axiom,
! [X7,X34,X6,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X34)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X34)) ) ) ),
file('<stdin>',fact_power__strict__increasing) ).
fof(c_0_229,axiom,
! [X24,X6,X7,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Omonom(X8,X7,X6),c_Polynomial_Omonom(X8,X24,X6)) = c_Polynomial_Omonom(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X6) ),
file('<stdin>',fact_add__monom) ).
fof(c_0_230,axiom,
! [X39,X24,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X39) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),c_Polynomial_Osmult(X8,X24,X39)) ),
file('<stdin>',fact_smult__add__left) ).
fof(c_0_231,axiom,
! [X24,X6,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_Omonom(X8,X7,X6),c_Polynomial_Omonom(X8,X24,X6)) = c_Polynomial_Omonom(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24),X6) ),
file('<stdin>',fact_diff__monom) ).
fof(c_0_232,axiom,
! [X39,X24,X7,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24),X39) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),c_Polynomial_Osmult(X8,X24,X39)) ),
file('<stdin>',fact_smult__diff__left) ).
fof(c_0_233,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X24)
=> ( c_Rings_Odvd__class_Odvd(X8,X27,X40)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ),
file('<stdin>',fact_mult__dvd__mono) ).
fof(c_0_234,axiom,
! [X17,X6,X8] :
( class_Power_Opower(X8)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X17),X6) = c_Groups_Oone__class_Oone(X8) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X17),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X17),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('<stdin>',fact_realpow__num__eq__if) ).
fof(c_0_235,axiom,
! [X17,X6,X11,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),X17)) ) ) ),
file('<stdin>',fact_dvd__power__le) ).
fof(c_0_236,axiom,
! [X39,X24,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X7,c_Polynomial_OpCons(X8,X24,X39)) = c_Polynomial_OpCons(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Polynomial_Osmult(X8,X7,X39)) ),
file('<stdin>',fact_smult__pCons) ).
fof(c_0_237,axiom,
! [X27,X24,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X27),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X27)) ) ),
file('<stdin>',fact_diff__less__mono) ).
fof(c_0_238,axiom,
! [X54,X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X54)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X54)) ) ),
file('<stdin>',fact_add__le__mono) ).
fof(c_0_239,axiom,
! [X23,X69,X22,X70] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X70,X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,X23)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X69),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X23)) ) ),
file('<stdin>',fact_zadd__zless__mono) ).
fof(c_0_240,axiom,
! [X54,X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X54)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X17)) ) ),
file('<stdin>',fact_diff__less__mono2) ).
fof(c_0_241,axiom,
! [X54,X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X48,X54)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X54)) ) ),
file('<stdin>',fact_add__less__mono) ).
fof(c_0_242,axiom,
! [X35,X15,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X35),X35)) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X8)
& X35 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('<stdin>',fact_sum__squares__eq__zero__iff) ).
fof(c_0_243,axiom,
! [X32,X24,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ominus__class_Ominus(X8,X24,X32)) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X32)) ),
file('<stdin>',fact_mult_Odiff__right) ).
fof(c_0_244,axiom,
! [X11,X9,X31,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),c_Groups_Ominus__class_Ominus(X8,X9,X11)) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X11)) ),
file('<stdin>',fact_mult__right_Odiff) ).
fof(c_0_245,axiom,
! [X23,X11,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),c_Groups_Oplus__class_Oplus(X8,X11,X23)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X23)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(c_0_246,axiom,
! [X32,X24,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Oplus__class_Oplus(X8,X24,X32)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X32)) ),
file('<stdin>',fact_mult_Oadd__right) ).
fof(c_0_247,axiom,
! [X11,X9,X31,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),c_Groups_Oplus__class_Oplus(X8,X9,X11)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X11)) ),
file('<stdin>',fact_mult__right_Oadd) ).
fof(c_0_248,axiom,
! [X24,X6,X7] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24),X6))
=> ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X24) ) ),
file('<stdin>',fact_pow__divides__pow__int) ).
fof(c_0_249,axiom,
! [X25,X26,X16] :
( X16 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X16),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X25),X16))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X26,X25) ) ),
file('<stdin>',fact_pow__divides__eq__int) ).
fof(c_0_250,axiom,
! [X25,X26,X16] :
( X16 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X16),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X16))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25) ) ),
file('<stdin>',fact_pow__divides__eq__nat) ).
fof(c_0_251,axiom,
! [X24,X6,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X6))
=> ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24) ) ),
file('<stdin>',fact_pow__divides__pow__nat) ).
fof(c_0_252,axiom,
! [X16,X36,X50] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X16) ) ),
file('<stdin>',fact_nat__mult__dvd__cancel__disj) ).
fof(c_0_253,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X6))
=> ( X48 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,X6) ) ),
file('<stdin>',fact_zdvd__mult__cancel) ).
fof(c_0_254,axiom,
! [X83,X36,X50] :
( X50 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X36,X83)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X83)) ) ),
file('<stdin>',fact_zdvd__mono) ).
fof(c_0_255,axiom,
! [X16,X50,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X50))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ) ),
file('<stdin>',fact_mult__less__cancel2) ).
fof(c_0_256,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ) ),
file('<stdin>',fact_mult__less__cancel1) ).
fof(c_0_257,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24) ) ) ),
file('<stdin>',fact_zero__less__mult__pos) ).
fof(c_0_258,axiom,
! [X7,X24,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24) ) ) ),
file('<stdin>',fact_zero__less__mult__pos2) ).
fof(c_0_259,axiom,
! [X42,X44,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),X42) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X44),X42)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(c_0_260,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oab__semigroup__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)),X27) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ),
file('<stdin>',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(c_0_261,axiom,
! [X41,X42,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X42)),X41) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(c_0_262,axiom,
! [X6,X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ),
file('<stdin>',fact_power__commutes) ).
fof(c_0_263,axiom,
! [X9,X6,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_Omonom(X8,X7,X6)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6)) ),
file('<stdin>',fact_poly__monom) ).
fof(c_0_264,axiom,
! [X14,X38,X27,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,c_Polynomial_Osmult(X8,X27,X38)) = c_Polynomial_OpCons(X8,X14,X38)
=> ( X14 = hAPP(c_Polynomial_Opoly(X8,X39),X27)
& X38 = c_Polynomial_Osynthetic__div(X8,X39,X27) ) ) ),
file('<stdin>',fact_synthetic__div__unique) ).
fof(c_0_265,axiom,
! [X27,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osynthetic__div(X8,c_Polynomial_OpCons(X8,X7,X39),X27) = c_Polynomial_OpCons(X8,hAPP(c_Polynomial_Opoly(X8,X39),X27),c_Polynomial_Osynthetic__div(X8,X39,X27)) ),
file('<stdin>',fact_synthetic__div__pCons) ).
fof(c_0_266,axiom,
! [X38,X39,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X39)),X38) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(c_0_267,axiom,
! [X6,X17,X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17)),X6) ),
file('<stdin>',fact_power__mult) ).
fof(c_0_268,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X49)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X49)) ) ),
file('<stdin>',fact_zmult__zless__mono2) ).
fof(c_0_269,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X48)) ) ),
file('<stdin>',fact_mult__less__mono1) ).
fof(c_0_270,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X49)) ) ),
file('<stdin>',fact_mult__less__mono2) ).
fof(c_0_271,axiom,
! [X11,X9,X23] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X23)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X9,X11)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X11)) ) ),
file('<stdin>',fact_real__mult__less__mono2) ).
fof(c_0_272,axiom,
! [X39,X17] :
( ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X39),X17) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X39),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X39),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('<stdin>',fact_power__eq__if) ).
fof(c_0_273,axiom,
! [X57,X50,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X50),X57)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X50)) ),
file('<stdin>',fact_le__diff__conv) ).
fof(c_0_274,axiom,
! [X50,X56,X57] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X50))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X50),X56) ),
file('<stdin>',fact_less__diff__conv) ).
fof(c_0_275,axiom,
! [X54,X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X54)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X54)) ) ),
file('<stdin>',fact_mult__le__mono) ).
fof(c_0_276,axiom,
! [X18,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X48),X49) ),
file('<stdin>',fact_diff__diff__right) ).
fof(c_0_277,axiom,
! [X18,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X49),X48) ),
file('<stdin>',fact_add__diff__assoc) ).
fof(c_0_278,axiom,
! [X18,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X49),X48) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48)) ),
file('<stdin>',fact_diff__add__assoc) ).
fof(c_0_279,axiom,
! [X18,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48),X18) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X18),X48) ),
file('<stdin>',fact_add__diff__assoc2) ).
fof(c_0_280,axiom,
! [X18,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X18),X48) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48),X18) ),
file('<stdin>',fact_diff__add__assoc2) ).
fof(c_0_281,axiom,
! [X38,X7,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),c_Polynomial_Osmult(X8,X7,X38)) = c_Polynomial_Osmult(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38)) ),
file('<stdin>',fact_mult__smult__right) ).
fof(c_0_282,axiom,
! [X9,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_Osmult(X8,X7,X39)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(c_Polynomial_Opoly(X8,X39),X9)) ),
file('<stdin>',fact_poly__smult) ).
fof(c_0_283,axiom,
! [X25,X26,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X25),c_Groups_Ozero__class_Ozero(X8))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
& c_Orderings_Oord__class_Oless__eq(X8,X25,c_Groups_Ozero__class_Ozero(X8)) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X25) ) ) ) ),
file('<stdin>',fact_mult__le__0__iff) ).
fof(c_0_284,axiom,
! [X25,X26,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X25))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X25) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,X25,c_Groups_Ozero__class_Ozero(X8)) ) ) ) ),
file('<stdin>',fact_zero__le__mult__iff) ).
fof(c_0_285,axiom,
! [X24,X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),c_Nat_OSuc(X6))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> X7 = X24 ) ) ) ),
file('<stdin>',fact_power__inject__base) ).
fof(c_0_286,axiom,
! [X6,X17] :
( ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6) = X6 )
& ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6)) ) ),
file('<stdin>',fact_add__eq__if) ).
fof(c_0_287,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X48,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X17,X6))
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X48,X6)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X48,X17) ) ),
file('<stdin>',fact_zdvd__zdiffD) ).
fof(c_0_288,axiom,
! [X20,X21,X22] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X21,X20)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X20)),
file('<stdin>',fact_zdiff__zmult__distrib2) ).
fof(c_0_289,axiom,
! [X20,X21,X22] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X20)),
file('<stdin>',fact_zadd__zmult__distrib2) ).
fof(c_0_290,axiom,
! [X6,X17,X48] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X6)),
file('<stdin>',fact_diff__mult__distrib2) ).
fof(c_0_291,axiom,
! [X6,X17,X48] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X6)),
file('<stdin>',fact_add__mult__distrib2) ).
fof(c_0_292,axiom,
! [X9,X38,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_Opcompose(X8,X39,X38)),X9) = hAPP(c_Polynomial_Opoly(X8,X39),hAPP(c_Polynomial_Opoly(X8,X38),X9)) ),
file('<stdin>',fact_poly__pcompose) ).
fof(c_0_293,axiom,
! [X17,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X17,X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Oone__class_Oone(X8))),X17) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(c_0_294,axiom,
! [X9,X14,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,c_RealVector_Onorm__class_Onorm(X8,X9))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Rings_Oinverse__class_Oinverse(X8,X9)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X14)) ) ) ),
file('<stdin>',fact_Bseq__inverse__lemma) ).
fof(c_0_295,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6)),c_Groups_Oone__class_Oone(X8)) ) ) ),
file('<stdin>',fact_power__Suc__less__one) ).
fof(c_0_296,axiom,
! [X35,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X35),X35)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X35 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('<stdin>',fact_real__two__squares__add__zero__iff) ).
fof(c_0_297,axiom,
! [X47] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X47))),
file('<stdin>',fact_cq0) ).
fof(c_0_298,axiom,
! [X6,X14,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X14)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X14,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X14),c_Nat_OSuc(X6)),X14) ) ) ),
file('<stdin>',fact_realpow__Suc__le__self) ).
fof(c_0_299,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_add__nonpos__neg) ).
fof(c_0_300,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_add__neg__nonpos) ).
fof(c_0_301,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)) ) ) ),
file('<stdin>',fact_add__nonneg__pos) ).
fof(c_0_302,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)) ) ) ),
file('<stdin>',fact_add__pos__nonneg) ).
fof(c_0_303,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_add__nonpos__nonpos) ).
fof(c_0_304,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)) ) ) ),
file('<stdin>',fact_add__nonneg__nonneg) ).
fof(c_0_305,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)) ) ) ),
file('<stdin>',fact_add__pos__pos) ).
fof(c_0_306,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_add__neg__neg) ).
fof(c_0_307,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16))
<=> ( 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16) ) ),
file('<stdin>',fact_add__gr__0) ).
fof(c_0_308,axiom,
! [X19,X20,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X20)),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X19)),
file('<stdin>',fact_zmult__assoc) ).
fof(c_0_309,axiom,
! [X23,X11,X9] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X11)),X23) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X23)),
file('<stdin>',fact_zpower__zpower) ).
fof(c_0_310,axiom,
! [X48,X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)),X48) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X48)),
file('<stdin>',fact_nat__mult__assoc) ).
fof(c_0_311,axiom,
! [X19,X20,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X20)),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),X19)),
file('<stdin>',fact_real__mult__assoc) ).
fof(c_0_312,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
& c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8)) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24) ) )
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_split__mult__neg__le) ).
fof(c_0_313,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__ring(X8)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8)) ) )
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ) ),
file('<stdin>',fact_split__mult__pos__le) ).
fof(c_0_314,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ) ) ),
file('<stdin>',fact_mult__nonpos__nonpos) ).
fof(c_0_315,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_mult__nonpos__nonneg) ).
fof(c_0_316,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_mult__nonneg__nonpos2) ).
fof(c_0_317,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_mult__nonneg__nonpos) ).
fof(c_0_318,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ) ) ),
file('<stdin>',fact_mult__nonneg__nonneg) ).
fof(c_0_319,axiom,
! [X6,X17,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X17)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X6)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),X6)) ) ) ),
file('<stdin>',fact_less__1__mult) ).
fof(c_0_320,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ) ) ),
file('<stdin>',fact_mult__pos__pos) ).
fof(c_0_321,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_mult__pos__neg) ).
fof(c_0_322,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_mult__pos__neg2) ).
fof(c_0_323,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_mult__neg__pos) ).
fof(c_0_324,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ) ) ),
file('<stdin>',fact_mult__neg__neg) ).
fof(c_0_325,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X27)) ) ),
file('<stdin>',fact_add__right__mono) ).
fof(c_0_326,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X27,X7),c_Groups_Oplus__class_Oplus(X8,X27,X24)) ) ),
file('<stdin>',fact_add__left__mono) ).
fof(c_0_327,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X27,X7),c_Groups_Oplus__class_Oplus(X8,X27,X24)) ) ),
file('<stdin>',fact_add__strict__left__mono) ).
fof(c_0_328,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X27)) ) ),
file('<stdin>',fact_add__strict__right__mono) ).
fof(c_0_329,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)) ) ),
file('<stdin>',fact_one__less__mult) ).
fof(c_0_330,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16) ) ),
file('<stdin>',fact_one__le__mult__iff) ).
fof(c_0_331,axiom,
! [X23,X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X23)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X11) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X23)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X9) ) ) ),
file('<stdin>',fact_dvd_Oless__trans) ).
fof(c_0_332,axiom,
~ ! [X73] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X73)
=> ~ ! [X55] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X55),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X55)),X73) ) ),
file('<stdin>',fact__096_B_Bthesis_O_A_I_B_Bm_O_A_091_124_A0_A_060_Am_059_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(c_0_333,axiom,
? [X73] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X73)
& ! [X55] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X55),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X55)),X73) ) ),
file('<stdin>',fact__096EX_Am_0620_O_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_096) ).
fof(c_0_334,axiom,
! [X55] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X55),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X55)),v_m____) ),
file('<stdin>',fact_m_I2_J) ).
fof(c_0_335,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ? [X3] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X6) = X7
& ! [X62] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X62),X6) = X7 )
=> X62 = X3 ) ) ) ),
file('<stdin>',fact_realpow__pos__nth__unique) ).
fof(c_0_336,axiom,
! [X47] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X47))),
file('<stdin>',fact_c) ).
fof(c_0_337,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ) ),
file('<stdin>',fact_one__less__power) ).
fof(c_0_338,axiom,
! [X6,X11,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X9,X11)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),X6)) ) ),
file('<stdin>',fact_dvd__power__same) ).
fof(c_0_339,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X27)
=> c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Oplus__class_Oplus(X8,X7,X27)) ) ) ),
file('<stdin>',fact_add__strict__increasing2) ).
fof(c_0_340,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X27)
=> c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Oplus__class_Oplus(X8,X7,X27)) ) ) ),
file('<stdin>',fact_add__strict__increasing) ).
fof(c_0_341,axiom,
! [X7,X24,X27,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Oplus__class_Oplus(X8,X7,X27)) ) ) ),
file('<stdin>',fact_add__increasing2) ).
fof(c_0_342,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X27)
=> c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Oplus__class_Oplus(X8,X7,X27)) ) ) ),
file('<stdin>',fact_add__increasing) ).
fof(c_0_343,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X27)
=> c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Oplus__class_Oplus(X8,X7,X27)) ) ) ),
file('<stdin>',fact_pos__add__strict) ).
fof(c_0_344,axiom,
! [X7,X6,X17,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ),
file('<stdin>',fact_le__imp__power__dvd) ).
fof(c_0_345,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)) ) ),
file('<stdin>',fact_n__less__m__mult__n) ).
fof(c_0_346,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X17)) ) ),
file('<stdin>',fact_n__less__n__mult__m) ).
fof(c_0_347,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,X6)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X6,X17)
=> X17 = X6 ) ) ) ),
file('<stdin>',fact_zdvd__antisym__nonneg) ).
fof(c_0_348,axiom,
! [X9,X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X9)),
file('<stdin>',fact_real__minus__mult__self__le) ).
fof(c_0_349,axiom,
! [X23,X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X23,X9),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X23,X11)) ),
file('<stdin>',fact_real__add__left__mono) ).
fof(c_0_350,axiom,
! [X54,X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X17)) ),
file('<stdin>',fact_diff__le__mono2) ).
fof(c_0_351,axiom,
! [X54,X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X54),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X54)) ),
file('<stdin>',fact_diff__le__mono) ).
fof(c_0_352,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X48)) ),
file('<stdin>',fact_add__le__mono1) ).
fof(c_0_353,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X49)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X48),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X48)) ),
file('<stdin>',fact_zadd__strict__right__mono) ).
fof(c_0_354,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,X18),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,X49)) ),
file('<stdin>',fact_zadd__left__mono) ).
fof(c_0_355,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X48)) ),
file('<stdin>',fact_add__less__mono1) ).
fof(c_0_356,axiom,
! [X23,X11,X9,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X9,X11)
=> ( c_Rings_Odvd__class_Odvd(X8,X9,X23)
=> c_Rings_Odvd__class_Odvd(X8,X9,c_Groups_Ominus__class_Ominus(X8,X11,X23)) ) ) ),
file('<stdin>',fact_dvd__diff) ).
fof(c_0_357,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X24)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X27)
=> c_Rings_Odvd__class_Odvd(X8,X7,c_Groups_Oplus__class_Oplus(X8,X24,X27)) ) ) ),
file('<stdin>',fact_dvd__add) ).
fof(c_0_358,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X9,X11)) ) ),
file('<stdin>',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
fof(c_0_359,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X11)) ) ),
file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(c_0_360,axiom,
! [X80,X63,X26,X8] :
( class_Fields_Ofield(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X26,X63),X80)
<=> ( ( X26 = c_Groups_Ozero__class_Ozero(X8)
=> X80 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) )
& ( X26 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X63,X80) ) ) ) ),
file('<stdin>',fact_smult__dvd__iff) ).
fof(c_0_361,axiom,
! [X80,X63,X26,X8] :
( class_Fields_Ofield(X8)
=> ( X26 != c_Groups_Ozero__class_Ozero(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X63,c_Polynomial_Osmult(X8,X26,X80))
<=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X63,X80) ) ) ),
file('<stdin>',fact_dvd__smult__iff) ).
fof(c_0_362,axiom,
! [X38,X7,X39,X8] :
( class_Fields_Ofield(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,c_Polynomial_Osmult(X8,X7,X38))
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,X38) ) ) ),
file('<stdin>',fact_dvd__smult__cancel) ).
fof(c_0_363,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X16)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X50) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X50)
<=> X36 = X16 ) ) ),
file('<stdin>',fact_eq__diff__iff) ).
fof(c_0_364,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),X17) ) ),
file('<stdin>',fact_diff__less) ).
fof(c_0_365,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),X38)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,X38) ) ),
file('<stdin>',fact_smult__dvd__cancel) ).
fof(c_0_366,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X26,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(c_0_367,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X26,X26))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
file('<stdin>',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(c_0_368,axiom,
! [X26,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X26,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_even__less__0__iff) ).
fof(c_0_369,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X26,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(c_0_370,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X26,X26))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
file('<stdin>',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(c_0_371,axiom,
! [X48,X6,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X17),X6),c_Nat_OSuc(X48)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),X48),
file('<stdin>',fact_Suc__diff__diff) ).
fof(c_0_372,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X27) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),X24) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(c_0_373,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oab__semigroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X27) = c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oplus__class_Oplus(X8,X24,X27)) ),
file('<stdin>',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(c_0_374,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X27) = c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oplus__class_Oplus(X8,X24,X27)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(c_0_375,axiom,
! [X40,X27,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oplus__class_Oplus(X8,X27,X40)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),X40) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(c_0_376,axiom,
! [X40,X27,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oplus__class_Oplus(X8,X27,X40)) = c_Groups_Oplus__class_Oplus(X8,X27,c_Groups_Oplus__class_Oplus(X8,X7,X40)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(c_0_377,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X35),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X35,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15)) ),
file('<stdin>',fact_real__add__le__0__iff) ).
fof(c_0_378,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15),X35) ),
file('<stdin>',fact_real__0__le__add__iff) ).
fof(c_0_379,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X35),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X35,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15)) ),
file('<stdin>',fact_real__add__less__0__iff) ).
fof(c_0_380,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X35))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15),X35) ),
file('<stdin>',fact_real__0__less__add__iff) ).
fof(c_0_381,axiom,
! [X24,X7,X27,X8] :
( class_Divides_Osemiring__div(X8)
=> ( X27 != c_Groups_Ozero__class_Ozero(X8)
=> c_Divides_Odiv__class_Odiv(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) = c_Divides_Odiv__class_Odiv(X8,X7,X24) ) ),
file('<stdin>',fact_div__mult__mult2) ).
fof(c_0_382,axiom,
! [X24,X7,X27,X8] :
( class_Divides_Osemiring__div(X8)
=> ( ( X27 = c_Groups_Ozero__class_Ozero(X8)
=> c_Divides_Odiv__class_Odiv(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) = c_Groups_Ozero__class_Ozero(X8) )
& ( X27 != c_Groups_Ozero__class_Ozero(X8)
=> c_Divides_Odiv__class_Odiv(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) = c_Divides_Odiv__class_Odiv(X8,X7,X24) ) ) ),
file('<stdin>',fact_div__mult__mult1__if) ).
fof(c_0_383,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24))
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,X24,X7) ) ) ),
file('<stdin>',fact_inverse__le__imp__le__neg) ).
fof(c_0_384,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,X24,X7) ) ) ),
file('<stdin>',fact_inverse__le__imp__le) ).
fof(c_0_385,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,X25)
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ominus__class_Ominus(X8,X26,X25),c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_le__iff__diff__le__0) ).
fof(c_0_386,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X26,X25)
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ominus__class_Ominus(X8,X26,X25),c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_less__iff__diff__less__0) ).
fof(c_0_387,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,X24,X7) ) ) ),
file('<stdin>',fact_inverse__less__imp__less) ).
fof(c_0_388,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24))
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,X24,X7) ) ) ),
file('<stdin>',fact_inverse__less__imp__less__neg) ).
fof(c_0_389,axiom,
! [X6,X24,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X7,c_Polynomial_Omonom(X8,X24,X6)) = c_Polynomial_Omonom(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),X6) ),
file('<stdin>',fact_smult__monom) ).
fof(c_0_390,axiom,
! [X39,X24,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X7,c_Polynomial_Osmult(X8,X24,X39)) = c_Polynomial_Osmult(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),X39) ),
file('<stdin>',fact_smult__smult) ).
fof(c_0_391,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X17)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X6)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)) ) ),
file('<stdin>',fact_dvd__diff__nat) ).
fof(c_0_392,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9),X11)) ) ),
file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(c_0_393,axiom,
! [X16,X36] :
( 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),X36),X16))
<=> ( 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16) ) ),
file('<stdin>',fact_nat__0__less__mult__iff) ).
fof(c_0_394,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X11)) ) ),
file('<stdin>',fact_real__mult__order) ).
fof(c_0_395,axiom,
! [X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X17))),
file('<stdin>',fact_le__cube) ).
fof(c_0_396,axiom,
! [X6,X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)),X7) ),
file('<stdin>',fact_power__Suc2) ).
fof(c_0_397,axiom,
! [X38,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X38)),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Nat_OSuc(X38)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(c_0_398,axiom,
! [X45,X33,X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X26,X25) = c_Groups_Ominus__class_Ominus(X8,X33,X45)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,X25)
<=> c_Orderings_Oord__class_Oless__eq(X8,X33,X45) ) ) ),
file('<stdin>',fact_diff__eq__diff__less__eq) ).
fof(c_0_399,axiom,
! [X45,X33,X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X26,X25) = c_Groups_Ominus__class_Ominus(X8,X33,X45)
=> ( c_Orderings_Oord__class_Oless(X8,X26,X25)
<=> c_Orderings_Oord__class_Oless(X8,X33,X45) ) ) ),
file('<stdin>',fact_diff__eq__diff__less) ).
fof(c_0_400,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X36),X36)
<=> X16 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('<stdin>',fact_dvd__mult__cancel2) ).
fof(c_0_401,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16),X36)
<=> X16 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('<stdin>',fact_dvd__mult__cancel1) ).
fof(c_0_402,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X49)) ),
file('<stdin>',fact_mult__le__mono2) ).
fof(c_0_403,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X48)) ),
file('<stdin>',fact_mult__le__mono1) ).
fof(c_0_404,axiom,
! [X41,X42,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X41)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(c_0_405,axiom,
! [X19,X20,X21] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20),X19) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,X19)),
file('<stdin>',fact_zadd__assoc) ).
fof(c_0_406,axiom,
! [X23,X11,X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X23)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X23)),
file('<stdin>',fact_zadd__left__commute) ).
fof(c_0_407,axiom,
! [X48,X49,X18] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X49),X48) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X48),X49),
file('<stdin>',fact_diff__commute) ).
fof(c_0_408,axiom,
! [X48,X49,X18] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X49),X48) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X48)),
file('<stdin>',fact_diff__diff__left) ).
fof(c_0_409,axiom,
! [X6,X17,X48] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X17),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),
file('<stdin>',fact_diff__cancel) ).
fof(c_0_410,axiom,
! [X6,X48,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X48)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),
file('<stdin>',fact_diff__cancel2) ).
fof(c_0_411,axiom,
! [X23,X11,X9] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X23)),
file('<stdin>',fact_nat__add__left__commute) ).
fof(c_0_412,axiom,
! [X48,X6,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6),X48) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X48)),
file('<stdin>',fact_nat__add__assoc) ).
fof(c_0_413,axiom,
! [X37,X46] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,X37)
| X46 = X37 ) ),
file('<stdin>',fact_zless__add1__eq) ).
fof(c_0_414,axiom,
! [X37,X46] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X46,X37) ),
file('<stdin>',fact_zle__add1__eq__le) ).
fof(c_0_415,axiom,
! [X37,X46] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)),X37)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,X37) ),
file('<stdin>',fact_add1__zle__eq) ).
fof(c_0_416,axiom,
! [X37,X46] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X46,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X37,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,X37) ),
file('<stdin>',fact_zle__diff1__eq) ).
fof(c_0_417,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),X27)
=> c_Rings_Odvd__class_Odvd(X8,X7,X27) ) ),
file('<stdin>',fact_dvd__mult__left) ).
fof(c_0_418,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),X27)
=> c_Rings_Odvd__class_Odvd(X8,X24,X27) ) ),
file('<stdin>',fact_dvd__mult__right) ).
fof(c_0_419,axiom,
! [X23,X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X23)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X23)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X9) ) ) ),
file('<stdin>',fact_dvd_Oless__le__trans) ).
fof(c_0_420,axiom,
! [X23,X11,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X23)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X11) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X23)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X9) ) ) ),
file('<stdin>',fact_dvd_Ole__less__trans) ).
fof(c_0_421,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X35)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X15,X35),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('<stdin>',fact_real__le__eq__diff) ).
fof(c_0_422,axiom,
! [X64,X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X64)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X50,X64),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('<stdin>',fact_less__bin__lemma) ).
fof(c_0_423,axiom,
! [X36,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X36))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ),
file('<stdin>',fact_zero__less__diff) ).
fof(c_0_424,axiom,
! [X6,X17,X54,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X48,X54)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X54) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ) ),
file('<stdin>',fact_less__add__eq__less) ).
fof(c_0_425,axiom,
! [X16,X50] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X50,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X50))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X50,X16) ),
file('<stdin>',fact_dvd__reduce) ).
fof(c_0_426,axiom,
! [X6,X48,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X48),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X6) ),
file('<stdin>',fact_add__leD2) ).
fof(c_0_427,axiom,
! [X6,X48,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X48),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ),
file('<stdin>',fact_add__leD1) ).
fof(c_0_428,axiom,
! [X6,X48,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X48),X6)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X6) ) ),
file('<stdin>',fact_add__leE) ).
fof(c_0_429,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X49),X48)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X48) ),
file('<stdin>',fact_add__lessD1) ).
fof(c_0_430,axiom,
! [X35,X15,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X15)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X35)
=> ( c_Groups_Oplus__class_Oplus(X8,X15,X35) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X8)
& X35 = c_Groups_Ozero__class_Ozero(X8) ) ) ) ) ),
file('<stdin>',fact_add__nonneg__eq__0__iff) ).
fof(c_0_431,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X24),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
file('<stdin>',fact_le__imp__inverse__le__neg) ).
fof(c_0_432,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X24),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
file('<stdin>',fact_le__imp__inverse__le) ).
fof(c_0_433,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X24),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
file('<stdin>',fact_less__imp__inverse__less) ).
fof(c_0_434,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X24),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
file('<stdin>',fact_less__imp__inverse__less__neg) ).
fof(c_0_435,axiom,
! [X1,X2,X8,X77] :
( class_Orderings_Oord(X77)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X8,X77),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X77),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X77),X1,X2) ) ) ),
file('<stdin>',fact_less__fun__def) ).
fof(c_0_436,axiom,
! [X16,X15] :
( 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),X15),X16))
<=> ( X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) ) ),
file('<stdin>',fact_zero__less__power__nat__eq) ).
fof(c_0_437,axiom,
! [X16,X15] :
( 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),X15),X16))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
| X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_nat__zero__less__power__iff) ).
fof(c_0_438,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
file('<stdin>',fact_one__le__inverse) ).
fof(c_0_439,axiom,
! [X15,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X15))
<=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X15)
& c_Orderings_Oord__class_Oless__eq(X8,X15,c_Groups_Oone__class_Oone(X8)) ) ) ),
file('<stdin>',fact_one__le__inverse__iff) ).
fof(c_0_440,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
file('<stdin>',fact_one__less__inverse) ).
fof(c_0_441,axiom,
! [X15,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X15))
<=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X15)
& c_Orderings_Oord__class_Oless(X8,X15,c_Groups_Oone__class_Oone(X8)) ) ) ),
file('<stdin>',fact_one__less__inverse__iff) ).
fof(c_0_442,axiom,
! [X35,X15,X8] :
( class_Rings_Oidom(X8)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X15),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X35),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( X15 = X35
| X15 = c_Groups_Ouminus__class_Ouminus(X8,X35) ) ) ),
file('<stdin>',fact_realpow__two__disj) ).
fof(c_0_443,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6))) ) ),
file('<stdin>',fact_power__gt1) ).
fof(c_0_444,axiom,
! [X35,X15,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X8),X15,X35)
<=> ( X15 = X35
| c_Polynomial_Opos__poly(X8,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X35,X15)) ) ) ),
file('<stdin>',fact_less__eq__poly__def) ).
fof(c_0_445,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ? [X61] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X61),X6) = X7 ) ) ),
file('<stdin>',fact_realpow__pos__nth) ).
fof(c_0_446,axiom,
! [X7,X38,X39,X8] :
( class_Fields_Ofield(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,X38)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),X38) ) ) ),
file('<stdin>',fact_smult__dvd) ).
fof(c_0_447,axiom,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11) ) ),
file('<stdin>',fact_dvd_Oless__asym) ).
fof(c_0_448,axiom,
! [X24,X7] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X7) )
=> ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X7)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24) ) ),
file('<stdin>',fact_dvd_Oless__asym_H) ).
fof(c_0_449,axiom,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11) ) ),
file('<stdin>',fact_dvd_Oless__imp__not__less) ).
fof(c_0_450,axiom,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11) ) ),
file('<stdin>',fact_dvd_Oless__not__sym) ).
fof(c_0_451,axiom,
! [X63,X26,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Polynomial_Opos__poly(X8,c_Polynomial_OpCons(X8,X26,X63))
<=> ( c_Polynomial_Opos__poly(X8,X63)
| ( X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
& c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ) ) ),
file('<stdin>',fact_pos__poly__pCons) ).
fof(c_0_452,axiom,
! [X63] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X63),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))
=> ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X63))
=> ? [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X63),X55) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
file('<stdin>',fact_less_Ohyps) ).
fof(c_0_453,axiom,
! [X7,X38,X39,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,X38)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,c_Polynomial_Osmult(X8,X7,X38)) ) ),
file('<stdin>',fact_dvd__smult) ).
fof(c_0_454,axiom,
! [X16,X36,X26,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X26)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X26),X36) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X26),X16)
<=> X36 = X16 ) ) ),
file('<stdin>',fact_power__inject__exp) ).
fof(c_0_455,axiom,
! [X17,X18] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))),
file('<stdin>',fact_less__add__Suc1) ).
fof(c_0_456,axiom,
! [X17,X18] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X18))),
file('<stdin>',fact_less__add__Suc2) ).
fof(c_0_457,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ),
file('<stdin>',fact_one__le__power) ).
fof(c_0_458,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ),
file('<stdin>',fact_zero__le__power) ).
fof(c_0_459,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ),
file('<stdin>',fact_zero__less__power) ).
fof(c_0_460,axiom,
! [X15,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X15),c_Groups_Oone__class_Oone(X8))
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,c_Groups_Ozero__class_Ozero(X8))
| c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X15) ) ) ),
file('<stdin>',fact_inverse__less__1__iff) ).
fof(c_0_461,axiom,
! [X15,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X15),c_Groups_Oone__class_Oone(X8))
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,c_Groups_Ozero__class_Ozero(X8))
| c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),X15) ) ) ),
file('<stdin>',fact_inverse__le__1__iff) ).
fof(c_0_462,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X24)),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
file('<stdin>',fact_nonzero__inverse__mult__distrib) ).
fof(c_0_463,axiom,
! [X7,X8] :
( class_Rings_Olinordered__ring(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7),c_Groups_Ozero__class_Ozero(X8)) ),
file('<stdin>',fact_not__square__less__zero) ).
fof(c_0_464,axiom,
! [X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23),X23) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('<stdin>',fact_odd__nonzero) ).
fof(c_0_465,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X9,X11)) ) ),
file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(c_0_466,axiom,
! [X6,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X6)) ),
file('<stdin>',fact_nat__one__le__power) ).
fof(c_0_467,axiom,
! [X18,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Nat_OSuc(X18)),X6) ),
file('<stdin>',fact_diff__Suc__less) ).
fof(c_0_468,axiom,
! [X26,X59,X60,X8] : hAPP(hAPP(c_Power_Opower_Opower(X8,X60,X59),X26),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X60,
file('<stdin>',fact_power_Opower_Opower__0) ).
fof(c_0_469,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X6,X17) ) ),
file('<stdin>',fact_nat__dvd__not__less) ).
fof(c_0_470,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X6)
=> ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X6,X17) ) ),
file('<stdin>',fact_zdvd__not__zless) ).
fof(c_0_471,axiom,
! [X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23)) ),
file('<stdin>',fact_le__imp__0__less) ).
fof(c_0_472,axiom,
! [X24,X7,X8] :
( class_Fields_Ofield__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),c_Rings_Oinverse__class_Oinverse(X8,X24)) ),
file('<stdin>',fact_inverse__mult__distrib) ).
fof(c_0_473,axiom,
! [X9,X6,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
| X9 = c_Groups_Oone__class_Oone(X8) )
=> c_Rings_Odvd__class_Odvd(X8,X9,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6)) ) ),
file('<stdin>',fact_dvd__power) ).
fof(c_0_474,axiom,
! [X39,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X7,X39)) = c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X39)) ),
file('<stdin>',fact_minus__pCons) ).
fof(c_0_475,axiom,
! [X39,X7,X77] :
( class_Groups_Oab__group__add(X77)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X77),c_Polynomial_OpCons(X77,X7,X39)) = c_Polynomial_OpCons(X77,c_Groups_Ouminus__class_Ouminus(X77,X7),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X77),X39)) ),
file('<stdin>',fact_minus__poly__code_I2_J) ).
fof(c_0_476,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X17),X6) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)) ),
file('<stdin>',fact_Suc__diff__le) ).
fof(c_0_477,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X24)
=> c_Rings_Odvd__class_Odvd(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ),
file('<stdin>',fact_dvd__mult2) ).
fof(c_0_478,axiom,
! [X24,X27,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X27)
=> c_Rings_Odvd__class_Odvd(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ),
file('<stdin>',fact_dvd__mult) ).
fof(c_0_479,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24)) = c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X24,X7)) ),
file('<stdin>',fact_norm__minus__commute) ).
fof(c_0_480,axiom,
! [X11,X9,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9)),c_RealVector_Onorm__class_Onorm(X8,X11)) ),
file('<stdin>',fact_norm__mult) ).
fof(c_0_481,axiom,
! [X23,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,c_Groups_Oone__class_Oone(tc_Int_Oint)),X23) ),
file('<stdin>',fact_zless__imp__add1__zle) ).
fof(c_0_482,axiom,
! [X49,X18] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X49),X18),
file('<stdin>',fact_not__add__less1) ).
fof(c_0_483,axiom,
! [X18,X49] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X18),X18),
file('<stdin>',fact_not__add__less2) ).
fof(c_0_484,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
<=> ? [X71] : X16 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X71)) ),
file('<stdin>',fact_less__iff__Suc__add) ).
fof(c_0_485,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)) = X17 ),
file('<stdin>',fact_le__add__diff__inverse) ).
fof(c_0_486,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),X6) = X17 ),
file('<stdin>',fact_le__add__diff__inverse2) ).
fof(c_0_487,axiom,
! [X6,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X6)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X18)) = X18 ),
file('<stdin>',fact_diff__diff__cancel) ).
fof(c_0_488,axiom,
! [X15,X1,X2,X8,X77] :
( class_Orderings_Oord(X77)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X77),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X77,hAPP(X2,X15),hAPP(X1,X15)) ) ),
file('<stdin>',fact_le__funD) ).
fof(c_0_489,axiom,
! [X15,X1,X2,X8,X77] :
( class_Orderings_Oord(X77)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X77),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X77,hAPP(X2,X15),hAPP(X1,X15)) ) ),
file('<stdin>',fact_le__funE) ).
fof(c_0_490,axiom,
! [X17,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X17)) ),
file('<stdin>',fact_trans__le__add1) ).
fof(c_0_491,axiom,
! [X17,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X49)) ),
file('<stdin>',fact_trans__le__add2) ).
fof(c_0_492,axiom,
! [X11,X23,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) ),
file('<stdin>',fact_termination__basic__simps_I4_J) ).
fof(c_0_493,axiom,
! [X23,X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) ),
file('<stdin>',fact_termination__basic__simps_I3_J) ).
fof(c_0_494,axiom,
! [X23,X11,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X11)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) ),
file('<stdin>',fact_termination__basic__simps_I1_J) ).
fof(c_0_495,axiom,
! [X6,X48,X49] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X49,X48)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X6),X48) ),
file('<stdin>',fact_less__imp__diff__less) ).
fof(c_0_496,axiom,
! [X11,X23,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X23)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) ),
file('<stdin>',fact_termination__basic__simps_I2_J) ).
fof(c_0_497,axiom,
! [X17,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X17)) ),
file('<stdin>',fact_trans__less__add1) ).
fof(c_0_498,axiom,
! [X17,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X49)) ),
file('<stdin>',fact_trans__less__add2) ).
fof(c_0_499,axiom,
! [X15] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X15))
<=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('<stdin>',fact_not__real__square__gt__zero) ).
fof(c_0_500,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16)
<=> X36 = X16 ) ),
file('<stdin>',fact_nat__mult__eq__cancel1) ).
fof(c_0_501,axiom,
! [X6,X7,X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_Omonom(X8,X7,c_Nat_OSuc(X6)) = c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),c_Polynomial_Omonom(X8,X7,X6)) ),
file('<stdin>',fact_monom__Suc) ).
fof(c_0_502,axiom,
! [X6,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X6)) ),
file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(c_0_503,axiom,
! [X23,X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X23)
=> c_Orderings_Oord__class_Oless(X8,X9,X23) ) ) ),
file('<stdin>',fact_order__less__le__trans) ).
fof(c_0_504,axiom,
! [X23,X9,X11,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X11,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X11)
=> c_Orderings_Oord__class_Oless(X8,X23,X9) ) ) ),
file('<stdin>',fact_xt1_I7_J) ).
fof(c_0_505,axiom,
! [X23,X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless(X8,X11,X23)
=> c_Orderings_Oord__class_Oless(X8,X9,X23) ) ) ),
file('<stdin>',fact_order__le__less__trans) ).
fof(c_0_506,axiom,
! [X23,X9,X11,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> ( c_Orderings_Oord__class_Oless(X8,X23,X11)
=> c_Orderings_Oord__class_Oless(X8,X23,X9) ) ) ),
file('<stdin>',fact_xt1_I8_J) ).
fof(c_0_507,axiom,
! [X23,X9,X11,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X11,X9)
=> ( c_Orderings_Oord__class_Oless(X8,X23,X11)
=> c_Orderings_Oord__class_Oless(X8,X23,X9) ) ) ),
file('<stdin>',fact_xt1_I10_J) ).
fof(c_0_508,axiom,
! [X23,X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless(X8,X11,X23)
=> c_Orderings_Oord__class_Oless(X8,X9,X23) ) ) ),
file('<stdin>',fact_order__less__trans) ).
fof(c_0_509,axiom,
! [X23,X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X23)
=> c_Orderings_Oord__class_Oless__eq(X8,X9,X23) ) ) ),
file('<stdin>',fact_order__trans) ).
fof(c_0_510,axiom,
! [X23,X9,X11,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X11)
=> c_Orderings_Oord__class_Oless__eq(X8,X23,X9) ) ) ),
file('<stdin>',fact_xt1_I6_J) ).
fof(c_0_511,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X24)
=> ( c_Rings_Odvd__class_Odvd(X8,X24,X27)
=> c_Rings_Odvd__class_Odvd(X8,X7,X27) ) ) ),
file('<stdin>',fact_dvd__trans) ).
fof(c_0_512,axiom,
! [X24,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Groups_Ouminus__class_Ouminus(X8,X24)) = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24)) ),
file('<stdin>',fact_Limits_Ominus__diff__minus) ).
fof(c_0_513,axiom,
! [X24,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Groups_Ouminus__class_Ouminus(X8,X24)) ),
file('<stdin>',fact_minus__add__distrib) ).
fof(c_0_514,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X24),c_Groups_Ouminus__class_Ouminus(X8,X7)) ),
file('<stdin>',fact_minus__add) ).
fof(c_0_515,axiom,
! [X6,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),X6) ) ),
file('<stdin>',fact_nonzero__power__inverse) ).
fof(c_0_516,axiom,
! [X26,X25,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,X25) ) ),
file('<stdin>',fact_neg__le__iff__le) ).
fof(c_0_517,axiom,
! [X26,X25,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless(X8,X26,X25) ) ),
file('<stdin>',fact_neg__less__iff__less) ).
fof(c_0_518,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ) ),
file('<stdin>',fact_dvd__pos__nat) ).
fof(c_0_519,axiom,
! [X24,X7,X8] :
( class_Rings_Oring(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),X24) ),
file('<stdin>',fact_minus__mult__left) ).
fof(c_0_520,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),X24) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ),
file('<stdin>',fact_mult_Ominus__left) ).
fof(c_0_521,axiom,
! [X11,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X9)),X11) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11)) ),
file('<stdin>',fact_mult__left_Ominus) ).
fof(c_0_522,axiom,
! [X6,X7,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),X6) ),
file('<stdin>',fact_power__inverse) ).
fof(c_0_523,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X49,X48)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X18),X48) ) ),
file('<stdin>',fact_less__trans__Suc) ).
fof(c_0_524,axiom,
! [X39,X7,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,X7,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X39)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39)) ),
file('<stdin>',fact_smult__minus__right) ).
fof(c_0_525,axiom,
! [X6,X48] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X6) ) ),
file('<stdin>',fact_dvd__imp__le) ).
fof(c_0_526,axiom,
! [X6,X23] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X23,X6)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X6) ) ),
file('<stdin>',fact_zdvd__imp__le) ).
fof(c_0_527,axiom,
! [X27,X24,X7] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X7) )
=> ( X24 = X27
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X27)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X27,X7) ) ) ),
file('<stdin>',fact_dvd_Oord__less__eq__trans) ).
fof(c_0_528,axiom,
! [X27,X24,X7] :
( X7 = X24
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X27)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X27,X24) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X27)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X27,X7) ) ) ),
file('<stdin>',fact_dvd_Oord__eq__less__trans) ).
fof(c_0_529,axiom,
! [X50,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X57) = X50
<=> X56 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X57) ) ),
file('<stdin>',fact_le__imp__diff__is__add) ).
fof(c_0_530,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X6 ),
file('<stdin>',fact_Suc__pred) ).
fof(c_0_531,axiom,
! [X6,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Nat_OSuc(X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6),
file('<stdin>',fact_diff__Suc__eq__diff__pred) ).
fof(c_0_532,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('<stdin>',fact_wm1) ).
fof(c_0_533,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),X24)) = X24 ),
file('<stdin>',fact_add__minus__cancel) ).
fof(c_0_534,axiom,
! [X6,X9,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9)),X6) ),
file('<stdin>',fact_norm__power) ).
fof(c_0_535,axiom,
! [X23,X11,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X23)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X23) ) ),
file('<stdin>',fact_dvd_Oorder__trans) ).
fof(c_0_536,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X49)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,X48)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X48) ) ),
file('<stdin>',fact_zle__trans) ).
fof(c_0_537,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X49)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X49,X48)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X48) ) ),
file('<stdin>',fact_real__le__trans) ).
fof(c_0_538,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49,X48)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X48) ) ),
file('<stdin>',fact_le__trans) ).
fof(c_0_539,axiom,
! [X6,X7,X8] :
( class_Power_Opower(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ),
file('<stdin>',fact_power__Suc) ).
fof(c_0_540,axiom,
! [X38,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X38)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Nat_OSuc(X38)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(c_0_541,axiom,
! [X38,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Nat_OSuc(X38)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X38)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
fof(c_0_542,axiom,
! [X38,X39,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Polynomial_Opos__poly(X8,X39)
=> ( c_Polynomial_Opos__poly(X8,X38)
=> c_Polynomial_Opos__poly(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38)) ) ) ),
file('<stdin>',fact_pos__poly__mult) ).
fof(c_0_543,axiom,
! [X9,X39,X8] :
( class_Rings_Ocomm__ring(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X39)),X9) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(c_Polynomial_Opoly(X8,X39),X9)) ),
file('<stdin>',fact_poly__minus) ).
fof(c_0_544,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X25)
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),X26) ) ),
file('<stdin>',fact_minus__le__iff) ).
fof(c_0_545,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ouminus__class_Ouminus(X8,X25))
<=> c_Orderings_Oord__class_Oless__eq(X8,X25,c_Groups_Ouminus__class_Ouminus(X8,X26)) ) ),
file('<stdin>',fact_le__minus__iff) ).
fof(c_0_546,axiom,
! [X22,X23] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X22)),
file('<stdin>',fact_zminus__zadd__distrib) ).
fof(c_0_547,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ouminus__class_Ouminus(X8,X25))
<=> c_Orderings_Oord__class_Oless(X8,X25,c_Groups_Ouminus__class_Ouminus(X8,X26)) ) ),
file('<stdin>',fact_less__minus__iff) ).
fof(c_0_548,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X25)
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),X26) ) ),
file('<stdin>',fact_minus__less__iff) ).
fof(c_0_549,axiom,
! [X6,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_Omonom(X8,X7,X6)) = c_Polynomial_Omonom(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),X6) ),
file('<stdin>',fact_minus__monom) ).
fof(c_0_550,axiom,
! [X39,X7,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),X39) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39)) ),
file('<stdin>',fact_smult__minus__left) ).
fof(c_0_551,axiom,
! [X6,X17] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)) = X17 ),
file('<stdin>',fact_add__diff__inverse) ).
fof(c_0_552,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X7))
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7) ) ) ),
file('<stdin>',fact_inverse__positive__imp__positive) ).
fof(c_0_553,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Groups_Ozero__class_Ozero(X8))
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('<stdin>',fact_inverse__negative__imp__negative) ).
fof(c_0_554,axiom,
! [X26,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_inverse__nonpositive__iff__nonpositive) ).
fof(c_0_555,axiom,
! [X26,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X26))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
file('<stdin>',fact_inverse__nonnegative__iff__nonnegative) ).
fof(c_0_556,axiom,
! [X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_neg__0__le__iff__le) ).
fof(c_0_557,axiom,
! [X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
file('<stdin>',fact_neg__le__0__iff__le) ).
fof(c_0_558,axiom,
! [X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_neg__0__less__iff__less) ).
fof(c_0_559,axiom,
! [X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
file('<stdin>',fact_neg__less__0__iff__less) ).
fof(c_0_560,axiom,
! [X26,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X26))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
file('<stdin>',fact_inverse__positive__iff__positive) ).
fof(c_0_561,axiom,
! [X26,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_inverse__negative__iff__negative) ).
fof(c_0_562,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X6 ),
file('<stdin>',fact_Suc__diff__1) ).
fof(c_0_563,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> X6 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('<stdin>',fact_Suc__pred_H) ).
fof(c_0_564,axiom,
! [X35,X15,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
& ~ c_Orderings_Oord__class_Oless__eq(X8,X35,X15) ) ) ),
file('<stdin>',fact_less__le__not__le) ).
fof(c_0_565,axiom,
! [X24,X7,X8] :
( class_Rings_Oring(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ouminus__class_Ouminus(X8,X24)) ),
file('<stdin>',fact_minus__mult__right) ).
fof(c_0_566,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ouminus__class_Ouminus(X8,X24)) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ),
file('<stdin>',fact_mult_Ominus__right) ).
fof(c_0_567,axiom,
! [X9,X31,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),c_Groups_Ouminus__class_Ouminus(X8,X9)) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X9)) ),
file('<stdin>',fact_mult__right_Ominus) ).
fof(c_0_568,axiom,
! [X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X17)),X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)),
file('<stdin>',fact_mult__Suc) ).
fof(c_0_569,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X24),c_Groups_Ouminus__class_Ouminus(X8,X7)) ) ),
file('<stdin>',fact_le__imp__neg__le) ).
fof(c_0_570,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Oone__class_Oone(X8))) ),
file('<stdin>',fact_zero__less__two) ).
fof(c_0_571,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Groups_Oplus__class_Oplus(X8,X7,X24)) = X24 ),
file('<stdin>',fact_minus__add__cancel) ).
fof(c_0_572,axiom,
! [X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),c_Nat_OSuc(X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)),
file('<stdin>',fact_mult__Suc__right) ).
fof(c_0_573,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_le__minus__self__iff) ).
fof(c_0_574,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X26)
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
file('<stdin>',fact_minus__le__self__iff) ).
fof(c_0_575,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X26)
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
file('<stdin>',fact_neg__less__nonneg) ).
fof(c_0_576,axiom,
! [X26,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_less__minus__self__iff) ).
fof(c_0_577,axiom,
! [X22,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23)),X22) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X22)),
file('<stdin>',fact_zmult__zminus) ).
fof(c_0_578,axiom,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11) ),
file('<stdin>',fact_dvd_Oless__imp__le) ).
fof(c_0_579,axiom,
! [X35,X15] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X15) )
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
& X15 != X35 ) ),
file('<stdin>',fact_dvd_Oless__le) ).
fof(c_0_580,axiom,
! [X35,X15] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
<=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X15) )
| X15 = X35 ) ),
file('<stdin>',fact_dvd_Ole__less) ).
fof(c_0_581,axiom,
! [X7,X39,X27,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Polynomial_Osmult(X8,X27,X39) = c_Polynomial_OpCons(X8,X7,X39)
=> X39 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
file('<stdin>',fact_synthetic__div__unique__lemma) ).
fof(c_0_582,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ),
file('<stdin>',fact_positive__imp__inverse__positive) ).
fof(c_0_583,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Groups_Ozero__class_Ozero(X8)) ) ),
file('<stdin>',fact_negative__imp__inverse__negative) ).
fof(c_0_584,axiom,
! [X24,X7,X8] :
( class_Rings_Oring(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ouminus__class_Ouminus(X8,X24)) ),
file('<stdin>',fact_minus__mult__commute) ).
fof(c_0_585,axiom,
! [X24,X7,X8] :
( class_Rings_Oring(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),c_Groups_Ouminus__class_Ouminus(X8,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24) ),
file('<stdin>',fact_minus__mult__minus) ).
fof(c_0_586,axiom,
! [X35,X15,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,c_Groups_Ouminus__class_Ouminus(X8,X15),X35)
<=> c_Rings_Odvd__class_Odvd(X8,X15,X35) ) ),
file('<stdin>',fact_minus__dvd__iff) ).
fof(c_0_587,axiom,
! [X35,X15,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X15,c_Groups_Ouminus__class_Ouminus(X8,X35))
<=> c_Rings_Odvd__class_Odvd(X8,X15,X35) ) ),
file('<stdin>',fact_dvd__minus__iff) ).
fof(c_0_588,axiom,
! [X25,X26,X8] :
( class_Rings_Oidom(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X25)
<=> ( X26 = X25
| X26 = c_Groups_Ouminus__class_Ouminus(X8,X25) ) ) ),
file('<stdin>',fact_square__eq__iff) ).
fof(c_0_589,axiom,
! [X38,X39,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Polynomial_Opos__poly(X8,X39)
=> ( c_Polynomial_Opos__poly(X8,X38)
=> c_Polynomial_Opos__poly(X8,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,X38)) ) ) ),
file('<stdin>',fact_pos__poly__add) ).
fof(c_0_590,axiom,
! [X16,X36,X50] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X16)
<=> X36 = X16 ),
file('<stdin>',fact_Suc__mult__cancel1) ).
fof(c_0_591,axiom,
! [X45,X33,X25,X26,X8] :
( class_Groups_Oab__group__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X26,X25) = c_Groups_Ominus__class_Ominus(X8,X33,X45)
=> ( X26 = X25
<=> X33 = X45 ) ) ),
file('<stdin>',fact_diff__eq__diff__eq) ).
fof(c_0_592,axiom,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> X15 = X35 ) ) ),
file('<stdin>',fact_linorder__antisym__conv2) ).
fof(c_0_593,axiom,
! [X24,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24)) = c_Groups_Ominus__class_Ominus(X8,X24,X7) ),
file('<stdin>',fact_minus__diff__eq) ).
fof(c_0_594,axiom,
! [X35,X15,X8] :
( class_Orderings_Oorder(X8)
=> ( X15 = X35
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
& c_Orderings_Oord__class_Oless__eq(X8,X35,X15) ) ) ),
file('<stdin>',fact_order__eq__iff) ).
fof(c_0_595,axiom,
! [X15,X35,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X35,X15)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
<=> X15 = X35 ) ) ),
file('<stdin>',fact_order__antisym__conv) ).
fof(c_0_596,axiom,
! [X11,X9,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> X9 = X11 ) ) ),
file('<stdin>',fact_order__antisym) ).
fof(c_0_597,axiom,
! [X9,X11,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> X9 = X11 ) ) ),
file('<stdin>',fact_xt1_I5_J) ).
fof(c_0_598,axiom,
! [X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oone__class_Oone(X8))) ),
file('<stdin>',fact_less__add__one) ).
fof(c_0_599,axiom,
! [X25,X16,X26,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_Omonom(X8,X26,X16) = c_Polynomial_Omonom(X8,X25,X16)
<=> X26 = X25 ) ),
file('<stdin>',fact_monom__eq__iff) ).
fof(c_0_600,axiom,
! [X80,X25,X63,X26,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_OpCons(X8,X26,X63) = c_Polynomial_OpCons(X8,X25,X80)
<=> ( X26 = X25
& X63 = X80 ) ) ),
file('<stdin>',fact_pCons__eq__iff) ).
fof(c_0_601,axiom,
! [X27,X7,X24,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X24,X7) = c_Groups_Oplus__class_Oplus(X8,X27,X7)
=> X24 = X27 ) ),
file('<stdin>',fact_add__right__imp__eq) ).
fof(c_0_602,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Ocancel__ab__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X7,X24) = c_Groups_Oplus__class_Oplus(X8,X7,X27)
=> X24 = X27 ) ),
file('<stdin>',fact_add__imp__eq) ).
fof(c_0_603,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X7,X24) = c_Groups_Oplus__class_Oplus(X8,X7,X27)
=> X24 = X27 ) ),
file('<stdin>',fact_add__left__imp__eq) ).
fof(c_0_604,axiom,
! [X33,X26,X25,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X25,X26) = c_Groups_Oplus__class_Oplus(X8,X33,X26)
<=> X25 = X33 ) ),
file('<stdin>',fact_add__right__cancel) ).
fof(c_0_605,axiom,
! [X33,X25,X26,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X26,X25) = c_Groups_Oplus__class_Oplus(X8,X26,X33)
<=> X25 = X33 ) ),
file('<stdin>',fact_add__left__cancel) ).
fof(c_0_606,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
file('<stdin>',fact_k1n) ).
fof(c_0_607,axiom,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> c_Orderings_Oord__class_Oless__eq(X8,X35,X15) ) ),
file('<stdin>',fact_linorder__not__less) ).
fof(c_0_608,axiom,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
<=> c_Orderings_Oord__class_Oless(X8,X35,X15) ) ),
file('<stdin>',fact_linorder__not__le) ).
fof(c_0_609,axiom,
! [X9,X11,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> ~ c_Orderings_Oord__class_Oless(X8,X9,X11) ) ),
file('<stdin>',fact_leD) ).
fof(c_0_610,axiom,
! [X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ~ c_Orderings_Oord__class_Oless(X8,X11,X9) ) ),
file('<stdin>',fact_order__less__asym) ).
fof(c_0_611,axiom,
! [X7,X24,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X7)
=> ~ c_Orderings_Oord__class_Oless(X8,X7,X24) ) ),
file('<stdin>',fact_xt1_I9_J) ).
fof(c_0_612,axiom,
! [X24,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ~ c_Orderings_Oord__class_Oless(X8,X24,X7) ) ),
file('<stdin>',fact_order__less__asym_H) ).
fof(c_0_613,axiom,
! [X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ~ c_Orderings_Oord__class_Oless(X8,X11,X9) ) ),
file('<stdin>',fact_order__less__imp__not__less) ).
fof(c_0_614,axiom,
! [X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ~ c_Orderings_Oord__class_Oless(X8,X11,X9) ) ),
file('<stdin>',fact_order__less__not__sym) ).
fof(c_0_615,axiom,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> ( c_Orderings_Oord__class_Oless(X8,X35,X15)
| X15 = X35 ) ) ),
file('<stdin>',fact_not__less__iff__gr__or__eq) ).
fof(c_0_616,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(X36))
<=> X16 = X36 ) ),
file('<stdin>',fact_le__less__Suc__eq) ).
fof(c_0_617,axiom,
! [X26,X63,X8] :
( class_Rings_Oidom(X8)
=> ( hAPP(c_Polynomial_Opoly(X8,X63),X26) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
| c_Polynomial_Oorder(X8,X26,X63) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('<stdin>',fact_order__root) ).
fof(c_0_618,axiom,
! [X16,X36] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(X36)) ),
file('<stdin>',fact_not__less__eq) ).
fof(c_0_619,axiom,
! [X16,X36] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X16),X36) ),
file('<stdin>',fact_not__less__eq__eq) ).
fof(c_0_620,axiom,
! [X6,X17] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X17 = X6 ) ),
file('<stdin>',fact_diffs0__imp__equal) ).
fof(c_0_621,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Nat_OSuc(X16))
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X72] :
( X36 = c_Nat_OSuc(X72)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X72,X16) ) ) ),
file('<stdin>',fact_less__Suc__eq__0__disj) ).
fof(c_0_622,axiom,
! [X83,X45] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X45,X83)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X45),X83) ),
file('<stdin>',fact_uminus__dvd__conv_I1_J) ).
fof(c_0_623,axiom,
! [X83,X45] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X45,X83)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X45,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X83)) ),
file('<stdin>',fact_uminus__dvd__conv_I2_J) ).
fof(c_0_624,axiom,
! [X24,X7] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X7,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X7)),c_Complex_Oexpi(X24)),
file('<stdin>',fact_expi__add) ).
fof(c_0_625,axiom,
! [X7,X24,X8] :
( class_Divides_Osemiring__div(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Divides_Odiv__class_Odiv(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7),X24) = X7 ) ),
file('<stdin>',fact_div__mult__self1__is__id) ).
fof(c_0_626,axiom,
! [X7,X24,X8] :
( class_Divides_Osemiring__div(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Divides_Odiv__class_Odiv(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),X24) = X7 ) ),
file('<stdin>',fact_div__mult__self2__is__id) ).
fof(c_0_627,axiom,
! [X7,X8] :
( class_Rings_Olinordered__ring(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7)) ),
file('<stdin>',fact_zero__le__square) ).
fof(c_0_628,axiom,
! [X11,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9)
=> X9 = X11 ) ),
file('<stdin>',fact_dvd_Oantisym) ).
fof(c_0_629,axiom,
! [X6,X17] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X6)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X6,X17)
=> X17 = X6 ) ),
file('<stdin>',fact_dvd__antisym) ).
fof(c_0_630,axiom,
! [X24,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
=> ( X7 != X24
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X7) ) ) ),
file('<stdin>',fact_dvd_Ole__neq__trans) ).
fof(c_0_631,axiom,
! [X11,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
| X9 = X11 ) ),
file('<stdin>',fact_dvd_Ole__imp__less__or__eq) ).
fof(c_0_632,axiom,
! [X15,X35] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X15)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
<=> X15 = X35 ) ),
file('<stdin>',fact_dvd_Oantisym__conv) ).
fof(c_0_633,axiom,
! [X24,X7] :
( X7 != X24
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X7) ) ) ),
file('<stdin>',fact_dvd_Oneq__le__trans) ).
fof(c_0_634,axiom,
! [X35,X15] :
( X15 = X35
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X15) ) ),
file('<stdin>',fact_dvd_Oeq__iff) ).
fof(c_0_635,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X23)
=> X23 = X22 ) ),
file('<stdin>',fact_zle__antisym) ).
fof(c_0_636,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X23)
=> X23 = X22 ) ),
file('<stdin>',fact_real__le__antisym) ).
fof(c_0_637,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> X17 = X6 ) ),
file('<stdin>',fact_le__antisym) ).
fof(c_0_638,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24),X24) = X7 ),
file('<stdin>',fact_diff__add__cancel) ).
fof(c_0_639,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X24) = X7 ),
file('<stdin>',fact_add__diff__cancel) ).
fof(c_0_640,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X16) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X16 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('<stdin>',fact_pos__zmult__eq__1__iff) ).
fof(c_0_641,axiom,
! [X16,X36,X50] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X16)
<=> X36 = X16 ),
file('<stdin>',fact_nat__add__left__cancel) ).
fof(c_0_642,axiom,
! [X16,X50,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X50) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X50)
<=> X36 = X16 ),
file('<stdin>',fact_nat__add__right__cancel) ).
fof(c_0_643,axiom,
~ ! [X76] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X76) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
=> ~ ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X76),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)) ),
file('<stdin>',fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(c_0_644,axiom,
? [X76] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X76) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X76),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)) ),
file('<stdin>',fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096) ).
fof(c_0_645,axiom,
! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)),
file('<stdin>',fact_q_I2_J) ).
fof(c_0_646,axiom,
! [X6,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Nat_OSuc(X6)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)),
file('<stdin>',fact_add__Suc__right) ).
fof(c_0_647,axiom,
! [X6,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X17),X6) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)),
file('<stdin>',fact_add__Suc) ).
fof(c_0_648,axiom,
! [X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ),
file('<stdin>',fact_dvd__triv__left) ).
fof(c_0_649,axiom,
! [X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7)) ),
file('<stdin>',fact_dvd__triv__right) ).
fof(c_0_650,axiom,
! [X64,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X64)
<=> ? [X81] : X64 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X81) ),
file('<stdin>',fact_le__Suc__ex__iff) ).
fof(c_0_651,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
<=> ? [X71] : X16 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X71) ),
file('<stdin>',fact_le__iff__add) ).
fof(c_0_652,axiom,
! [X6,X17] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),c_Nat_OSuc(X17)),
file('<stdin>',fact_diff__less__Suc) ).
fof(c_0_653,axiom,
! [X17,X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X17)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_diff__add__0) ).
fof(c_0_654,axiom,
! [X6,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6),X6) = X17,
file('<stdin>',fact_diff__add__inverse2) ).
fof(c_0_655,axiom,
! [X17,X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X17),X6) = X17,
file('<stdin>',fact_diff__add__inverse) ).
fof(c_0_656,axiom,
! [X6,X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),X17),
file('<stdin>',fact_diff__le__self) ).
fof(c_0_657,axiom,
! [X17,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)),
file('<stdin>',fact_le__add2) ).
fof(c_0_658,axiom,
! [X17,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X17)),
file('<stdin>',fact_le__add1) ).
fof(c_0_659,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X36),c_Nat_OSuc(X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ),
file('<stdin>',fact_Suc__less__eq) ).
fof(c_0_660,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),c_Nat_OSuc(X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ),
file('<stdin>',fact_Suc__less__SucD) ).
fof(c_0_661,axiom,
! [X36,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X16),c_Nat_OSuc(X36))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X36) ),
file('<stdin>',fact_Suc__le__mono) ).
fof(c_0_662,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Nat_OSuc(X6))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> X17 = c_Nat_OSuc(X6) ) ),
file('<stdin>',fact_le__SucE) ).
fof(c_0_663,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,c_Nat_OSuc(X16))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
| X36 = c_Nat_OSuc(X16) ) ),
file('<stdin>',fact_le__Suc__eq) ).
fof(c_0_664,axiom,
! [X27,X7,X24,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X7)
=> ( X24 = X27
=> c_Orderings_Oord__class_Oless(X8,X27,X7) ) ) ),
file('<stdin>',fact_xt1_I2_J) ).
fof(c_0_665,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oord(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( X24 = X27
=> c_Orderings_Oord__class_Oless(X8,X7,X27) ) ) ),
file('<stdin>',fact_ord__less__eq__trans) ).
fof(c_0_666,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( X7 = X24
=> ( c_Orderings_Oord__class_Oless(X8,X27,X24)
=> c_Orderings_Oord__class_Oless(X8,X27,X7) ) ) ),
file('<stdin>',fact_xt1_I1_J) ).
fof(c_0_667,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oord(X8)
=> ( X7 = X24
=> ( c_Orderings_Oord__class_Oless(X8,X24,X27)
=> c_Orderings_Oord__class_Oless(X8,X7,X27) ) ) ),
file('<stdin>',fact_ord__eq__less__trans) ).
fof(c_0_668,axiom,
! [X15,X35,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X35,X15)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> X15 = X35 ) ) ),
file('<stdin>',fact_linorder__antisym__conv3) ).
fof(c_0_669,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oord(X8)
=> ( X7 = X24
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X27)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X27) ) ) ),
file('<stdin>',fact_ord__eq__le__trans) ).
fof(c_0_670,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( X7 = X24
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X24)
=> c_Orderings_Oord__class_Oless__eq(X8,X27,X7) ) ) ),
file('<stdin>',fact_xt1_I3_J) ).
fof(c_0_671,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oord(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( X24 = X27
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X27) ) ) ),
file('<stdin>',fact_ord__le__eq__trans) ).
fof(c_0_672,axiom,
! [X27,X7,X24,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> ( X24 = X27
=> c_Orderings_Oord__class_Oless__eq(X8,X27,X7) ) ) ),
file('<stdin>',fact_xt1_I4_J) ).
fof(c_0_673,axiom,
! [X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> ? [X5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,X4) ) ),
file('<stdin>',fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096) ).
fof(c_0_674,axiom,
! [X16,X50,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X50) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X50)
<=> ( X36 = X16
| X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_mult__cancel2) ).
fof(c_0_675,axiom,
! [X16,X36,X50] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16)
<=> ( X36 = X16
| X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_mult__cancel1) ).
fof(c_0_676,axiom,
! [X16,X36,X50] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16)
<=> ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X36 = X16 ) ),
file('<stdin>',fact_nat__mult__eq__cancel__disj) ).
fof(c_0_677,axiom,
! [X25,X26,X33] :
( X33 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X33)
<=> X26 = X25 ) ),
file('<stdin>',fact_real__mult__right__cancel) ).
fof(c_0_678,axiom,
! [X25,X26,X33] :
( X33 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X33),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X33),X25)
<=> X26 = X25 ) ),
file('<stdin>',fact_real__mult__left__cancel) ).
fof(c_0_679,axiom,
! [X9,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X9)
=> c_Nat__Transfer_Otsub(X9,X11) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X11) ),
file('<stdin>',fact_tsub__eq) ).
fof(c_0_680,axiom,
! [X9,X11] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X9)
=> c_Nat__Transfer_Otsub(X9,X11) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X11) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X9)
=> c_Nat__Transfer_Otsub(X9,X11) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('<stdin>',fact_tsub__def) ).
fof(c_0_681,axiom,
! [X35,X15,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
& X15 != X35 ) ) ),
file('<stdin>',fact_order__less__le) ).
fof(c_0_682,axiom,
! [X35,X15,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
<=> ( c_Orderings_Oord__class_Oless(X8,X15,X35)
| X15 = X35 ) ) ),
file('<stdin>',fact_order__le__less) ).
fof(c_0_683,axiom,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X15,X35)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
<=> X15 = X35 ) ) ),
file('<stdin>',fact_linorder__antisym__conv1) ).
fof(c_0_684,axiom,
! [X24,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( X7 != X24
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
file('<stdin>',fact_order__neq__le__trans) ).
fof(c_0_685,axiom,
! [X24,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( X7 != X24
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> c_Orderings_Oord__class_Oless(X8,X24,X7) ) ) ),
file('<stdin>',fact_xt1_I12_J) ).
fof(c_0_686,axiom,
! [X11,X9,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
| X9 = X11 ) ) ),
file('<stdin>',fact_order__le__imp__less__or__eq) ).
fof(c_0_687,axiom,
! [X24,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( X7 != X24
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
file('<stdin>',fact_order__le__neq__trans) ).
fof(c_0_688,axiom,
! [X7,X24,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> ( X7 != X24
=> c_Orderings_Oord__class_Oless(X8,X24,X7) ) ) ),
file('<stdin>',fact_xt1_I11_J) ).
fof(c_0_689,axiom,
! [X9,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8))),X9) ),
file('<stdin>',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(c_0_690,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),c_Nat_OSuc(X6)) ),
file('<stdin>',fact_Suc__mono) ).
fof(c_0_691,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Nat_OSuc(X16))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
| X36 = X16 ) ),
file('<stdin>',fact_less__Suc__eq) ).
fof(c_0_692,axiom,
! [X36,X16] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X36)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(X36))
<=> X16 = X36 ) ),
file('<stdin>',fact_not__less__less__Suc__eq) ).
fof(c_0_693,axiom,
! [X17,X6] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X17)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(X17))
=> X17 = X6 ) ),
file('<stdin>',fact_less__antisym) ).
fof(c_0_694,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X6))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> X17 = X6 ) ),
file('<stdin>',fact_less__SucE) ).
fof(c_0_695,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> ( c_Nat_OSuc(X17) != X6
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),X6) ) ),
file('<stdin>',fact_Suc__lessI) ).
fof(c_0_696,axiom,
! [X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(X8,X9,X11) ) ),
file('<stdin>',fact_order__less__imp__le) ).
fof(c_0_697,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ),
file('<stdin>',fact_Suc__lessD) ).
fof(c_0_698,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ),
file('<stdin>',fact_Suc__leD) ).
fof(c_0_699,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ),
file('<stdin>',fact_Suc__le__lessD) ).
fof(c_0_700,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X36),X16)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ),
file('<stdin>',fact_Suc__le__eq) ).
fof(c_0_701,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Nat_OSuc(X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ),
file('<stdin>',fact_less__Suc__eq__le) ).
fof(c_0_702,axiom,
! [X36,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X36)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X16),X36) ),
file('<stdin>',fact_less__eq__Suc__le) ).
fof(c_0_703,axiom,
! [X48,X24,X7,X8] :
( class_Rings_Odvd(X8)
=> ( X7 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X48)
=> c_Rings_Odvd__class_Odvd(X8,X24,X7) ) ),
file('<stdin>',fact_dvdI) ).
fof(c_0_704,axiom,
! [X37] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X37)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X37) ),
file('<stdin>',fact_int__one__le__iff__zero__less) ).
fof(c_0_705,axiom,
! [X15,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X15))
<=> X15 != c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_zero__less__norm__iff) ).
fof(c_0_706,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9)),
file('<stdin>',fact_complex__mod__minus__le__complex__mod) ).
fof(c_0_707,axiom,
! [X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X9 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('<stdin>',fact_nat__lt__two__imp__zero__or__one) ).
fof(c_0_708,axiom,
! [X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X17)),
file('<stdin>',fact_le__square) ).
fof(c_0_709,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X6)) ),
file('<stdin>',fact_less__SucI) ).
fof(c_0_710,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Nat_OSuc(X6)) ),
file('<stdin>',fact_le__SucI) ).
fof(c_0_711,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X6) ),
file('<stdin>',fact_Suc__leI) ).
fof(c_0_712,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X6)) ),
file('<stdin>',fact_le__imp__less__Suc) ).
fof(c_0_713,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,X24) = c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ouminus__class_Ouminus(X8,X24)) ),
file('<stdin>',fact_diff__def) ).
fof(c_0_714,axiom,
! [X24,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,X24) = c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ouminus__class_Ouminus(X8,X24)) ),
file('<stdin>',fact_ab__diff__minus) ).
fof(c_0_715,axiom,
! [X11,X9,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Ominus__class_Ominus(X8,X9,X11) = c_Groups_Oplus__class_Oplus(X8,X9,c_Groups_Ouminus__class_Ouminus(X8,X11)) ),
file('<stdin>',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(c_0_716,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,c_Groups_Ouminus__class_Ouminus(X8,X24)) = c_Groups_Oplus__class_Oplus(X8,X7,X24) ),
file('<stdin>',fact_diff__minus__eq__add) ).
fof(c_0_717,axiom,
! [X15,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X15 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_norm__le__zero__iff) ).
fof(c_0_718,axiom,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> X11 != X9 ),
file('<stdin>',fact_dvd_Oless__imp__not__eq2) ).
fof(c_0_719,axiom,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> X9 != X11 ),
file('<stdin>',fact_dvd_Oless__imp__not__eq) ).
fof(c_0_720,axiom,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> X9 != X11 ),
file('<stdin>',fact_dvd_Oless__imp__neq) ).
fof(c_0_721,axiom,
! [X27,X24,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
=> ( X24 = X27
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X27) ) ),
file('<stdin>',fact_dvd_Oord__le__eq__trans) ).
fof(c_0_722,axiom,
! [X27,X24,X7] :
( X7 = X24
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X27)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X27) ) ),
file('<stdin>',fact_dvd_Oord__eq__le__trans) ).
fof(c_0_723,axiom,
! [X16,X36] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ),
file('<stdin>',fact_diff__is__0__eq) ).
fof(c_0_724,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_diff__is__0__eq_H) ).
fof(c_0_725,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X35)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X35)
| X15 = X35 ) ),
file('<stdin>',fact_less__eq__real__def) ).
fof(c_0_726,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X35)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X35)
& X15 != X35 ) ),
file('<stdin>',fact_real__less__def) ).
fof(c_0_727,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
& X36 != X16 ) ),
file('<stdin>',fact_nat__less__le) ).
fof(c_0_728,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
| X36 = X16 ) ),
file('<stdin>',fact_le__eq__less__or__eq) ).
fof(c_0_729,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> ( X17 != X6
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ) ),
file('<stdin>',fact_le__neq__implies__less) ).
fof(c_0_730,axiom,
! [X46,X37] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,X46)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X37,X46)
& X37 != X46 ) ),
file('<stdin>',fact_zless__le) ).
fof(c_0_731,axiom,
! [X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X9)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X9),
file('<stdin>',fact_complex__i__mult__minus) ).
fof(c_0_732,axiom,
! [X7,X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_Omonom(X8,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X8,X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) ),
file('<stdin>',fact_monom__0) ).
fof(c_0_733,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ),
file('<stdin>',fact_less__imp__le__nat) ).
fof(c_0_734,axiom,
! [X6,X17] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
| X17 = X6 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ),
file('<stdin>',fact_less__or__eq__imp__le) ).
fof(c_0_735,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X11) ),
file('<stdin>',fact_termination__basic__simps_I5_J) ).
fof(c_0_736,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('<stdin>',fact_norm__not__less__zero) ).
fof(c_0_737,axiom,
! [X38,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))),X38) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('<stdin>',fact_mult__poly__0__left) ).
fof(c_0_738,axiom,
! [X22,X23] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X22)),
file('<stdin>',fact_diff__int__def) ).
fof(c_0_739,axiom,
! [X22,X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X22)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X22),
file('<stdin>',fact_diff__int__def__symmetric) ).
fof(c_0_740,axiom,
! [X11,X9] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X9,X11) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11)),
file('<stdin>',fact_minus__real__def) ).
fof(c_0_741,axiom,
! [X13,X14] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,X13) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13)),
file('<stdin>',fact_real__diff__def) ).
fof(c_0_742,axiom,
! [X11,X9] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X9,X11) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X9,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X11)),
file('<stdin>',fact_complex__diff__def) ).
fof(c_0_743,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('<stdin>',fact_ext) ).
fof(c_0_744,axiom,
! [X63,X26,X8] :
( class_Rings_Oidom(X8)
=> ( c_Polynomial_Osmult(X8,X26,X63) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> ( X26 = c_Groups_Ozero__class_Ozero(X8)
| X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ) ),
file('<stdin>',fact_smult__eq__0__iff) ).
fof(c_0_745,axiom,
! [X26,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X26)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X15 = X26 ),
file('<stdin>',fact_real__add__minus__iff) ).
fof(c_0_746,axiom,
! [X16,X26,X8] :
( ( class_Power_Opower(X8)
& class_Rings_Omult__zero(X8)
& class_Rings_Ono__zero__divisors(X8)
& class_Rings_Ozero__neq__one(X8) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X26),X16) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X26 = c_Groups_Ozero__class_Ozero(X8)
& X16 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('<stdin>',fact_power__eq__0__iff) ).
fof(c_0_747,axiom,
! [X15,X8] :
( class_Rings_Oring__1__no__zero__divisors(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X15) = c_Groups_Oone__class_Oone(X8)
<=> ( X15 = c_Groups_Oone__class_Oone(X8)
| X15 = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8)) ) ) ),
file('<stdin>',fact_square__eq__1__iff) ).
fof(c_0_748,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),X7) = c_Groups_Oone__class_Oone(X8) ) ),
file('<stdin>',fact_left__inverse) ).
fof(c_0_749,axiom,
! [X7,X8] :
( class_Fields_Ofield(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),X7) = c_Groups_Oone__class_Oone(X8) ) ),
file('<stdin>',fact_field__inverse) ).
fof(c_0_750,axiom,
! [X63,X26,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_OpCons(X8,X26,X63) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> ( X26 = c_Groups_Ozero__class_Ozero(X8)
& X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ) ),
file('<stdin>',fact_pCons__eq__0__iff) ).
fof(c_0_751,axiom,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ( X9 != X11
=> c_Orderings_Oord__class_Oless(X8,X11,X9) ) ) ),
file('<stdin>',fact_linorder__cases) ).
fof(c_0_752,axiom,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( X9 != X11
=> ( ~ c_Orderings_Oord__class_Oless(X8,X9,X11)
=> c_Orderings_Oord__class_Oless(X8,X11,X9) ) ) ),
file('<stdin>',fact_linorder__neqE) ).
fof(c_0_753,axiom,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
| X9 = X11
| c_Orderings_Oord__class_Oless(X8,X11,X9) ) ),
file('<stdin>',fact_linorder__less__linear) ).
fof(c_0_754,axiom,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( X15 != X35
<=> ( c_Orderings_Oord__class_Oless(X8,X15,X35)
| c_Orderings_Oord__class_Oless(X8,X35,X15) ) ) ),
file('<stdin>',fact_linorder__neq__iff) ).
fof(c_0_755,axiom,
! [X11,X9,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( X9 != X11
=> ( ~ c_Orderings_Oord__class_Oless(X8,X9,X11)
=> c_Orderings_Oord__class_Oless(X8,X11,X9) ) ) ),
file('<stdin>',fact_linorder__neqE__linordered__idom) ).
fof(c_0_756,axiom,
! [X2,X77,X8] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X8,X77,X2)
<=> ! [X3,X62] : hAPP(X2,X3) = hAPP(X2,X62) ),
file('<stdin>',fact_constant__def) ).
fof(c_0_757,axiom,
! [X6,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X17),c_Nat_OSuc(X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),
file('<stdin>',fact_diff__Suc__Suc) ).
fof(c_0_758,axiom,
! [X6,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X17),X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Nat_OSuc(X6)),
file('<stdin>',fact_add__Suc__shift) ).
fof(c_0_759,axiom,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
| c_Orderings_Oord__class_Oless(X8,X11,X9) ) ),
file('<stdin>',fact_linorder__le__less__linear) ).
fof(c_0_760,axiom,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(X8,X11,X9) ) ),
file('<stdin>',fact_leI) ).
fof(c_0_761,axiom,
! [X9,X11,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> c_Orderings_Oord__class_Oless(X8,X9,X11) ) ),
file('<stdin>',fact_not__leE) ).
fof(c_0_762,axiom,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
| c_Orderings_Oord__class_Oless__eq(X8,X11,X9) ) ),
file('<stdin>',fact_linorder__linear) ).
fof(c_0_763,axiom,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(X8,X11,X9) ) ),
file('<stdin>',fact_linorder__le__cases) ).
fof(c_0_764,axiom,
! [X27,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,X27) = c_Groups_Oplus__class_Oplus(X8,X27,X7) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(c_0_765,axiom,
! [X25,X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( X26 = c_Groups_Ouminus__class_Ouminus(X8,X25)
<=> c_Groups_Oplus__class_Oplus(X8,X26,X25) = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_eq__neg__iff__add__eq__0) ).
fof(c_0_766,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X7,X24) = c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,X7) = X24 ) ),
file('<stdin>',fact_minus__unique) ).
fof(c_0_767,axiom,
! [X35,X15,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X15,X35) = c_Groups_Ozero__class_Ozero(X8)
<=> X35 = c_Groups_Ouminus__class_Ouminus(X8,X15) ) ),
file('<stdin>',fact_add__eq__0__iff) ).
fof(c_0_768,axiom,
! [X16,X26,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_Omonom(X8,X26,X16) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_monom__eq__0__iff) ).
fof(c_0_769,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> ~ c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(X8)) ),
file('<stdin>',fact_not__one__le__zero) ).
fof(c_0_770,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
file('<stdin>',fact_qnc) ).
fof(c_0_771,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
file('<stdin>',fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096) ).
fof(c_0_772,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
file('<stdin>',fact_less_Oprems) ).
fof(c_0_773,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
file('<stdin>',fact_assms) ).
fof(c_0_774,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(X8)) ),
file('<stdin>',fact_not__one__less__zero) ).
fof(c_0_775,axiom,
! [X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('<stdin>',fact_mult__poly__0__right) ).
fof(c_0_776,axiom,
! [X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(c_0_777,axiom,
! [X36] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('<stdin>',fact_dvd__1__iff__1) ).
fof(c_0_778,axiom,
! [X16,X36] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16)
<=> ( ( X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X16 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('<stdin>',fact_one__is__add) ).
fof(c_0_779,axiom,
! [X16,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X16 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('<stdin>',fact_add__is__1) ).
fof(c_0_780,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24) = c_Groups_Oone__class_Oone(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,X7) = X24 ) ),
file('<stdin>',fact_inverse__unique) ).
fof(c_0_781,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X11)
| X9 = X11
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,X9) ),
file('<stdin>',fact_zless__linear) ).
fof(c_0_782,axiom,
! [X16,X36] :
( X36 != X16
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X36) ) ),
file('<stdin>',fact_nat__neq__iff) ).
fof(c_0_783,axiom,
! [X11,X9] :
( X9 != X11
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X11)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9) ) ),
file('<stdin>',fact_linorder__neqE__nat) ).
fof(c_0_784,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> X7 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_dvd__0__left) ).
fof(c_0_785,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_less__Suc0) ).
fof(c_0_786,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X22)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X23) ),
file('<stdin>',fact_zle__linear) ).
fof(c_0_787,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X23) ),
file('<stdin>',fact_real__le__linear) ).
fof(c_0_788,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17) ),
file('<stdin>',fact_nat__le__linear) ).
fof(c_0_789,axiom,
! [X25,X26,X8] :
( class_Rings_Oring__no__zero__divisors(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X25) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X26 = c_Groups_Ozero__class_Ozero(X8)
| X25 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('<stdin>',fact_mult__eq__0__iff) ).
fof(c_0_790,axiom,
! [X24,X7,X8] :
( class_Rings_Ono__zero__divisors(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24) != c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('<stdin>',fact_no__zero__divisors) ).
fof(c_0_791,axiom,
! [X24,X7,X8] :
( class_Rings_Ono__zero__divisors(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24) = c_Groups_Ozero__class_Ozero(X8)
=> ( X7 = c_Groups_Ozero__class_Ozero(X8)
| X24 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('<stdin>',fact_divisors__zero) ).
fof(c_0_792,axiom,
! [X38,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X38) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X38) ),
file('<stdin>',fact_diff__poly__code_I1_J) ).
fof(c_0_793,axiom,
! [X22,X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X23),
file('<stdin>',fact_zadd__commute) ).
fof(c_0_794,axiom,
! [X6,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X17),
file('<stdin>',fact_nat__add__commute) ).
fof(c_0_795,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X26,X26) = c_Groups_Ozero__class_Ozero(X8)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_double__eq__0__iff) ).
fof(c_0_796,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = c_Groups_Oplus__class_Oplus(X8,X26,X26)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_double__zero__sym) ).
fof(c_0_797,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('<stdin>',fact_kn) ).
fof(c_0_798,axiom,
! [X25,X26,X8] :
( class_Groups_Oab__group__add(X8)
=> ( X26 = X25
<=> c_Groups_Ominus__class_Ominus(X8,X26,X25) = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_eq__iff__diff__eq__0) ).
fof(c_0_799,axiom,
! [X25,X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X26,X25) = c_Groups_Ozero__class_Ozero(X8)
<=> X26 = X25 ) ),
file('<stdin>',fact_right__minus__eq) ).
fof(c_0_800,axiom,
! [X35,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X35) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X35 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15) ),
file('<stdin>',fact_real__add__eq__0__iff) ).
fof(c_0_801,axiom,
! [X6,X7,X8] :
( class_Rings_Oring__1__no__zero__divisors(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6) != c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_field__power__not__zero) ).
fof(c_0_802,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16)
<=> ? [X73] : X16 = c_Nat_OSuc(X73) ),
file('<stdin>',fact_gr0__conv__Suc) ).
fof(c_0_803,axiom,
! [X26,X25,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( X25 = c_Groups_Oplus__class_Oplus(X8,X25,X26)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_add__0__iff) ).
fof(c_0_804,axiom,
! [X63,X8] :
( ( class_Int_Oring__char__0(X8)
& class_Rings_Oidom(X8) )
=> ( c_Polynomial_Opoly(X8,X63) = c_Polynomial_Opoly(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))
<=> X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
file('<stdin>',fact_poly__zero) ).
fof(c_0_805,axiom,
! [X9] :
( X9 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X9)),X9) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('<stdin>',fact_real__mult__inverse__left) ).
fof(c_0_806,axiom,
! [X11,X9,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> X11 != X9 ) ),
file('<stdin>',fact_order__less__imp__not__eq2) ).
fof(c_0_807,axiom,
! [X11,X9,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> X9 != X11 ) ),
file('<stdin>',fact_order__less__imp__not__eq) ).
fof(c_0_808,axiom,
! [X11,X9,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> X9 != X11 ) ),
file('<stdin>',fact_less__imp__neq) ).
fof(c_0_809,axiom,
! [X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X8)) = c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) ),
file('<stdin>',fact_one__poly__def) ).
fof(c_0_810,axiom,
! [X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('<stdin>',fact_pCons__0__0) ).
fof(c_0_811,axiom,
! [X36,X15] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X36) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X15 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('<stdin>',fact_nat__power__eq__Suc__0__iff) ).
fof(c_0_812,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Rings_Oinverse__class_Oinverse(X8,X7)) = c_Groups_Oone__class_Oone(X8) ) ),
file('<stdin>',fact_right__inverse) ).
fof(c_0_813,axiom,
! [X16] :
( X16 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16) ),
file('<stdin>',fact_neq0__conv) ).
fof(c_0_814,axiom,
! [X9,X8] :
( class_Orderings_Opreorder(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,X9,X9) ),
file('<stdin>',fact_order__less__irrefl) ).
fof(c_0_815,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X6),X6),
file('<stdin>',fact_Suc__n__not__le__n) ).
fof(c_0_816,axiom,
! [X7,X8] :
( ( class_RealVector_Oreal__normed__div__algebra(X8)
& class_Rings_Odivision__ring__inverse__zero(X8) )
=> c_RealVector_Onorm__class_Onorm(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7)) ),
file('<stdin>',fact_norm__inverse) ).
fof(c_0_817,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ouminus__class_Ouminus(X8,X7)) = c_Groups_Ouminus__class_Ouminus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ),
file('<stdin>',fact_nonzero__inverse__minus__eq) ).
fof(c_0_818,axiom,
! [X36] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('<stdin>',fact_nat__dvd__1__iff__1) ).
fof(c_0_819,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_le__0__eq) ).
fof(c_0_820,axiom,
! [X16,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X16 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('<stdin>',fact_mult__eq__1__iff) ).
fof(c_0_821,axiom,
! [X22,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X22) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X23),
file('<stdin>',fact_zmult__commute) ).
fof(c_0_822,axiom,
! [X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X17),
file('<stdin>',fact_nat__mult__commute) ).
fof(c_0_823,axiom,
! [X22,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X22) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X23),
file('<stdin>',fact_real__mult__commute) ).
fof(c_0_824,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ouminus__class_Ouminus(X8,X7)) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_right__minus) ).
fof(c_0_825,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),X7) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_left__minus) ).
fof(c_0_826,axiom,
! [X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),X7) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_ab__left__minus) ).
fof(c_0_827,axiom,
! [X16,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_add__is__0) ).
fof(c_0_828,axiom,
! [X7,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7)) ) ),
file('<stdin>',fact_nonzero__norm__inverse) ).
fof(c_0_829,axiom,
! [X38,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Opcompose(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X38) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('<stdin>',fact_pcompose__0) ).
fof(c_0_830,axiom,
! [X27,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osynthetic__div(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X27) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('<stdin>',fact_synthetic__div__0) ).
fof(c_0_831,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('<stdin>',fact_smult__0__right) ).
fof(c_0_832,axiom,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ? [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X55) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',fact__096poly_Ap_Ac_A_061_A0_A_061_061_062_AEX_Az_O_Apoly_Ap_Az_A_061_A0_096) ).
fof(c_0_833,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_gr__implies__not0) ).
fof(c_0_834,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9)) ),
file('<stdin>',fact_norm__ge__zero) ).
fof(c_0_835,axiom,
! [X6,X8] :
( ( class_Power_Opower(X8)
& class_Rings_Osemiring__0(X8) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),c_Nat_OSuc(X6)) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_power__0__Suc) ).
fof(c_0_836,axiom,
! [X6,X8] :
( ( class_Power_Opower(X8)
& class_Rings_Osemiring__0(X8) )
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),X6) = c_Groups_Oone__class_Oone(X8) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),X6) = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('<stdin>',fact_power__0__left) ).
fof(c_0_837,axiom,
! [X6,X17] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6) = X17
=> X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_add__eq__self__zero) ).
fof(c_0_838,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('<stdin>',fact_less__nat__zero__code) ).
fof(c_0_839,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('<stdin>',fact_not__less0) ).
fof(c_0_840,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('<stdin>',fact_less__zeroE) ).
fof(c_0_841,axiom,
! [X9,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))),X9) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_poly__0) ).
fof(c_0_842,axiom,
! [X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X8))),X9) = c_Groups_Oone__class_Oone(X8) ),
file('<stdin>',fact_poly__1) ).
fof(c_0_843,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X17)
=> X17 != X6 ),
file('<stdin>',fact_less__not__refl2) ).
fof(c_0_844,axiom,
! [X53,X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X53)
=> X13 != X53 ),
file('<stdin>',fact_less__not__refl3) ).
fof(c_0_845,axiom,
! [X38,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X38) = X38 ),
file('<stdin>',fact_add__poly__code_I1_J) ).
fof(c_0_846,axiom,
! [X39,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = X39 ),
file('<stdin>',fact_add__poly__code_I2_J) ).
fof(c_0_847,axiom,
! [X39,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X39,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = X39 ),
file('<stdin>',fact_diff__poly__code_I2_J) ).
fof(c_0_848,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ouminus__class_Ouminus(X8,X7)) = c_Groups_Ouminus__class_Ouminus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) ),
file('<stdin>',fact_inverse__minus__eq) ).
fof(c_0_849,axiom,
! [X16,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_mult__is__0) ).
fof(c_0_850,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X6),
file('<stdin>',fact_less__not__refl) ).
fof(c_0_851,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X6),
file('<stdin>',fact_less__irrefl__nat) ).
fof(c_0_852,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Ozero__class_Ozero(X8),X7) = c_Groups_Ouminus__class_Ouminus(X8,X7) ),
file('<stdin>',fact_diff__0) ).
fof(c_0_853,axiom,
! [X6,X17] :
( X17 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)
=> ( X6 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_mult__eq__self__implies__10) ).
fof(c_0_854,axiom,
! [X16,X36] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X16 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('<stdin>',fact_nat__1__eq__mult__iff) ).
fof(c_0_855,axiom,
! [X16,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X16 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('<stdin>',fact_nat__mult__eq__1__iff) ).
fof(c_0_856,axiom,
! [X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23),X23) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('<stdin>',fact_zadd__zminus__inverse2) ).
fof(c_0_857,axiom,
! [X6,X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_Omonom(X8,c_Groups_Ozero__class_Ozero(X8),X6) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('<stdin>',fact_monom__eq__0) ).
fof(c_0_858,axiom,
! [X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Ozero__class_Ozero(X8),X39) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('<stdin>',fact_smult__0__left) ).
fof(c_0_859,axiom,
! [X8] :
( class_Power_Opower(X8)
=> c_Power_Opower__class_Opower(X8) = c_Power_Opower_Opower(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Otimes__class_Otimes(X8)) ),
file('<stdin>',fact_power__power__power) ).
fof(c_0_860,axiom,
! [X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X6) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('<stdin>',fact_power__Suc__0) ).
fof(c_0_861,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X7) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(c_0_862,axiom,
! [X6,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Oone__class_Oone(X8)),X6) = c_Groups_Oone__class_Oone(X8) ),
file('<stdin>',fact_power__one) ).
fof(c_0_863,axiom,
! [X7,X8] :
( class_Rings_Omult__zero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X7) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_mult__zero__left) ).
fof(c_0_864,axiom,
! [X24,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X24) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_mult_Ozero__left) ).
fof(c_0_865,axiom,
! [X11,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X11) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_mult__left_Ozero) ).
fof(c_0_866,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oone__class_Oone(X8)) ),
file('<stdin>',fact_zero__le__one) ).
fof(c_0_867,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oone__class_Oone(X8)) ),
file('<stdin>',fact_zero__less__one) ).
fof(c_0_868,axiom,
! [X7,X8] :
( class_Groups_Ocomm__monoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X7) = X7 ),
file('<stdin>',fact_mult__1) ).
fof(c_0_869,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X7) = X7 ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(c_0_870,axiom,
! [X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X7) = X7 ),
file('<stdin>',fact_mult__1__left) ).
fof(c_0_871,axiom,
! [X7,X8] :
( class_Divides_Osemiring__div(X8)
=> c_Divides_Odiv__class_Odiv(X8,c_Groups_Ozero__class_Ozero(X8),X7) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_div__0) ).
fof(c_0_872,axiom,
! [X7,X8] :
( class_Divides_Osemiring__div(X8)
=> c_Divides_Odiv__class_Odiv(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_div__by__0) ).
fof(c_0_873,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(c_0_874,axiom,
! [X7,X8] :
( class_Rings_Omult__zero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_mult__zero__right) ).
fof(c_0_875,axiom,
! [X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_mult_Ozero__right) ).
fof(c_0_876,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_mult__right_Ozero) ).
fof(c_0_877,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('<stdin>',fact_pqc0) ).
fof(c_0_878,axiom,
! [X39,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Oone__class_Oone(X8),X39) = X39 ),
file('<stdin>',fact_smult__1__left) ).
fof(c_0_879,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = X7 ),
file('<stdin>',fact_diff__0__right) ).
fof(c_0_880,axiom,
! [X7,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = X7 ),
file('<stdin>',fact_add_Ocomm__neutral) ).
fof(c_0_881,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = X7 ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(c_0_882,axiom,
! [X7,X8] :
( class_Groups_Omonoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = X7 ),
file('<stdin>',fact_add__0__right) ).
fof(c_0_883,axiom,
! [X7,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ozero__class_Ozero(X8),X7) = X7 ),
file('<stdin>',fact_add__0) ).
fof(c_0_884,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ozero__class_Ozero(X8),X7) = X7 ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(c_0_885,axiom,
! [X7,X8] :
( class_Groups_Omonoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ozero__class_Ozero(X8),X7) = X7 ),
file('<stdin>',fact_add__0__left) ).
fof(c_0_886,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,c_Groups_Oone__class_Oone(X8),X7) ),
file('<stdin>',fact_one__dvd) ).
fof(c_0_887,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X7,c_Groups_Ozero__class_Ozero(X8)) ),
file('<stdin>',fact_dvd__0__right) ).
fof(c_0_888,axiom,
! [X7,X8] :
( class_Groups_Ocomm__monoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Oone__class_Oone(X8)) = X7 ),
file('<stdin>',fact_mult_Ocomm__neutral) ).
fof(c_0_889,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Oone__class_Oone(X8)) = X7 ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(c_0_890,axiom,
! [X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Oone__class_Oone(X8)) = X7 ),
file('<stdin>',fact_mult__1__right) ).
fof(c_0_891,axiom,
! [X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X8) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(c_0_892,axiom,
! [X7,X8] :
( class_Power_Opower(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X8) ),
file('<stdin>',fact_power__0) ).
fof(c_0_893,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,X7) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_diff__self) ).
fof(c_0_894,axiom,
! [X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( X9 = X11
=> c_Orderings_Oord__class_Oless__eq(X8,X9,X11) ) ),
file('<stdin>',fact_order__eq__refl) ).
fof(c_0_895,axiom,
! [X48] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X48),
file('<stdin>',fact_dvd__1__left) ).
fof(c_0_896,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X7) = c_Rings_Oinverse__class_Oinverse(X8,X24)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> X7 = X24 ) ) ) ),
file('<stdin>',fact_nonzero__inverse__eq__imp__eq) ).
fof(c_0_897,axiom,
! [X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X9 ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(c_0_898,axiom,
! [X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X7 ),
file('<stdin>',fact_power__one__right) ).
fof(c_0_899,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6,
file('<stdin>',fact_diff__Suc__1) ).
fof(c_0_900,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X6)),
file('<stdin>',fact_zero__less__Suc) ).
fof(c_0_901,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',fact_a00) ).
fof(c_0_902,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X7,X7) ),
file('<stdin>',fact_dvd__refl) ).
fof(c_0_903,axiom,
! [X9,X8] :
( class_Orderings_Opreorder(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,X9,X9) ),
file('<stdin>',fact_order__refl) ).
fof(c_0_904,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ouminus__class_Ouminus(X8,X9)) = c_RealVector_Onorm__class_Onorm(X8,X9) ),
file('<stdin>',fact_norm__minus__cancel) ).
fof(c_0_905,axiom,
! [X80,X63,X8] :
( ( class_Int_Oring__char__0(X8)
& class_Rings_Oidom(X8) )
=> ( c_Polynomial_Opoly(X8,X63) = c_Polynomial_Opoly(X8,X80)
<=> X63 = X80 ) ),
file('<stdin>',fact_poly__eq__iff) ).
fof(c_0_906,axiom,
! [X6] : c_Nat_OSuc(X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('<stdin>',fact_Suc__eq__plus1) ).
fof(c_0_907,axiom,
! [X6] : c_Nat_OSuc(X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X6),
file('<stdin>',fact_Suc__eq__plus1__left) ).
fof(c_0_908,axiom,
! [X6] :
( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) ),
file('<stdin>',fact_gr0I) ).
fof(c_0_909,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(c_0_910,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(c_0_911,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('<stdin>',fact_int__0__less__1) ).
fof(c_0_912,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(X6)),
file('<stdin>',fact_lessI) ).
fof(c_0_913,axiom,
! [X24] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('<stdin>',fact_zdiv__zero) ).
fof(c_0_914,axiom,
! [X8] :
( class_Rings_Olinordered__idom(X8)
=> ~ c_Polynomial_Opos__poly(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) ),
file('<stdin>',fact_not__pos__poly__0) ).
fof(c_0_915,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_diff__0__eq__0) ).
fof(c_0_916,axiom,
! [X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23) = X23,
file('<stdin>',fact_zadd__0) ).
fof(c_0_917,axiom,
! [X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X23,
file('<stdin>',fact_zadd__0__right) ).
fof(c_0_918,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('<stdin>',fact_i__mult__eq2) ).
fof(c_0_919,axiom,
! [X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17,
file('<stdin>',fact_minus__nat_Odiff__0) ).
fof(c_0_920,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) = X6,
file('<stdin>',fact_plus__nat_Oadd__0) ).
fof(c_0_921,axiom,
! [X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17,
file('<stdin>',fact_Nat_Oadd__0__right) ).
fof(c_0_922,axiom,
! [X11,X9] :
( X9 = X11
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11) ),
file('<stdin>',fact_dvd_Oeq__refl) ).
fof(c_0_923,axiom,
! [X6,X17] :
( X17 = X6
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ),
file('<stdin>',fact_eq__imp__le) ).
fof(c_0_924,axiom,
! [X9] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9),
file('<stdin>',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
fof(c_0_925,axiom,
! [X9] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('<stdin>',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
fof(c_0_926,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6),
file('<stdin>',fact_less__eq__nat_Osimps_I1_J) ).
fof(c_0_927,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6),
file('<stdin>',fact_le0) ).
fof(c_0_928,axiom,
! [X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('<stdin>',fact_minus__poly__code_I1_J) ).
fof(c_0_929,axiom,
! [X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_diff__self__eq__0) ).
fof(c_0_930,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',fact_pc0) ).
fof(c_0_931,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_mult__0) ).
fof(c_0_932,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('<stdin>',fact_m_I1_J) ).
fof(c_0_933,axiom,
! [X25,X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X26) = c_Groups_Ouminus__class_Ouminus(X8,X25)
<=> X26 = X25 ) ),
file('<stdin>',fact_neg__equal__iff__equal) ).
fof(c_0_934,axiom,
! [X25,X26,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X26) = c_Rings_Oinverse__class_Oinverse(X8,X25)
<=> X26 = X25 ) ),
file('<stdin>',fact_inverse__eq__iff__eq) ).
fof(c_0_935,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X7) = c_Rings_Oinverse__class_Oinverse(X8,X24)
=> X7 = X24 ) ),
file('<stdin>',fact_inverse__eq__imp__eq) ).
fof(c_0_936,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) = X7 ) ),
file('<stdin>',fact_nonzero__inverse__inverse__eq) ).
fof(c_0_937,axiom,
! [X9] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X9),
file('<stdin>',fact_dvd_Oorder__refl) ).
fof(c_0_938,axiom,
! [X22] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X22),
file('<stdin>',fact_zle__refl) ).
fof(c_0_939,axiom,
! [X22] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X22),
file('<stdin>',fact_real__le__refl) ).
fof(c_0_940,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X6),
file('<stdin>',fact_le__refl) ).
fof(c_0_941,axiom,
! [X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23) = X23,
file('<stdin>',fact_zmult__1) ).
fof(c_0_942,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6) = X6,
file('<stdin>',fact_nat__mult__1) ).
fof(c_0_943,axiom,
! [X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X23) = X23,
file('<stdin>',fact_real__mult__1) ).
fof(c_0_944,axiom,
! [X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_mult__0__right) ).
fof(c_0_945,axiom,
! [X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X23,
file('<stdin>',fact_zmult__1__right) ).
fof(c_0_946,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6,
file('<stdin>',fact_nat__mult__1__right) ).
fof(c_0_947,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7)) = X7 ),
file('<stdin>',fact_minus__minus) ).
fof(c_0_948,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) = X7 ),
file('<stdin>',fact_inverse__inverse__eq) ).
fof(c_0_949,axiom,
! [X25,X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( X26 = c_Groups_Ouminus__class_Ouminus(X8,X25)
<=> X25 = c_Groups_Ouminus__class_Ouminus(X8,X26) ) ),
file('<stdin>',fact_equation__minus__iff) ).
fof(c_0_950,axiom,
! [X25,X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X26) = X25
<=> c_Groups_Ouminus__class_Ouminus(X8,X25) = X26 ) ),
file('<stdin>',fact_minus__equation__iff) ).
fof(c_0_951,axiom,
! [X63,X8] :
( class_Groups_Ozero(X8)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X8,X63) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
file('<stdin>',fact_psize__eq__0__iff) ).
fof(c_0_952,axiom,
! [X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = c_Groups_Ouminus__class_Ouminus(X8,X26)
<=> c_Groups_Ozero__class_Ozero(X8) = X26 ) ),
file('<stdin>',fact_neg__0__equal__iff__equal) ).
fof(c_0_953,axiom,
! [X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X26) = c_Groups_Ozero__class_Ozero(X8)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_neg__equal__0__iff__equal) ).
fof(c_0_954,axiom,
! [X15,X8] :
( class_Fields_Ofield__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X15) = c_Groups_Oone__class_Oone(X8)
<=> X15 = c_Groups_Oone__class_Oone(X8) ) ),
file('<stdin>',fact_inverse__eq__1__iff) ).
fof(c_0_955,axiom,
! [X26,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X26) = c_Groups_Ozero__class_Ozero(X8)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_inverse__nonzero__iff__nonzero) ).
fof(c_0_956,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,X7) != c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_nonzero__imp__inverse__nonzero) ).
fof(c_0_957,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X7) = c_Groups_Ozero__class_Ozero(X8)
=> X7 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_inverse__zero__imp__zero) ).
fof(c_0_958,axiom,
! [X15,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_RealVector_Onorm__class_Onorm(X8,X15) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X15 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_norm__eq__zero) ).
fof(c_0_959,axiom,
! [X90,X89] :
( class_Orderings_Oord(X89)
=> class_Orderings_Oord(tc_fun(X90,X89)) ),
file('<stdin>',arity_fun__Orderings_Oord) ).
fof(c_0_960,axiom,
! [X90,X89] :
( class_Orderings_Oorder(X89)
=> class_Orderings_Oorder(tc_fun(X90,X89)) ),
file('<stdin>',arity_fun__Orderings_Oorder) ).
fof(c_0_961,axiom,
! [X90,X89] :
( class_Orderings_Opreorder(X89)
=> class_Orderings_Opreorder(tc_fun(X90,X89)) ),
file('<stdin>',arity_fun__Orderings_Opreorder) ).
fof(c_0_962,axiom,
! [X23] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23)) = X23,
file('<stdin>',fact_zminus__zminus) ).
fof(c_0_963,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( X26 = c_Groups_Ouminus__class_Ouminus(X8,X26)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_equal__neg__zero) ).
fof(c_0_964,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X26) = X26
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_neg__equal__zero) ).
fof(c_0_965,axiom,
! [X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_minus__zero) ).
fof(c_0_966,axiom,
! [X8] :
( class_Rings_Odivision__ring(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Oone__class_Oone(X8)) = c_Groups_Oone__class_Oone(X8) ),
file('<stdin>',fact_inverse__1) ).
fof(c_0_967,axiom,
! [X8] :
( class_Fields_Ofield__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_field__inverse__zero) ).
fof(c_0_968,axiom,
! [X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_inverse__zero) ).
fof(c_0_969,axiom,
! [X8] :
( class_RealVector_Oreal__normed__algebra__1(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oone__class_Oone(X8)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('<stdin>',fact_norm__one) ).
fof(c_0_970,axiom,
! [X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('<stdin>',fact_norm__zero) ).
fof(c_0_971,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
file('<stdin>',fact_q_I1_J) ).
fof(c_0_972,axiom,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
file('<stdin>',fact_inverse__i) ).
fof(c_0_973,axiom,
! [X15,X8] :
( class_Groups_Oone(X8)
=> ( c_Groups_Oone__class_Oone(X8) = X15
<=> X15 = c_Groups_Oone__class_Oone(X8) ) ),
file('<stdin>',fact_one__reorient) ).
fof(c_0_974,axiom,
! [X15,X8] :
( class_Groups_Ozero(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = X15
<=> X15 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('<stdin>',fact_zero__reorient) ).
fof(c_0_975,axiom,
! [X8] :
( class_Rings_Ozero__neq__one(X8)
=> c_Groups_Oone__class_Oone(X8) != c_Groups_Ozero__class_Ozero(X8) ),
file('<stdin>',fact_one__neq__zero) ).
fof(c_0_976,axiom,
! [X8] :
( class_Rings_Ozero__neq__one(X8)
=> c_Groups_Ozero__class_Ozero(X8) != c_Groups_Oone__class_Oone(X8) ),
file('<stdin>',fact_zero__neq__one) ).
fof(c_0_977,axiom,
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('<stdin>',fact_zminus__0) ).
fof(c_0_978,axiom,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('<stdin>',fact_INVERSE__ZERO) ).
fof(c_0_979,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Odvd) ).
fof(c_0_980,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Oone(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oone) ).
fof(c_0_981,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(c_0_982,axiom,
! [X89] :
( class_Rings_Ocomm__ring(X89)
=> class_Rings_Oring(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oring) ).
fof(c_0_983,axiom,
! [X89] :
( class_Groups_Ozero(X89)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(c_0_984,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Power_Opower(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Power_Opower) ).
fof(c_0_985,axiom,
! [X89] :
( class_Rings_Ocomm__ring__1(X89)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(c_0_986,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(c_0_987,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(c_0_988,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(c_0_989,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(c_0_990,axiom,
! [X89] :
( class_Rings_Ocomm__ring(X89)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(c_0_991,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(c_0_992,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(c_0_993,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(c_0_994,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(c_0_995,axiom,
! [X89] :
( class_Rings_Ocomm__ring__1(X89)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(c_0_996,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(c_0_997,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(c_0_998,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(c_0_999,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(c_0_1000,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(c_0_1001,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(c_0_1002,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(c_0_1003,axiom,
! [X89] :
( class_Fields_Ofield(X89)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(c_0_1004,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(c_0_1005,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(c_0_1006,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(c_0_1007,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(c_0_1008,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(c_0_1009,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(c_0_1010,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(c_0_1011,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(c_0_1012,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(c_0_1013,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(c_0_1014,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(c_0_1015,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(c_0_1016,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(c_0_1017,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(c_0_1018,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(c_0_1019,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(c_0_1020,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(c_0_1021,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(c_0_1022,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(c_0_1023,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(c_0_1024,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1025,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(c_0_1026,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(c_0_1027,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(c_0_1028,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(c_0_1029,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(c_0_1030,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_1031,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(c_0_1032,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(c_0_1033,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(c_0_1034,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X89)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(c_0_1035,axiom,
! [X11,X9] :
( c_Nat_OSuc(X9) = c_Nat_OSuc(X11)
=> X9 = X11 ),
file('<stdin>',fact_Suc__inject) ).
fof(c_0_1036,axiom,
! [X67,X68] :
( c_Nat_OSuc(X68) = c_Nat_OSuc(X67)
<=> X68 = X67 ),
file('<stdin>',fact_nat_Oinject) ).
fof(c_0_1037,axiom,
! [X17] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X17),
file('<stdin>',fact_Zero__not__Suc) ).
fof(c_0_1038,axiom,
! [X66] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X66),
file('<stdin>',fact_nat_Osimps_I2_J) ).
fof(c_0_1039,axiom,
! [X17] : c_Nat_OSuc(X17) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_Suc__not__Zero) ).
fof(c_0_1040,axiom,
! [X65] : c_Nat_OSuc(X65) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_nat_Osimps_I3_J) ).
fof(c_0_1041,axiom,
! [X17] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X17),
file('<stdin>',fact_Zero__neq__Suc) ).
fof(c_0_1042,axiom,
! [X17] : c_Nat_OSuc(X17) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_Suc__neq__Zero) ).
fof(c_0_1043,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('<stdin>',fact_One__nat__def) ).
fof(c_0_1044,axiom,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('<stdin>',fact_expi__zero) ).
fof(c_0_1045,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('<stdin>',fact_int__0__neq__1) ).
fof(c_0_1046,axiom,
! [X6] : c_Nat_OSuc(X6) != X6,
file('<stdin>',fact_Suc__n__not__n) ).
fof(c_0_1047,axiom,
! [X6] : X6 != c_Nat_OSuc(X6),
file('<stdin>',fact_n__not__Suc__n) ).
fof(c_0_1048,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('<stdin>',fact_real__zero__not__eq__one) ).
fof(c_0_1049,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('<stdin>',fact_complex__i__not__one) ).
fof(c_0_1050,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',fact_complex__i__not__zero) ).
fof(c_0_1051,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',fact_w0) ).
fof(c_0_1052,axiom,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',fact_kas_I1_J) ).
fof(c_0_1053,axiom,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_kas_I2_J) ).
fof(c_0_1054,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Odvd) ).
fof(c_0_1055,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Oone) ).
fof(c_0_1056,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(c_0_1057,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Oring) ).
fof(c_0_1058,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(c_0_1059,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Power_Opower) ).
fof(c_0_1060,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(c_0_1061,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(c_0_1062,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(c_0_1063,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(c_0_1064,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(c_0_1065,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(c_0_1066,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(c_0_1067,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(c_0_1068,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(c_0_1069,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(c_0_1070,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(c_0_1071,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(c_0_1072,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(c_0_1073,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(c_0_1074,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(c_0_1075,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(c_0_1076,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(c_0_1077,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(c_0_1078,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(c_0_1079,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(c_0_1080,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(c_0_1081,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(c_0_1082,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(c_0_1083,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(c_0_1084,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(c_0_1085,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(c_0_1086,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(c_0_1087,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1088,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(c_0_1089,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(c_0_1090,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(c_0_1091,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(c_0_1092,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(c_0_1093,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Odvd) ).
fof(c_0_1094,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oone) ).
fof(c_0_1095,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oidom) ).
fof(c_0_1096,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oring) ).
fof(c_0_1097,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ozero) ).
fof(c_0_1098,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Power_Opower) ).
fof(c_0_1099,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Fields_Ofield) ).
fof(c_0_1100,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(c_0_1101,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Orderings_Oord) ).
fof(c_0_1102,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(c_0_1103,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(c_0_1104,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(c_0_1105,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(c_0_1106,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(c_0_1107,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(c_0_1108,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(c_0_1109,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(c_0_1110,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(c_0_1111,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(c_0_1112,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(c_0_1113,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(c_0_1114,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(c_0_1115,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(c_0_1116,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(c_0_1117,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(c_0_1118,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(c_0_1119,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
fof(c_0_1120,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(c_0_1121,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(c_0_1122,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(c_0_1123,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(c_0_1124,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(c_0_1125,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(c_0_1126,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(c_0_1127,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(c_0_1128,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(c_0_1129,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(c_0_1130,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(c_0_1131,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(c_0_1132,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(c_0_1133,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(c_0_1134,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(c_0_1135,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(c_0_1136,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(c_0_1137,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(c_0_1138,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(c_0_1139,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(c_0_1140,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(c_0_1141,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(c_0_1142,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1143,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(c_0_1144,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(c_0_1145,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(c_0_1146,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(c_0_1147,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(c_0_1148,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(c_0_1149,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(c_0_1150,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(c_0_1151,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(c_0_1152,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(c_0_1153,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_1154,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(c_0_1155,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(c_0_1156,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(c_0_1157,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('<stdin>',arity_HOL__Obool__Orderings_Oord) ).
fof(c_0_1158,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('<stdin>',arity_HOL__Obool__Orderings_Oorder) ).
fof(c_0_1159,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('<stdin>',arity_HOL__Obool__Orderings_Opreorder) ).
fof(c_0_1160,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Odvd) ).
fof(c_0_1161,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oone) ).
fof(c_0_1162,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ozero) ).
fof(c_0_1163,axiom,
class_Power_Opower(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Power_Opower) ).
fof(c_0_1164,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Orderings_Oord) ).
fof(c_0_1165,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Osemiring) ).
fof(c_0_1166,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Orderings_Oorder) ).
fof(c_0_1167,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Omult__zero) ).
fof(c_0_1168,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(c_0_1169,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(c_0_1170,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(c_0_1171,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Orderings_Olinorder) ).
fof(c_0_1172,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Orderings_Opreorder) ).
fof(c_0_1173,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(c_0_1174,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(c_0_1175,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(c_0_1176,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(c_0_1177,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(c_0_1178,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(c_0_1179,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(c_0_1180,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(c_0_1181,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(c_0_1182,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(c_0_1183,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(c_0_1184,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(c_0_1185,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(c_0_1186,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(c_0_1187,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(c_0_1188,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(c_0_1189,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1190,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(c_0_1191,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(c_0_1192,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(c_0_1193,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_1194,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(c_0_1195,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(c_0_1196,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(c_0_1197,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Odvd) ).
fof(c_0_1198,axiom,
class_Groups_Oone(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oone) ).
fof(c_0_1199,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oidom) ).
fof(c_0_1200,axiom,
class_Rings_Oring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oring) ).
fof(c_0_1201,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ozero) ).
fof(c_0_1202,axiom,
class_Power_Opower(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Power_Opower) ).
fof(c_0_1203,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oring__1) ).
fof(c_0_1204,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Orderings_Oord) ).
fof(c_0_1205,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Osemiring) ).
fof(c_0_1206,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Int_Oring__char__0) ).
fof(c_0_1207,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Orderings_Oorder) ).
fof(c_0_1208,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(c_0_1209,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Omult__zero) ).
fof(c_0_1210,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ogroup__add) ).
fof(c_0_1211,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Osemiring__0) ).
fof(c_0_1212,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Omonoid__add) ).
fof(c_0_1213,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(c_0_1214,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(c_0_1215,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Orderings_Olinorder) ).
fof(c_0_1216,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Orderings_Opreorder) ).
fof(c_0_1217,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oordered__ring) ).
fof(c_0_1218,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(c_0_1219,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oab__group__add) ).
fof(c_0_1220,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(c_0_1221,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Divides_Osemiring__div) ).
fof(c_0_1222,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(c_0_1223,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(c_0_1224,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(c_0_1225,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(c_0_1226,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(c_0_1227,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(c_0_1228,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(c_0_1229,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(c_0_1230,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(c_0_1231,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(c_0_1232,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(c_0_1233,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(c_0_1234,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(c_0_1235,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(c_0_1236,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(c_0_1237,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(c_0_1238,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(c_0_1239,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(c_0_1240,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(c_0_1241,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(c_0_1242,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1243,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(c_0_1244,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(c_0_1245,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(c_0_1246,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(c_0_1247,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(c_0_1248,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_1249,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(c_0_1250,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(c_0_1251,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(c_0_1252,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(c_0_1253,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(c_0_1254,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
fof(c_0_1255,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(c_0_1256,axiom,
! [X85,X86,X8,X77] :
( ( class_RealVector_Oreal__normed__vector(X77)
& class_Orderings_Oord(X8) )
=> ( ! [X81] :
( c_Orderings_Oord__class_Oless__eq(X8,X86,X81)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X77,c_Groups_Ominus__class_Ominus(X77,hAPP(X85,X86),hAPP(X85,X81))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
=> ! [X81] :
( c_Orderings_Oord__class_Oless__eq(X8,X86,X81)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X77,hAPP(X85,X81)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X77,hAPP(X85,X86)))) ) ) ),
c_0_0 ).
fof(c_0_1257,axiom,
! [X46] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X46)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X46)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
c_0_1 ).
fof(c_0_1258,axiom,
? [X71,X82] :
( X82 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& X71 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X76] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X76),X71),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))
& ! [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X55) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X55),X71)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X82,X76)),X55))) ) ),
c_0_2 ).
fof(c_0_1259,axiom,
! [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X55) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X55),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X55))),
c_0_3 ).
fof(c_0_1260,plain,
! [X7,X39,X8] :
( class_Rings_Oidom(X8)
=> ( X39 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Nat_OSuc(c_Polynomial_Oorder(X8,X7,X39))),X39) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_1261,plain,
! [X7,X39,X8] :
( class_Rings_Oidom(X8)
=> ( X39 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Polynomial_Oorder(X8,X7,X39)),X39)
& ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Nat_OSuc(c_Polynomial_Oorder(X8,X7,X39))),X39) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_1262,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> ? [X47] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X47)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
c_0_6 ).
fof(c_0_1263,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
c_0_7 ).
fof(c_0_1264,axiom,
! [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X55)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
c_0_8 ).
fof(c_0_1265,axiom,
! [X1,X2,X8,X77] :
( class_Orderings_Oord(X77)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X77),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X77,hAPP(X2,X3),hAPP(X1,X3)) ) ),
c_0_9 ).
fof(c_0_1266,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
c_0_10 ).
fof(c_0_1267,axiom,
! [X24,X7,X11,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X9,X7)),c_Groups_Ominus__class_Ominus(X8,X11,X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X9,X7)),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ominus__class_Ominus(X8,X11,X24))) ),
c_0_11 ).
fof(c_0_1268,axiom,
~ ! [X3,X62] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X62),
c_0_12 ).
fof(c_0_1269,axiom,
! [X39,X27,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X27),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Polynomial_Osynthetic__div(X8,X39,X27)),c_Polynomial_OpCons(X8,hAPP(c_Polynomial_Opoly(X8,X39),X27),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))) = X39 ),
c_0_13 ).
fof(c_0_1270,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X26,X25)),X51),X33),X45) ) ),
c_0_14 ).
fof(c_0_1271,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45))
<=> c_Orderings_Oord__class_Oless__eq(X8,X33,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X25,X26)),X51),X45)) ) ),
c_0_15 ).
fof(c_0_1272,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45))
<=> c_Orderings_Oord__class_Oless(X8,X33,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X25,X26)),X51),X45)) ) ),
c_0_16 ).
fof(c_0_1273,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X26,X25)),X51),X33),X45) ) ),
c_0_17 ).
fof(c_0_1274,axiom,
! [X16,X36,X74,X57,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X57)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X57,X56)),X74),X36),X16) ) ),
c_0_18 ).
fof(c_0_1275,axiom,
! [X16,X36,X74,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X57)),X74),X16)) ) ),
c_0_19 ).
fof(c_0_1276,axiom,
! [X16,X36,X74,X57,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X57)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X57,X56)),X74),X36),X16) ) ),
c_0_20 ).
fof(c_0_1277,axiom,
! [X16,X36,X74,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X57)),X74),X16)) ) ),
c_0_21 ).
fof(c_0_1278,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_1279,axiom,
! [X39,X7,X8] :
( class_Rings_Oidom(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Polynomial_Oorder(X8,X7,X39)),X39) ),
c_0_23 ).
fof(c_0_1280,axiom,
! [X6,X24] :
( X24 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X55] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X24),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X55),X6)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
c_0_24 ).
fof(c_0_1281,axiom,
! [X40,X27,X24,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Oplus__class_Oplus(X8,X27,X40))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X7,X27)),c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X24,X40)))) ),
c_0_25 ).
fof(c_0_1282,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24)) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),c_Groups_Ominus__class_Ominus(X8,X7,X24))),c_Rings_Oinverse__class_Oinverse(X8,X24))) ) ) ),
c_0_26 ).
fof(c_0_1283,axiom,
! [X6,X17,X10,X18,X49] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49,X18)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X10),X17),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X10),X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X49)),X10),X17),X6) ),
c_0_27 ).
fof(c_0_1284,axiom,
! [X6,X17,X10,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X10),X17),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X10),X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X18)),X10),X6)) ),
c_0_28 ).
fof(c_0_1285,axiom,
! [X9,X39,X6,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_Omonom(X8,c_Groups_Oone__class_Oone(X8),X6)),X39)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6)),hAPP(c_Polynomial_Opoly(X8,X39),X9)) ),
c_0_29 ).
fof(c_0_1286,axiom,
? [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),X55) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_30 ).
fof(c_0_1287,axiom,
! [X83,X84,X45,X8] :
( ( class_Rings_Ocomm__ring(X8)
& class_Rings_Odvd(X8) )
=> ( c_Rings_Odvd__class_Odvd(X8,X45,X84)
=> ! [X3,X71] :
( c_Rings_Odvd__class_Odvd(X8,X45,c_Groups_Oplus__class_Oplus(X8,X3,X83))
<=> c_Rings_Odvd__class_Odvd(X8,X45,c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X71),X84)),X83)) ) ) ),
c_0_31 ).
fof(c_0_1288,axiom,
! [X83,X84,X45,X8] :
( ( class_Rings_Ocomm__ring(X8)
& class_Rings_Odvd(X8) )
=> ( c_Rings_Odvd__class_Odvd(X8,X45,X84)
=> ! [X3,X71] :
( c_Rings_Odvd__class_Odvd(X8,X45,c_Groups_Oplus__class_Oplus(X8,X3,X83))
<=> c_Rings_Odvd__class_Odvd(X8,X45,c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X71),X84)),X83)) ) ) ),
c_0_32 ).
fof(c_0_1289,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_1290,axiom,
! [X78,X79,X32,X14,X38,X24] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X38),X14) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X32)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X32)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,X79) ) ) ) ) ) ),
c_0_34 ).
fof(c_0_1291,axiom,
! [X78,X79,X32,X14,X38,X24] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X38),X14) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X14,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X32)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,X38) ) ) ) ) ) ),
c_0_35 ).
fof(c_0_1292,axiom,
! [X33,X83,X15,X45,X26] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X26,X45)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X83))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X45)),X83)) ) ),
c_0_36 ).
fof(c_0_1293,axiom,
! [X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ? [X87] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X87)
& ! [X82,X88] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X82),X88)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X82)),c_RealVector_Onorm__class_Onorm(X8,X88))),X87)) ) ),
c_0_37 ).
fof(c_0_1294,axiom,
! [X24,X7,X8] :
( class_Fields_Ofield(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)),c_Rings_Oinverse__class_Oinverse(X8,X7))),c_Rings_Oinverse__class_Oinverse(X8,X24)) ) ) ),
c_0_38 ).
fof(c_0_1295,axiom,
! [X14,X38,X78,X79,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X79),X78),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X38),X14))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X24)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X14,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,X38) ) ) ) ),
c_0_39 ).
fof(c_0_1296,axiom,
! [X14,X38,X78,X79,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X79),X78),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X38),X14))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,X14)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,X78)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,X79) ) ) ) ),
c_0_40 ).
fof(c_0_1297,axiom,
! [X16,X36,X74,X57,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X57)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X57,X56)),X74),X36) = X16 ) ),
c_0_41 ).
fof(c_0_1298,axiom,
! [X16,X36,X74,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X74),X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X74),X16)
<=> X36 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X57)),X74),X16) ) ),
c_0_42 ).
fof(c_0_1299,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oring(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45)
<=> X33 = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X25,X26)),X51),X45) ) ),
c_0_43 ).
fof(c_0_1300,axiom,
! [X45,X25,X33,X51,X26,X8] :
( class_Rings_Oring(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X51),X33) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X51),X45)
<=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X26,X25)),X51),X33) = X45 ) ),
c_0_44 ).
fof(c_0_1301,axiom,
! [X23] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X23) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X23,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X23,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X23,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X23,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
c_0_45 ).
fof(c_0_1302,axiom,
! [X24,X7,X11,X9,X8] :
( class_Rings_Oring(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),c_Groups_Ominus__class_Ominus(X8,X11,X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X9,X7)),X24)) ),
c_0_46 ).
fof(c_0_1303,axiom,
! [X27,X24,X28,X7,X8] :
( class_Rings_Osemiring(X8)
=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X28),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X28),X27)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)),X28),X27) ),
c_0_47 ).
fof(c_0_1304,axiom,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
c_0_48 ).
fof(c_0_1305,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),c_Groups_Ominus__class_Ominus(X8,X24,X7))),c_Rings_Oinverse__class_Oinverse(X8,X24)) ) ) ),
c_0_49 ).
fof(c_0_1306,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),c_Groups_Oplus__class_Oplus(X8,X7,X24))),c_Rings_Oinverse__class_Oinverse(X8,X24)) ) ) ),
c_0_50 ).
fof(c_0_1307,axiom,
! [X75,X10,X11,X7,X9,X8] :
( class_Rings_Olinordered__semiring__1__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X7)
=> ( c_Orderings_Oord__class_Oless(X8,X11,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X75)
=> ( c_Groups_Oplus__class_Oplus(X8,X10,X75) = c_Groups_Oone__class_Oone(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X75),X11)),X7) ) ) ) ) ) ),
c_0_51 ).
fof(c_0_1308,axiom,
! [X75,X10,X11,X7,X9,X8] :
( class_Rings_Olinordered__semiring__1(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X75)
=> ( c_Groups_Oplus__class_Oplus(X8,X10,X75) = c_Groups_Oone__class_Oone(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X75),X11)),X7) ) ) ) ) ) ),
c_0_52 ).
fof(c_0_1309,axiom,
! [X64,X52,X8] :
( ( class_Rings_Odvd(X8)
& class_Rings_Osemiring__0(X8) )
=> ( ? [X3] : hBOOL(hAPP(X52,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X64),X3)))
<=> ? [X3] :
( c_Rings_Odvd__class_Odvd(X8,X64,c_Groups_Oplus__class_Oplus(X8,X3,c_Groups_Ozero__class_Ozero(X8)))
& hBOOL(hAPP(X52,X3)) ) ) ),
c_0_53 ).
fof(c_0_1310,axiom,
! [X48,X49,X10,X18] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X10),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X10),X48)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X49)),X10),X48),
c_0_54 ).
fof(c_0_1311,axiom,
! [X10,X11,X12,X9] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X10))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X9)),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X12)),X10)) ) ) ),
c_0_55 ).
fof(c_0_1312,axiom,
! [X11,X6,X39,X8] :
( class_Groups_Omonoid__mult(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X6),X39)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X39))),X11) ) ),
c_0_56 ).
fof(c_0_1313,axiom,
! [X35,X15,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X35),X35)))
<=> ( X15 != c_Groups_Ozero__class_Ozero(X8)
| X35 != c_Groups_Ozero__class_Ozero(X8) ) ) ),
c_0_57 ).
fof(c_0_1314,axiom,
! [X41,X42,X44,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),X41)) ),
c_0_58 ).
fof(c_0_1315,axiom,
! [X35,X15,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X35),X35)),c_Groups_Ozero__class_Ozero(X8))
<=> ( X15 = c_Groups_Ozero__class_Ozero(X8)
& X35 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
c_0_59 ).
fof(c_0_1316,plain,
! [X11,X9,X8] :
( class_Rings_Olinordered__ring(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X11)),c_Groups_Ozero__class_Ozero(X8)) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_1317,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_61 ).
fof(c_0_1318,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,X7,X39)),X38) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X38),c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38))) ),
c_0_62 ).
fof(c_0_1319,axiom,
! [X33,X63,X8] :
( class_Rings_Oidom(X8)
=> ( hAPP(c_Polynomial_Opoly(X8,X63),X33) = c_Groups_Ozero__class_Ozero(X8)
<=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X33),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))),X63) ) ),
c_0_63 ).
fof(c_0_1320,axiom,
! [X10,X11,X12,X9] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X10))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X12))) ) ) ),
c_0_64 ).
fof(c_0_1321,axiom,
! [X9,X6,X8] :
( class_Groups_Omonoid__mult(X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6) ) ),
c_0_65 ).
fof(c_0_1322,axiom,
! [X63,X33,X8] :
( class_Rings_Oidom(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X33,c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))),X63)
<=> hAPP(c_Polynomial_Opoly(X8,X63),c_Groups_Ouminus__class_Ouminus(X8,X33)) = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_66 ).
fof(c_0_1323,axiom,
! [X37,X15,X35,X46,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X46),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X37)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X46),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X35))
<=> ( X46 = X15
| X35 = X37 ) ) ),
c_0_67 ).
fof(c_0_1324,axiom,
! [X45,X33,X25,X26,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( ( X26 != X25
& X33 != X45 )
<=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X45)) != c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X33)) ) ),
c_0_68 ).
fof(c_0_1325,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
c_0_69 ).
fof(c_0_1326,axiom,
! [X16,X26,X59,X60,X8] : hAPP(hAPP(c_Power_Opower_Opower(X8,X60,X59),X26),c_Nat_OSuc(X16)) = hAPP(hAPP(X59,X26),hAPP(hAPP(c_Power_Opower_Opower(X8,X60,X59),X26),X16)),
c_0_70 ).
fof(c_0_1327,axiom,
! [X38,X7,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),c_Polynomial_OpCons(X8,X7,X38)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38))) ),
c_0_71 ).
fof(c_0_1328,axiom,
! [X6,X7,X8] :
( class_Rings_Oring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8))),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ),
c_0_72 ).
fof(c_0_1329,axiom,
! [X78,X79,X32] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X32)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
c_0_73 ).
fof(c_0_1330,axiom,
! [X78,X79,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X79),X78))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X32)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X32)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79) ) ) ),
c_0_74 ).
fof(c_0_1331,axiom,
! [X11,X9,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X9,X11)),c_Groups_Oplus__class_Oplus(X8,X9,X11)) ),
c_0_75 ).
fof(c_0_1332,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Opcompose(X8,c_Polynomial_OpCons(X8,X7,X39),X38) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X38),c_Polynomial_Opcompose(X8,X39,X38))) ),
c_0_76 ).
fof(c_0_1333,axiom,
! [X41,X42,X44,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X42)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X44),X41)) ),
c_0_77 ).
fof(c_0_1334,axiom,
! [X41,X42,X44,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41))) ),
c_0_78 ).
fof(c_0_1335,axiom,
! [X7,X24] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X24,X7)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X24)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7)),
c_0_79 ).
fof(c_0_1336,axiom,
! [X23,X22] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X22),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X22,X23)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X23))),
c_0_80 ).
fof(c_0_1337,axiom,
! [X14,X38,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,X38)),X14) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X38),X14)) ),
c_0_81 ).
fof(c_0_1338,plain,
! [X25,X26,X52] :
( hBOOL(hAPP(X52,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X25)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
& ~ hBOOL(hAPP(X52,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X58] :
( X26 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X58)
& ~ hBOOL(hAPP(X52,X58)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_1339,axiom,
! [X25,X26,X52] :
( hBOOL(hAPP(X52,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X25)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
=> hBOOL(hAPP(X52,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X58] :
( X26 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X58)
=> hBOOL(hAPP(X52,X58)) ) ) ),
c_0_83 ).
fof(c_0_1340,axiom,
! [X6,X24,X17,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_Omonom(X8,X7,X17)),c_Polynomial_Omonom(X8,X24,X6)) = c_Polynomial_Omonom(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)) ),
c_0_84 ).
fof(c_0_1341,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ) ),
c_0_85 ).
fof(c_0_1342,axiom,
! [X37] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X37),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
c_0_86 ).
fof(c_0_1343,axiom,
! [X13,X11,X14,X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X9),X14)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X11),X13)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oplus__class_Oplus(X8,X9,X11)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,X13)) ) ) ),
c_0_87 ).
fof(c_0_1344,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
c_0_88 ).
fof(c_0_1345,axiom,
! [X9,X38,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Polynomial_Opoly(X8,X39),X9)),hAPP(c_Polynomial_Opoly(X8,X38),X9)) ),
c_0_89 ).
fof(c_0_1346,axiom,
! [X6,X17] :
( ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X6)) ) ),
c_0_90 ).
fof(c_0_1347,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X16)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X50),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X50))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ) ) ),
c_0_91 ).
fof(c_0_1348,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X16)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X50),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X50))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ) ) ),
c_0_92 ).
fof(c_0_1349,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
c_0_93 ).
fof(c_0_1350,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
c_0_94 ).
fof(c_0_1351,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
c_0_95 ).
fof(c_0_1352,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
c_0_96 ).
fof(c_0_1353,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
c_0_97 ).
fof(c_0_1354,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ) ) ),
c_0_98 ).
fof(c_0_1355,axiom,
! [X13,X11,X14,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X9),X14)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X11),X13)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X13)) ) ) ),
c_0_99 ).
fof(c_0_1356,axiom,
! [X27,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,c_Polynomial_Osmult(X8,X27,c_Polynomial_Osynthetic__div(X8,X39,X27))) = c_Polynomial_OpCons(X8,hAPP(c_Polynomial_Opoly(X8,X39),X27),c_Polynomial_Osynthetic__div(X8,X39,X27)) ),
c_0_100 ).
fof(c_0_1357,axiom,
! [X38,X11,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11)),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X38)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),X38)) ),
c_0_101 ).
fof(c_0_1358,axiom,
! [X6,X24,X7,X8] :
( class_Groups_Ocomm__monoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),X6)) ),
c_0_102 ).
fof(c_0_1359,axiom,
! [X24,X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),c_Nat_OSuc(X6)))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X24) ) ) ),
c_0_103 ).
fof(c_0_1360,axiom,
! [X11,X9,X8] :
( class_Rings_Olinordered__ring(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X11))) ),
c_0_104 ).
fof(c_0_1361,axiom,
! [X36,X16,X50] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X50,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X36)))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X50,X16) ),
c_0_105 ).
fof(c_0_1362,axiom,
! [X9,X8] :
( class_Rings_Oring__1(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X9),c_Groups_Oone__class_Oone(X8)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X9,c_Groups_Oone__class_Oone(X8))),c_Groups_Ominus__class_Ominus(X8,X9,c_Groups_Oone__class_Oone(X8))) ),
c_0_106 ).
fof(c_0_1363,axiom,
! [X9,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_OpCons(X8,X7,X39)),X9) = c_Groups_Oplus__class_Oplus(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),hAPP(c_Polynomial_Opoly(X8,X39),X9))) ),
c_0_107 ).
fof(c_0_1364,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6))) ) ),
c_0_108 ).
fof(c_0_1365,axiom,
! [X24,X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),X6))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
c_0_109 ).
fof(c_0_1366,axiom,
! [X24,X7,X27,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X24) ) ) ),
c_0_110 ).
fof(c_0_1367,axiom,
! [X24,X27,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X24) ) ) ),
c_0_111 ).
fof(c_0_1368,axiom,
! [X24,X7,X27,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
c_0_112 ).
fof(c_0_1369,axiom,
! [X24,X7,X27,X8] :
( class_Rings_Olinordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
c_0_113 ).
fof(c_0_1370,axiom,
! [X24,X27,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
c_0_114 ).
fof(c_0_1371,axiom,
! [X24,X27,X7,X8] :
( class_Rings_Olinordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
c_0_115 ).
fof(c_0_1372,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X33,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> c_Orderings_Oord__class_Oless__eq(X8,X25,X26) ) ) ),
c_0_116 ).
fof(c_0_1373,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X33)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,X25) ) ) ),
c_0_117 ).
fof(c_0_1374,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X33)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> c_Orderings_Oord__class_Oless(X8,X26,X25) ) ) ),
c_0_118 ).
fof(c_0_1375,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X33,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> c_Orderings_Oord__class_Oless(X8,X25,X26) ) ) ),
c_0_119 ).
fof(c_0_1376,axiom,
! [X6,X17,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ) ) ),
c_0_120 ).
fof(c_0_1377,axiom,
! [X35,X15,X25,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X25)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X25),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X25),X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X35) ) ) ),
c_0_121 ).
fof(c_0_1378,axiom,
! [X35,X15,X25,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X25)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X25),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X25),X35))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X35) ) ) ),
c_0_122 ).
fof(c_0_1379,axiom,
! [X6,X17,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ) ) ),
c_0_123 ).
fof(c_0_1380,axiom,
! [X38,X24,X39,X7,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X7,X39),c_Polynomial_OpCons(X8,X24,X38)) = c_Polynomial_OpCons(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,X38)) ),
c_0_124 ).
fof(c_0_1381,axiom,
! [X38,X24,X39,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X7,X39),c_Polynomial_OpCons(X8,X24,X38)) = c_Polynomial_OpCons(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X39,X38)) ),
c_0_125 ).
fof(c_0_1382,axiom,
! [X9,X6,X39,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),X39),X6)),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Polynomial_Opoly(X8,X39),X9)),X6) ),
c_0_126 ).
fof(c_0_1383,axiom,
! [X40,X24,X27,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24),c_Groups_Ominus__class_Ominus(X8,X27,X40)) ),
c_0_127 ).
fof(c_0_1384,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Oplus__class_Oplus(X8,X27,X40)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) ),
c_0_128 ).
fof(c_0_1385,axiom,
! [X7,X34,X6,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X34)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X34),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ) ) ),
c_0_129 ).
fof(c_0_1386,axiom,
! [X7,X34,X6,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X34)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X34),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ) ) ),
c_0_130 ).
fof(c_0_1387,axiom,
! [X6,X24,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),X6)) ) ) ) ),
c_0_131 ).
fof(c_0_1388,axiom,
! [X25,X33,X26,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X33))
<=> ( ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X33)
& c_Orderings_Oord__class_Oless(X8,X26,X25) )
| ( c_Orderings_Oord__class_Oless(X8,X33,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless(X8,X25,X26) ) ) ) ),
c_0_132 ).
fof(c_0_1389,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> ( ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X33)
& c_Orderings_Oord__class_Oless(X8,X26,X25) )
| ( c_Orderings_Oord__class_Oless(X8,X33,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless(X8,X25,X26) ) ) ) ),
c_0_133 ).
fof(c_0_1390,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ? [X87] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X87)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X3)),X87)) ) ),
c_0_134 ).
fof(c_0_1391,axiom,
! [X11,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ? [X87] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X87)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X3),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X3)),X87)) ) ),
c_0_135 ).
fof(c_0_1392,axiom,
! [X11,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9)),c_RealVector_Onorm__class_Onorm(X8,X11))) ),
c_0_136 ).
fof(c_0_1393,axiom,
! [X24,X30,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X7,X30)),X24) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X24)) ),
c_0_137 ).
fof(c_0_1394,axiom,
! [X29,X11,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X9,X11)),X29) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X29)) ),
c_0_138 ).
fof(c_0_1395,axiom,
! [X24,X17,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)),X17) ),
c_0_139 ).
fof(c_0_1396,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)),X27) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ),
c_0_140 ).
fof(c_0_1397,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)),X27) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ),
c_0_141 ).
fof(c_0_1398,axiom,
! [X24,X30,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X30)),X24) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X24)) ),
c_0_142 ).
fof(c_0_1399,axiom,
! [X29,X11,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X9,X11)),X29) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X29)) ),
c_0_143 ).
fof(c_0_1400,axiom,
! [X38,X39,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X39)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X38)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X38)) ),
c_0_144 ).
fof(c_0_1401,axiom,
! [X6,X17,X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ),
c_0_145 ).
fof(c_0_1402,axiom,
! [X42,X44,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),X42) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X42)),X44) ),
c_0_146 ).
fof(c_0_1403,axiom,
! [X17,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X48),c_Nat_OSuc(X49)) ),
c_0_147 ).
fof(c_0_1404,axiom,
! [X17,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48)),X17) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X49),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X17)) ),
c_0_148 ).
fof(c_0_1405,axiom,
! [X40,X27,X24,X7,X14,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( X14 != c_Groups_Ozero__class_Ozero(X8)
=> ( ( X7 = X24
& X27 != X40 )
=> c_Groups_Oplus__class_Oplus(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X14),X27)) != c_Groups_Oplus__class_Oplus(X8,X24,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X14),X40)) ) ) ),
c_0_149 ).
fof(c_0_1406,axiom,
! [X6,X17,X18] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X17),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X6))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X18)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ) ),
c_0_150 ).
fof(c_0_1407,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X6))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X6) ) ),
c_0_151 ).
fof(c_0_1408,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X16) ) ),
c_0_152 ).
fof(c_0_1409,axiom,
! [X35,X15,X37] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X37)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X37),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X37),X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X35) ) ),
c_0_153 ).
fof(c_0_1410,axiom,
! [X35,X15,X37] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X37)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X35),X37))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X35) ) ),
c_0_154 ).
fof(c_0_1411,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ) ),
c_0_155 ).
fof(c_0_1412,axiom,
! [X16,X50,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X50))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ) ),
c_0_156 ).
fof(c_0_1413,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ) ),
c_0_157 ).
fof(c_0_1414,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ) ),
c_0_158 ).
fof(c_0_1415,axiom,
! [X35,X15,X37] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X37)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X35),X37))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X35) ) ),
c_0_159 ).
fof(c_0_1416,axiom,
! [X6,X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X17),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ) ),
c_0_160 ).
fof(c_0_1417,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),c_RealVector_Onorm__class_Onorm(X8,X24)),c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24))) ),
c_0_161 ).
fof(c_0_1418,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),c_RealVector_Onorm__class_Onorm(X8,X24)),c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24))) ),
c_0_162 ).
fof(c_0_1419,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),c_RealVector_Onorm__class_Onorm(X8,X24))) ),
c_0_163 ).
fof(c_0_1420,axiom,
! [X11,X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oplus__class_Oplus(X8,X9,X11)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X9),c_RealVector_Onorm__class_Onorm(X8,X11))) ),
c_0_164 ).
fof(c_0_1421,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_Osmult(X8,X7,X39)),X38) = c_Polynomial_Osmult(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38)) ),
c_0_165 ).
fof(c_0_1422,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ),
c_0_166 ).
fof(c_0_1423,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ),
c_0_167 ).
fof(c_0_1424,axiom,
! [X9,X38,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,X38)),X9) = c_Groups_Oplus__class_Oplus(X8,hAPP(c_Polynomial_Opoly(X8,X39),X9),hAPP(c_Polynomial_Opoly(X8,X38),X9)) ),
c_0_168 ).
fof(c_0_1425,axiom,
! [X9,X38,X39,X8] :
( class_Rings_Ocomm__ring(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X39,X38)),X9) = c_Groups_Ominus__class_Ominus(X8,hAPP(c_Polynomial_Opoly(X8,X39),X9),hAPP(c_Polynomial_Opoly(X8,X38),X9)) ),
c_0_169 ).
fof(c_0_1426,axiom,
! [X17,X24,X6,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17),X24) ) ) ),
c_0_170 ).
fof(c_0_1427,axiom,
! [X48,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),X17),X48) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
c_0_171 ).
fof(c_0_1428,axiom,
! [X57,X56,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X56)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X50))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X50),X56) ) ),
c_0_172 ).
fof(c_0_1429,axiom,
! [X22,X20,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X21,X20)),X22) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X22)),
c_0_173 ).
fof(c_0_1430,axiom,
! [X22,X20,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20)),X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X22)),
c_0_174 ).
fof(c_0_1431,axiom,
! [X48,X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)),X48) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X48)),
c_0_175 ).
fof(c_0_1432,axiom,
! [X48,X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)),X48) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X48)),
c_0_176 ).
fof(c_0_1433,axiom,
! [X22,X20,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20)),X22) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),X22)),
c_0_177 ).
fof(c_0_1434,axiom,
! [X6,X9,X8] :
( class_RealVector_Oreal__normed__algebra__1(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9)),X6)) ),
c_0_178 ).
fof(c_0_1435,axiom,
! [X25,X33,X26,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X26,X33),c_Groups_Oplus__class_Oplus(X8,X25,X33))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,X25) ) ),
c_0_179 ).
fof(c_0_1436,axiom,
! [X25,X26,X33,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X33,X26),c_Groups_Oplus__class_Oplus(X8,X33,X25))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,X25) ) ),
c_0_180 ).
fof(c_0_1437,axiom,
! [X24,X27,X7,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X27))
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X24) ) ),
c_0_181 ).
fof(c_0_1438,axiom,
! [X24,X7,X27,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X27,X7),c_Groups_Oplus__class_Oplus(X8,X27,X24))
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X24) ) ),
c_0_182 ).
fof(c_0_1439,axiom,
! [X24,X7,X27,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X27,X7),c_Groups_Oplus__class_Oplus(X8,X27,X24))
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ),
c_0_183 ).
fof(c_0_1440,axiom,
! [X24,X27,X7,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X27))
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ),
c_0_184 ).
fof(c_0_1441,axiom,
! [X25,X26,X33,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X33,X26),c_Groups_Oplus__class_Oplus(X8,X33,X25))
<=> c_Orderings_Oord__class_Oless(X8,X26,X25) ) ),
c_0_185 ).
fof(c_0_1442,axiom,
! [X25,X33,X26,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X26,X33),c_Groups_Oplus__class_Oplus(X8,X25,X33))
<=> c_Orderings_Oord__class_Oless(X8,X26,X25) ) ),
c_0_186 ).
fof(c_0_1443,axiom,
! [X6,X17,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X6)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X48),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X48)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6) ) ),
c_0_187 ).
fof(c_0_1444,axiom,
! [X25,X33,X26,X8] :
( class_Rings_Oidom(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X33))
<=> ( X33 = c_Groups_Ozero__class_Ozero(X8)
| c_Rings_Odvd__class_Odvd(X8,X26,X25) ) ) ),
c_0_188 ).
fof(c_0_1445,axiom,
! [X25,X26,X33,X8] :
( class_Rings_Oidom(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X33),X25))
<=> ( X33 = c_Groups_Ozero__class_Ozero(X8)
| c_Rings_Odvd__class_Odvd(X8,X26,X25) ) ) ),
c_0_189 ).
fof(c_0_1446,axiom,
! [X52,X16,X36] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
=> hBOOL(hAPP(hAPP(X52,X16),X36)) )
=> ( ( X36 = X16
=> hBOOL(hAPP(hAPP(X52,X16),X36)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X36)
=> hBOOL(hAPP(hAPP(X52,X16),X36)) )
=> hBOOL(hAPP(hAPP(X52,X16),X36)) ) ) ),
c_0_190 ).
fof(c_0_1447,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6))) ) ),
c_0_191 ).
fof(c_0_1448,axiom,
~ ! [X47] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X47),v_k____)),v_a____)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_192 ).
fof(c_0_1449,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_193 ).
fof(c_0_1450,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6))
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X6) ) ) ),
c_0_194 ).
fof(c_0_1451,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6))
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X17) ) ) ),
c_0_195 ).
fof(c_0_1452,axiom,
! [X23,X11,X9] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X11)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X23)),
c_0_196 ).
fof(c_0_1453,axiom,
! [X7,X39,X27,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X27,X39),c_Polynomial_OpCons(X8,X7,X39)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> X39 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
c_0_197 ).
fof(c_0_1454,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ),
c_0_198 ).
fof(c_0_1455,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ),
c_0_199 ).
fof(c_0_1456,axiom,
! [X38,X14,X7] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> ( X7 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7),X38))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
c_0_200 ).
fof(c_0_1457,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
c_0_201 ).
fof(c_0_1458,axiom,
! [X38,X14,X7] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> ( X7 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7),X38))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X14,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X38) ) ) ),
c_0_202 ).
fof(c_0_1459,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X7,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,X38)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),c_Polynomial_Osmult(X8,X7,X38)) ),
c_0_203 ).
fof(c_0_1460,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,X7,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X39,X38)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),c_Polynomial_Osmult(X8,X7,X38)) ),
c_0_204 ).
fof(c_0_1461,axiom,
! [X24,X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),X6)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> X7 = X24 ) ) ) ) ),
c_0_205 ).
fof(c_0_1462,axiom,
! [X7,X17,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oone__class_Oone(X8))),X17) ),
c_0_206 ).
fof(c_0_1463,axiom,
! [X17,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X17),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oone__class_Oone(X8))),X17) ),
c_0_207 ).
fof(c_0_1464,axiom,
! [X11,X9,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X9),X9) ) ) ) ),
c_0_208 ).
fof(c_0_1465,axiom,
! [X11,X9,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11),X9) ) ) ) ),
c_0_209 ).
fof(c_0_1466,axiom,
! [X11,X9,X27,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),c_RealVector_Onorm__class_Onorm(X8,X11)))
=> X9 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
c_0_210 ).
fof(c_0_1467,axiom,
! [X6,X24,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),X6)) ) ) ),
c_0_211 ).
fof(c_0_1468,axiom,
! [X27,X7,X24,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
c_0_212 ).
fof(c_0_1469,axiom,
! [X27,X7,X24,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ) ),
c_0_213 ).
fof(c_0_1470,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Oordered__comm__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
c_0_214 ).
fof(c_0_1471,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
c_0_215 ).
fof(c_0_1472,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ) ),
c_0_216 ).
fof(c_0_1473,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ) ),
c_0_217 ).
fof(c_0_1474,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
c_0_218 ).
fof(c_0_1475,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Olinordered__comm__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
c_0_219 ).
fof(c_0_1476,axiom,
! [X27,X7,X24,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X7)
=> ( c_Orderings_Oord__class_Oless(X8,X27,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ) ),
c_0_220 ).
fof(c_0_1477,axiom,
! [X27,X7,X24,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X7)
=> ( c_Orderings_Oord__class_Oless(X8,X27,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) ) ) ),
c_0_221 ).
fof(c_0_1478,axiom,
! [X17,X6,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X17),X48)) ),
c_0_222 ).
fof(c_0_1479,axiom,
! [X40,X27,X24,X7,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X27,X40)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) ) ) ),
c_0_223 ).
fof(c_0_1480,axiom,
! [X40,X27,X24,X7,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X40)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) ) ) ),
c_0_224 ).
fof(c_0_1481,axiom,
! [X40,X27,X24,X7,X8] :
( class_Groups_Oordered__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X40)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) ) ) ),
c_0_225 ).
fof(c_0_1482,axiom,
! [X40,X27,X24,X7,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X27,X40)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X40)) ) ) ),
c_0_226 ).
fof(c_0_1483,axiom,
! [X7,X34,X6,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X34)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X34)) ) ) ),
c_0_227 ).
fof(c_0_1484,axiom,
! [X7,X34,X6,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X34)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X34)) ) ) ),
c_0_228 ).
fof(c_0_1485,axiom,
! [X24,X6,X7,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Omonom(X8,X7,X6),c_Polynomial_Omonom(X8,X24,X6)) = c_Polynomial_Omonom(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X6) ),
c_0_229 ).
fof(c_0_1486,axiom,
! [X39,X24,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X39) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),c_Polynomial_Osmult(X8,X24,X39)) ),
c_0_230 ).
fof(c_0_1487,axiom,
! [X24,X6,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_Omonom(X8,X7,X6),c_Polynomial_Omonom(X8,X24,X6)) = c_Polynomial_Omonom(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24),X6) ),
c_0_231 ).
fof(c_0_1488,axiom,
! [X39,X24,X7,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24),X39) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),c_Polynomial_Osmult(X8,X24,X39)) ),
c_0_232 ).
fof(c_0_1489,axiom,
! [X40,X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X24)
=> ( c_Rings_Odvd__class_Odvd(X8,X27,X40)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X40)) ) ) ),
c_0_233 ).
fof(c_0_1490,axiom,
! [X17,X6,X8] :
( class_Power_Opower(X8)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X17),X6) = c_Groups_Oone__class_Oone(X8) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X17),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X17),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
c_0_234 ).
fof(c_0_1491,axiom,
! [X17,X6,X11,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),X17)) ) ) ),
c_0_235 ).
fof(c_0_1492,axiom,
! [X39,X24,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X7,c_Polynomial_OpCons(X8,X24,X39)) = c_Polynomial_OpCons(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Polynomial_Osmult(X8,X7,X39)) ),
c_0_236 ).
fof(c_0_1493,axiom,
! [X27,X24,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X27),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X27)) ) ),
c_0_237 ).
fof(c_0_1494,axiom,
! [X54,X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X54)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X54)) ) ),
c_0_238 ).
fof(c_0_1495,axiom,
! [X23,X69,X22,X70] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X70,X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,X23)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X69),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X23)) ) ),
c_0_239 ).
fof(c_0_1496,axiom,
! [X54,X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X54)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X17)) ) ),
c_0_240 ).
fof(c_0_1497,axiom,
! [X54,X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X48,X54)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X54)) ) ),
c_0_241 ).
fof(c_0_1498,axiom,
! [X35,X15,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X35),X35)) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X8)
& X35 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
c_0_242 ).
fof(c_0_1499,axiom,
! [X32,X24,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ominus__class_Ominus(X8,X24,X32)) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X32)) ),
c_0_243 ).
fof(c_0_1500,axiom,
! [X11,X9,X31,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),c_Groups_Ominus__class_Ominus(X8,X9,X11)) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X11)) ),
c_0_244 ).
fof(c_0_1501,axiom,
! [X23,X11,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),c_Groups_Oplus__class_Oplus(X8,X11,X23)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X23)) ),
c_0_245 ).
fof(c_0_1502,axiom,
! [X32,X24,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Oplus__class_Oplus(X8,X24,X32)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X32)) ),
c_0_246 ).
fof(c_0_1503,axiom,
! [X11,X9,X31,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),c_Groups_Oplus__class_Oplus(X8,X9,X11)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X11)) ),
c_0_247 ).
fof(c_0_1504,axiom,
! [X24,X6,X7] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24),X6))
=> ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X24) ) ),
c_0_248 ).
fof(c_0_1505,axiom,
! [X25,X26,X16] :
( X16 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X16),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X25),X16))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X26,X25) ) ),
c_0_249 ).
fof(c_0_1506,axiom,
! [X25,X26,X16] :
( X16 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X16),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X16))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25) ) ),
c_0_250 ).
fof(c_0_1507,axiom,
! [X24,X6,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X6))
=> ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24) ) ),
c_0_251 ).
fof(c_0_1508,axiom,
! [X16,X36,X50] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X16) ) ),
c_0_252 ).
fof(c_0_1509,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X6))
=> ( X48 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,X6) ) ),
c_0_253 ).
fof(c_0_1510,axiom,
! [X83,X36,X50] :
( X50 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X36,X83)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X83)) ) ),
c_0_254 ).
fof(c_0_1511,axiom,
! [X16,X50,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X50))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ) ),
c_0_255 ).
fof(c_0_1512,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ) ),
c_0_256 ).
fof(c_0_1513,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24) ) ) ),
c_0_257 ).
fof(c_0_1514,axiom,
! [X7,X24,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24) ) ) ),
c_0_258 ).
fof(c_0_1515,axiom,
! [X42,X44,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X44)),X42) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X44),X42)) ),
c_0_259 ).
fof(c_0_1516,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oab__semigroup__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)),X27) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ),
c_0_260 ).
fof(c_0_1517,axiom,
! [X41,X42,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X42)),X41) ),
c_0_261 ).
fof(c_0_1518,axiom,
! [X6,X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ),
c_0_262 ).
fof(c_0_1519,axiom,
! [X9,X6,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_Omonom(X8,X7,X6)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6)) ),
c_0_263 ).
fof(c_0_1520,axiom,
! [X14,X38,X27,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,c_Polynomial_Osmult(X8,X27,X38)) = c_Polynomial_OpCons(X8,X14,X38)
=> ( X14 = hAPP(c_Polynomial_Opoly(X8,X39),X27)
& X38 = c_Polynomial_Osynthetic__div(X8,X39,X27) ) ) ),
c_0_264 ).
fof(c_0_1521,axiom,
! [X27,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osynthetic__div(X8,c_Polynomial_OpCons(X8,X7,X39),X27) = c_Polynomial_OpCons(X8,hAPP(c_Polynomial_Opoly(X8,X39),X27),c_Polynomial_Osynthetic__div(X8,X39,X27)) ),
c_0_265 ).
fof(c_0_1522,axiom,
! [X38,X39,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X39)),X38) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)) ),
c_0_266 ).
fof(c_0_1523,axiom,
! [X6,X17,X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17)),X6) ),
c_0_267 ).
fof(c_0_1524,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X49)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X49)) ) ),
c_0_268 ).
fof(c_0_1525,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X48)) ) ),
c_0_269 ).
fof(c_0_1526,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X49)) ) ),
c_0_270 ).
fof(c_0_1527,axiom,
! [X11,X9,X23] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X23)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X9,X11)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X11)) ) ),
c_0_271 ).
fof(c_0_1528,axiom,
! [X39,X17] :
( ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X39),X17) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X39),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X39),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
c_0_272 ).
fof(c_0_1529,axiom,
! [X57,X50,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X50),X57)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X50)) ),
c_0_273 ).
fof(c_0_1530,axiom,
! [X50,X56,X57] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X50))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X50),X56) ),
c_0_274 ).
fof(c_0_1531,axiom,
! [X54,X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X54)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X54)) ) ),
c_0_275 ).
fof(c_0_1532,axiom,
! [X18,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X48),X49) ),
c_0_276 ).
fof(c_0_1533,axiom,
! [X18,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X49),X48) ),
c_0_277 ).
fof(c_0_1534,axiom,
! [X18,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X49),X48) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48)) ),
c_0_278 ).
fof(c_0_1535,axiom,
! [X18,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48),X18) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X18),X48) ),
c_0_279 ).
fof(c_0_1536,axiom,
! [X18,X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X18),X48) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X48),X18) ),
c_0_280 ).
fof(c_0_1537,axiom,
! [X38,X7,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),c_Polynomial_Osmult(X8,X7,X38)) = c_Polynomial_Osmult(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38)) ),
c_0_281 ).
fof(c_0_1538,axiom,
! [X9,X39,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_Osmult(X8,X7,X39)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(c_Polynomial_Opoly(X8,X39),X9)) ),
c_0_282 ).
fof(c_0_1539,axiom,
! [X25,X26,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X25),c_Groups_Ozero__class_Ozero(X8))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
& c_Orderings_Oord__class_Oless__eq(X8,X25,c_Groups_Ozero__class_Ozero(X8)) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X25) ) ) ) ),
c_0_283 ).
fof(c_0_1540,axiom,
! [X25,X26,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X25))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X25) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,X25,c_Groups_Ozero__class_Ozero(X8)) ) ) ) ),
c_0_284 ).
fof(c_0_1541,axiom,
! [X24,X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X24),c_Nat_OSuc(X6))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> X7 = X24 ) ) ) ),
c_0_285 ).
fof(c_0_1542,axiom,
! [X6,X17] :
( ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6) = X6 )
& ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6)) ) ),
c_0_286 ).
fof(c_0_1543,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X48,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X17,X6))
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X48,X6)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X48,X17) ) ),
c_0_287 ).
fof(c_0_1544,axiom,
! [X20,X21,X22] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X21,X20)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X20)),
c_0_288 ).
fof(c_0_1545,axiom,
! [X20,X21,X22] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X20)),
c_0_289 ).
fof(c_0_1546,axiom,
! [X6,X17,X48] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X6)),
c_0_290 ).
fof(c_0_1547,axiom,
! [X6,X17,X48] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X6)),
c_0_291 ).
fof(c_0_1548,axiom,
! [X9,X38,X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_Opcompose(X8,X39,X38)),X9) = hAPP(c_Polynomial_Opoly(X8,X39),hAPP(c_Polynomial_Opoly(X8,X38),X9)) ),
c_0_292 ).
fof(c_0_1549,axiom,
! [X17,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X17,X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Oone__class_Oone(X8))),X17) ),
c_0_293 ).
fof(c_0_1550,axiom,
! [X9,X14,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,c_RealVector_Onorm__class_Onorm(X8,X9))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Rings_Oinverse__class_Oinverse(X8,X9)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X14)) ) ) ),
c_0_294 ).
fof(c_0_1551,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6)),c_Groups_Oone__class_Oone(X8)) ) ) ),
c_0_295 ).
fof(c_0_1552,axiom,
! [X35,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X35),X35)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X35 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
c_0_296 ).
fof(c_0_1553,axiom,
! [X47] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X47))),
c_0_297 ).
fof(c_0_1554,axiom,
! [X6,X14,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X14)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X14,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X14),c_Nat_OSuc(X6)),X14) ) ) ),
c_0_298 ).
fof(c_0_1555,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_299 ).
fof(c_0_1556,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_300 ).
fof(c_0_1557,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)) ) ) ),
c_0_301 ).
fof(c_0_1558,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)) ) ) ),
c_0_302 ).
fof(c_0_1559,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_303 ).
fof(c_0_1560,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)) ) ) ),
c_0_304 ).
fof(c_0_1561,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X7,X24)) ) ) ),
c_0_305 ).
fof(c_0_1562,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_306 ).
fof(c_0_1563,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16))
<=> ( 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16) ) ),
c_0_307 ).
fof(c_0_1564,axiom,
! [X19,X20,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X20)),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X19)),
c_0_308 ).
fof(c_0_1565,axiom,
! [X23,X11,X9] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X11)),X23) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X23)),
c_0_309 ).
fof(c_0_1566,axiom,
! [X48,X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)),X48) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X48)),
c_0_310 ).
fof(c_0_1567,axiom,
! [X19,X20,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X20)),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),X19)),
c_0_311 ).
fof(c_0_1568,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
& c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8)) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24) ) )
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_312 ).
fof(c_0_1569,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__ring(X8)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8)) ) )
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ) ),
c_0_313 ).
fof(c_0_1570,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ) ) ),
c_0_314 ).
fof(c_0_1571,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_315 ).
fof(c_0_1572,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_316 ).
fof(c_0_1573,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_317 ).
fof(c_0_1574,axiom,
! [X24,X7,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ) ) ),
c_0_318 ).
fof(c_0_1575,axiom,
! [X6,X17,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X17)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X6)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),X6)) ) ) ),
c_0_319 ).
fof(c_0_1576,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ) ) ),
c_0_320 ).
fof(c_0_1577,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_321 ).
fof(c_0_1578,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_322 ).
fof(c_0_1579,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X24)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_323 ).
fof(c_0_1580,axiom,
! [X24,X7,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ) ) ),
c_0_324 ).
fof(c_0_1581,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X27)) ) ),
c_0_325 ).
fof(c_0_1582,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X27,X7),c_Groups_Oplus__class_Oplus(X8,X27,X24)) ) ),
c_0_326 ).
fof(c_0_1583,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X27,X7),c_Groups_Oplus__class_Oplus(X8,X27,X24)) ) ),
c_0_327 ).
fof(c_0_1584,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),c_Groups_Oplus__class_Oplus(X8,X24,X27)) ) ),
c_0_328 ).
fof(c_0_1585,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)) ) ),
c_0_329 ).
fof(c_0_1586,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16) ) ),
c_0_330 ).
fof(c_0_1587,plain,
! [X23,X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X23)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X11) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X23)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X9) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_1588,axiom,
~ ! [X73] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X73)
=> ~ ! [X55] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X55),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X55)),X73) ) ),
c_0_332 ).
fof(c_0_1589,axiom,
? [X73] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X73)
& ! [X55] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X55),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X55)),X73) ) ),
c_0_333 ).
fof(c_0_1590,axiom,
! [X55] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X55),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X55)),v_m____) ),
c_0_334 ).
fof(c_0_1591,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ? [X3] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X6) = X7
& ! [X62] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X62),X6) = X7 )
=> X62 = X3 ) ) ) ),
c_0_335 ).
fof(c_0_1592,axiom,
! [X47] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X47))),
c_0_336 ).
fof(c_0_1593,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ) ),
c_0_337 ).
fof(c_0_1594,axiom,
! [X6,X11,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X9,X11)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),X6)) ) ),
c_0_338 ).
fof(c_0_1595,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X27)
=> c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Oplus__class_Oplus(X8,X7,X27)) ) ) ),
c_0_339 ).
fof(c_0_1596,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X27)
=> c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Oplus__class_Oplus(X8,X7,X27)) ) ) ),
c_0_340 ).
fof(c_0_1597,axiom,
! [X7,X24,X27,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X27)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Oplus__class_Oplus(X8,X7,X27)) ) ) ),
c_0_341 ).
fof(c_0_1598,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X27)
=> c_Orderings_Oord__class_Oless__eq(X8,X24,c_Groups_Oplus__class_Oplus(X8,X7,X27)) ) ) ),
c_0_342 ).
fof(c_0_1599,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X27)
=> c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Oplus__class_Oplus(X8,X7,X27)) ) ) ),
c_0_343 ).
fof(c_0_1600,axiom,
! [X7,X6,X17,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ),
c_0_344 ).
fof(c_0_1601,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)) ) ),
c_0_345 ).
fof(c_0_1602,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X17)) ) ),
c_0_346 ).
fof(c_0_1603,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,X6)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X6,X17)
=> X17 = X6 ) ) ) ),
c_0_347 ).
fof(c_0_1604,axiom,
! [X9,X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X9)),
c_0_348 ).
fof(c_0_1605,axiom,
! [X23,X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X23,X9),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X23,X11)) ),
c_0_349 ).
fof(c_0_1606,axiom,
! [X54,X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X17)) ),
c_0_350 ).
fof(c_0_1607,axiom,
! [X54,X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X54),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X54)) ),
c_0_351 ).
fof(c_0_1608,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X48)) ),
c_0_352 ).
fof(c_0_1609,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X49)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X48),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X48)) ),
c_0_353 ).
fof(c_0_1610,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,X18),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,X49)) ),
c_0_354 ).
fof(c_0_1611,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X48)) ),
c_0_355 ).
fof(c_0_1612,axiom,
! [X23,X11,X9,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X9,X11)
=> ( c_Rings_Odvd__class_Odvd(X8,X9,X23)
=> c_Rings_Odvd__class_Odvd(X8,X9,c_Groups_Ominus__class_Ominus(X8,X11,X23)) ) ) ),
c_0_356 ).
fof(c_0_1613,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X24)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X27)
=> c_Rings_Odvd__class_Odvd(X8,X7,c_Groups_Oplus__class_Oplus(X8,X24,X27)) ) ) ),
c_0_357 ).
fof(c_0_1614,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X9,X11)) ) ),
c_0_358 ).
fof(c_0_1615,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X11)) ) ),
c_0_359 ).
fof(c_0_1616,axiom,
! [X80,X63,X26,X8] :
( class_Fields_Ofield(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X26,X63),X80)
<=> ( ( X26 = c_Groups_Ozero__class_Ozero(X8)
=> X80 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) )
& ( X26 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X63,X80) ) ) ) ),
c_0_360 ).
fof(c_0_1617,axiom,
! [X80,X63,X26,X8] :
( class_Fields_Ofield(X8)
=> ( X26 != c_Groups_Ozero__class_Ozero(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X63,c_Polynomial_Osmult(X8,X26,X80))
<=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X63,X80) ) ) ),
c_0_361 ).
fof(c_0_1618,axiom,
! [X38,X7,X39,X8] :
( class_Fields_Ofield(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,c_Polynomial_Osmult(X8,X7,X38))
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,X38) ) ) ),
c_0_362 ).
fof(c_0_1619,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X16)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X50) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X50)
<=> X36 = X16 ) ) ),
c_0_363 ).
fof(c_0_1620,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),X17) ) ),
c_0_364 ).
fof(c_0_1621,axiom,
! [X38,X39,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),X38)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,X38) ) ),
c_0_365 ).
fof(c_0_1622,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X26,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_366 ).
fof(c_0_1623,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X26,X26))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
c_0_367 ).
fof(c_0_1624,axiom,
! [X26,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X26,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_368 ).
fof(c_0_1625,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X26,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_369 ).
fof(c_0_1626,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X26,X26))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
c_0_370 ).
fof(c_0_1627,axiom,
! [X48,X6,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X17),X6),c_Nat_OSuc(X48)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),X48),
c_0_371 ).
fof(c_0_1628,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X27) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),X24) ),
c_0_372 ).
fof(c_0_1629,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Oab__semigroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X27) = c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oplus__class_Oplus(X8,X24,X27)) ),
c_0_373 ).
fof(c_0_1630,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X27) = c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oplus__class_Oplus(X8,X24,X27)) ),
c_0_374 ).
fof(c_0_1631,axiom,
! [X40,X27,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oplus__class_Oplus(X8,X27,X40)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X27),X40) ),
c_0_375 ).
fof(c_0_1632,axiom,
! [X40,X27,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oplus__class_Oplus(X8,X27,X40)) = c_Groups_Oplus__class_Oplus(X8,X27,c_Groups_Oplus__class_Oplus(X8,X7,X40)) ),
c_0_376 ).
fof(c_0_1633,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X35),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X35,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15)) ),
c_0_377 ).
fof(c_0_1634,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15),X35) ),
c_0_378 ).
fof(c_0_1635,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X35),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X35,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15)) ),
c_0_379 ).
fof(c_0_1636,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X35))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15),X35) ),
c_0_380 ).
fof(c_0_1637,axiom,
! [X24,X7,X27,X8] :
( class_Divides_Osemiring__div(X8)
=> ( X27 != c_Groups_Ozero__class_Ozero(X8)
=> c_Divides_Odiv__class_Odiv(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) = c_Divides_Odiv__class_Odiv(X8,X7,X24) ) ),
c_0_381 ).
fof(c_0_1638,axiom,
! [X24,X7,X27,X8] :
( class_Divides_Osemiring__div(X8)
=> ( ( X27 = c_Groups_Ozero__class_Ozero(X8)
=> c_Divides_Odiv__class_Odiv(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) = c_Groups_Ozero__class_Ozero(X8) )
& ( X27 != c_Groups_Ozero__class_Ozero(X8)
=> c_Divides_Odiv__class_Odiv(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X27),X24)) = c_Divides_Odiv__class_Odiv(X8,X7,X24) ) ) ),
c_0_382 ).
fof(c_0_1639,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24))
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,X24,X7) ) ) ),
c_0_383 ).
fof(c_0_1640,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,X24,X7) ) ) ),
c_0_384 ).
fof(c_0_1641,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,X25)
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ominus__class_Ominus(X8,X26,X25),c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_385 ).
fof(c_0_1642,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X26,X25)
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ominus__class_Ominus(X8,X26,X25),c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_386 ).
fof(c_0_1643,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,X24,X7) ) ) ),
c_0_387 ).
fof(c_0_1644,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Rings_Oinverse__class_Oinverse(X8,X24))
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,X24,X7) ) ) ),
c_0_388 ).
fof(c_0_1645,axiom,
! [X6,X24,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X7,c_Polynomial_Omonom(X8,X24,X6)) = c_Polynomial_Omonom(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),X6) ),
c_0_389 ).
fof(c_0_1646,axiom,
! [X39,X24,X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X7,c_Polynomial_Osmult(X8,X24,X39)) = c_Polynomial_Osmult(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),X39) ),
c_0_390 ).
fof(c_0_1647,axiom,
! [X6,X17,X48] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X17)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X6)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)) ) ),
c_0_391 ).
fof(c_0_1648,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9),X11)) ) ),
c_0_392 ).
fof(c_0_1649,axiom,
! [X16,X36] :
( 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),X36),X16))
<=> ( 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16) ) ),
c_0_393 ).
fof(c_0_1650,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X11)) ) ),
c_0_394 ).
fof(c_0_1651,axiom,
! [X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X17))),
c_0_395 ).
fof(c_0_1652,axiom,
! [X6,X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)),X7) ),
c_0_396 ).
fof(c_0_1653,axiom,
! [X38,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X38)),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Nat_OSuc(X38)) ),
c_0_397 ).
fof(c_0_1654,axiom,
! [X45,X33,X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X26,X25) = c_Groups_Ominus__class_Ominus(X8,X33,X45)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,X25)
<=> c_Orderings_Oord__class_Oless__eq(X8,X33,X45) ) ) ),
c_0_398 ).
fof(c_0_1655,axiom,
! [X45,X33,X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X26,X25) = c_Groups_Ominus__class_Ominus(X8,X33,X45)
=> ( c_Orderings_Oord__class_Oless(X8,X26,X25)
<=> c_Orderings_Oord__class_Oless(X8,X33,X45) ) ) ),
c_0_399 ).
fof(c_0_1656,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X36),X36)
<=> X16 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
c_0_400 ).
fof(c_0_1657,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16),X36)
<=> X16 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
c_0_401 ).
fof(c_0_1658,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X49)) ),
c_0_402 ).
fof(c_0_1659,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X48)) ),
c_0_403 ).
fof(c_0_1660,axiom,
! [X41,X42,X43,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),X41)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X43),X41)) ),
c_0_404 ).
fof(c_0_1661,axiom,
! [X19,X20,X21] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20),X19) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,X19)),
c_0_405 ).
fof(c_0_1662,axiom,
! [X23,X11,X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X23)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X23)),
c_0_406 ).
fof(c_0_1663,axiom,
! [X48,X49,X18] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X49),X48) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X48),X49),
c_0_407 ).
fof(c_0_1664,axiom,
! [X48,X49,X18] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X49),X48) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X48)),
c_0_408 ).
fof(c_0_1665,axiom,
! [X6,X17,X48] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X17),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),
c_0_409 ).
fof(c_0_1666,axiom,
! [X6,X48,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X48),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X48)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),
c_0_410 ).
fof(c_0_1667,axiom,
! [X23,X11,X9] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X23)),
c_0_411 ).
fof(c_0_1668,axiom,
! [X48,X6,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6),X48) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X48)),
c_0_412 ).
fof(c_0_1669,axiom,
! [X37,X46] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,X37)
| X46 = X37 ) ),
c_0_413 ).
fof(c_0_1670,axiom,
! [X37,X46] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X46,X37) ),
c_0_414 ).
fof(c_0_1671,axiom,
! [X37,X46] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)),X37)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,X37) ),
c_0_415 ).
fof(c_0_1672,axiom,
! [X37,X46] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X46,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X37,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,X37) ),
c_0_416 ).
fof(c_0_1673,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),X27)
=> c_Rings_Odvd__class_Odvd(X8,X7,X27) ) ),
c_0_417 ).
fof(c_0_1674,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),X27)
=> c_Rings_Odvd__class_Odvd(X8,X24,X27) ) ),
c_0_418 ).
fof(c_0_1675,plain,
! [X23,X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X23)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X23)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X9) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_1676,plain,
! [X23,X11,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X23)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X11) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X23)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X9) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_1677,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X35)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X15,X35),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
c_0_421 ).
fof(c_0_1678,axiom,
! [X64,X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X64)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X50,X64),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
c_0_422 ).
fof(c_0_1679,axiom,
! [X36,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X36))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ),
c_0_423 ).
fof(c_0_1680,axiom,
! [X6,X17,X54,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X48,X54)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X54) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ) ),
c_0_424 ).
fof(c_0_1681,axiom,
! [X16,X50] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X50,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X50))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X50,X16) ),
c_0_425 ).
fof(c_0_1682,axiom,
! [X6,X48,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X48),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X6) ),
c_0_426 ).
fof(c_0_1683,axiom,
! [X6,X48,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X48),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ),
c_0_427 ).
fof(c_0_1684,plain,
! [X6,X48,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X48),X6)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X6) ) ),
inference(fof_simplification,[status(thm)],[c_0_428]) ).
fof(c_0_1685,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X49),X48)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X48) ),
c_0_429 ).
fof(c_0_1686,axiom,
! [X35,X15,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X15)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X35)
=> ( c_Groups_Oplus__class_Oplus(X8,X15,X35) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X8)
& X35 = c_Groups_Ozero__class_Ozero(X8) ) ) ) ) ),
c_0_430 ).
fof(c_0_1687,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X24),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
c_0_431 ).
fof(c_0_1688,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X24),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
c_0_432 ).
fof(c_0_1689,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X24),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
c_0_433 ).
fof(c_0_1690,axiom,
! [X24,X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( c_Orderings_Oord__class_Oless(X8,X24,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X24),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
c_0_434 ).
fof(c_0_1691,plain,
! [X1,X2,X8,X77] :
( class_Orderings_Oord(X77)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X8,X77),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X77),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X77),X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_435]) ).
fof(c_0_1692,axiom,
! [X16,X15] :
( 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),X15),X16))
<=> ( X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) ) ),
c_0_436 ).
fof(c_0_1693,axiom,
! [X16,X15] :
( 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),X15),X16))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
| X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_437 ).
fof(c_0_1694,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
c_0_438 ).
fof(c_0_1695,axiom,
! [X15,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X15))
<=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X15)
& c_Orderings_Oord__class_Oless__eq(X8,X15,c_Groups_Oone__class_Oone(X8)) ) ) ),
c_0_439 ).
fof(c_0_1696,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
c_0_440 ).
fof(c_0_1697,axiom,
! [X15,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X15))
<=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X15)
& c_Orderings_Oord__class_Oless(X8,X15,c_Groups_Oone__class_Oone(X8)) ) ) ),
c_0_441 ).
fof(c_0_1698,axiom,
! [X35,X15,X8] :
( class_Rings_Oidom(X8)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X15),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X35),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( X15 = X35
| X15 = c_Groups_Ouminus__class_Ouminus(X8,X35) ) ) ),
c_0_442 ).
fof(c_0_1699,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6))) ) ),
c_0_443 ).
fof(c_0_1700,axiom,
! [X35,X15,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X8),X15,X35)
<=> ( X15 = X35
| c_Polynomial_Opos__poly(X8,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X35,X15)) ) ) ),
c_0_444 ).
fof(c_0_1701,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ? [X61] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X61),X6) = X7 ) ) ),
c_0_445 ).
fof(c_0_1702,axiom,
! [X7,X38,X39,X8] :
( class_Fields_Ofield(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,X38)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39),X38) ) ) ),
c_0_446 ).
fof(c_0_1703,plain,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11) ) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_1704,plain,
! [X24,X7] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X7) )
=> ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X7)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24) ) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_1705,plain,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11) ) ),
inference(fof_simplification,[status(thm)],[c_0_449]) ).
fof(c_0_1706,plain,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11) ) ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_1707,axiom,
! [X63,X26,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Polynomial_Opos__poly(X8,c_Polynomial_OpCons(X8,X26,X63))
<=> ( c_Polynomial_Opos__poly(X8,X63)
| ( X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
& c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ) ) ),
c_0_451 ).
fof(c_0_1708,plain,
! [X63] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X63),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))
=> ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X63))
=> ? [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X63),X55) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(fof_simplification,[status(thm)],[c_0_452]) ).
fof(c_0_1709,axiom,
! [X7,X38,X39,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,X38)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X39,c_Polynomial_Osmult(X8,X7,X38)) ) ),
c_0_453 ).
fof(c_0_1710,axiom,
! [X16,X36,X26,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X26)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X26),X36) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X26),X16)
<=> X36 = X16 ) ) ),
c_0_454 ).
fof(c_0_1711,axiom,
! [X17,X18] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))),
c_0_455 ).
fof(c_0_1712,axiom,
! [X17,X18] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X18))),
c_0_456 ).
fof(c_0_1713,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ),
c_0_457 ).
fof(c_0_1714,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ),
c_0_458 ).
fof(c_0_1715,axiom,
! [X6,X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ) ),
c_0_459 ).
fof(c_0_1716,axiom,
! [X15,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X15),c_Groups_Oone__class_Oone(X8))
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,c_Groups_Ozero__class_Ozero(X8))
| c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X15) ) ) ),
c_0_460 ).
fof(c_0_1717,axiom,
! [X15,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X15),c_Groups_Oone__class_Oone(X8))
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,c_Groups_Ozero__class_Ozero(X8))
| c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),X15) ) ) ),
c_0_461 ).
fof(c_0_1718,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X24)),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
c_0_462 ).
fof(c_0_1719,plain,
! [X7,X8] :
( class_Rings_Olinordered__ring(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7),c_Groups_Ozero__class_Ozero(X8)) ),
inference(fof_simplification,[status(thm)],[c_0_463]) ).
fof(c_0_1720,axiom,
! [X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23),X23) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_464 ).
fof(c_0_1721,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X9,X11)) ) ),
c_0_465 ).
fof(c_0_1722,axiom,
! [X6,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X6)) ),
c_0_466 ).
fof(c_0_1723,axiom,
! [X18,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Nat_OSuc(X18)),X6) ),
c_0_467 ).
fof(c_0_1724,axiom,
! [X26,X59,X60,X8] : hAPP(hAPP(c_Power_Opower_Opower(X8,X60,X59),X26),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X60,
c_0_468 ).
fof(c_0_1725,plain,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X6,X17) ) ),
inference(fof_simplification,[status(thm)],[c_0_469]) ).
fof(c_0_1726,plain,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X6)
=> ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X6,X17) ) ),
inference(fof_simplification,[status(thm)],[c_0_470]) ).
fof(c_0_1727,axiom,
! [X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23)) ),
c_0_471 ).
fof(c_0_1728,axiom,
! [X24,X7,X8] :
( class_Fields_Ofield__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),c_Rings_Oinverse__class_Oinverse(X8,X24)) ),
c_0_472 ).
fof(c_0_1729,axiom,
! [X9,X6,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
| X9 = c_Groups_Oone__class_Oone(X8) )
=> c_Rings_Odvd__class_Odvd(X8,X9,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6)) ) ),
c_0_473 ).
fof(c_0_1730,axiom,
! [X39,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X7,X39)) = c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X39)) ),
c_0_474 ).
fof(c_0_1731,axiom,
! [X39,X7,X77] :
( class_Groups_Oab__group__add(X77)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X77),c_Polynomial_OpCons(X77,X7,X39)) = c_Polynomial_OpCons(X77,c_Groups_Ouminus__class_Ouminus(X77,X7),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X77),X39)) ),
c_0_475 ).
fof(c_0_1732,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X17),X6) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)) ),
c_0_476 ).
fof(c_0_1733,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X24)
=> c_Rings_Odvd__class_Odvd(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ),
c_0_477 ).
fof(c_0_1734,axiom,
! [X24,X27,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X27)
=> c_Rings_Odvd__class_Odvd(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X27)) ) ),
c_0_478 ).
fof(c_0_1735,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24)) = c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X24,X7)) ),
c_0_479 ).
fof(c_0_1736,axiom,
! [X11,X9,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9)),c_RealVector_Onorm__class_Onorm(X8,X11)) ),
c_0_480 ).
fof(c_0_1737,axiom,
! [X23,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,c_Groups_Oone__class_Oone(tc_Int_Oint)),X23) ),
c_0_481 ).
fof(c_0_1738,plain,
! [X49,X18] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X49),X18),
inference(fof_simplification,[status(thm)],[c_0_482]) ).
fof(c_0_1739,plain,
! [X18,X49] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X18),X18),
inference(fof_simplification,[status(thm)],[c_0_483]) ).
fof(c_0_1740,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
<=> ? [X71] : X16 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X71)) ),
c_0_484 ).
fof(c_0_1741,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)) = X17 ),
c_0_485 ).
fof(c_0_1742,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),X6) = X17 ),
c_0_486 ).
fof(c_0_1743,axiom,
! [X6,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X6)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X18)) = X18 ),
c_0_487 ).
fof(c_0_1744,axiom,
! [X15,X1,X2,X8,X77] :
( class_Orderings_Oord(X77)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X77),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X77,hAPP(X2,X15),hAPP(X1,X15)) ) ),
c_0_488 ).
fof(c_0_1745,axiom,
! [X15,X1,X2,X8,X77] :
( class_Orderings_Oord(X77)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X77),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X77,hAPP(X2,X15),hAPP(X1,X15)) ) ),
c_0_489 ).
fof(c_0_1746,axiom,
! [X17,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X17)) ),
c_0_490 ).
fof(c_0_1747,axiom,
! [X17,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X49)) ),
c_0_491 ).
fof(c_0_1748,axiom,
! [X11,X23,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) ),
c_0_492 ).
fof(c_0_1749,axiom,
! [X23,X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) ),
c_0_493 ).
fof(c_0_1750,axiom,
! [X23,X11,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X11)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) ),
c_0_494 ).
fof(c_0_1751,axiom,
! [X6,X48,X49] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X49,X48)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X6),X48) ),
c_0_495 ).
fof(c_0_1752,axiom,
! [X11,X23,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X23)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X23)) ),
c_0_496 ).
fof(c_0_1753,axiom,
! [X17,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X17)) ),
c_0_497 ).
fof(c_0_1754,axiom,
! [X17,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X49)) ),
c_0_498 ).
fof(c_0_1755,plain,
! [X15] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X15))
<=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[c_0_499]) ).
fof(c_0_1756,axiom,
! [X16,X36,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16)
<=> X36 = X16 ) ),
c_0_500 ).
fof(c_0_1757,axiom,
! [X6,X7,X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_Omonom(X8,X7,c_Nat_OSuc(X6)) = c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),c_Polynomial_Omonom(X8,X7,X6)) ),
c_0_501 ).
fof(c_0_1758,axiom,
! [X6,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X6)) ),
c_0_502 ).
fof(c_0_1759,axiom,
! [X23,X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X23)
=> c_Orderings_Oord__class_Oless(X8,X9,X23) ) ) ),
c_0_503 ).
fof(c_0_1760,axiom,
! [X23,X9,X11,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X11,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X11)
=> c_Orderings_Oord__class_Oless(X8,X23,X9) ) ) ),
c_0_504 ).
fof(c_0_1761,axiom,
! [X23,X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless(X8,X11,X23)
=> c_Orderings_Oord__class_Oless(X8,X9,X23) ) ) ),
c_0_505 ).
fof(c_0_1762,axiom,
! [X23,X9,X11,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> ( c_Orderings_Oord__class_Oless(X8,X23,X11)
=> c_Orderings_Oord__class_Oless(X8,X23,X9) ) ) ),
c_0_506 ).
fof(c_0_1763,axiom,
! [X23,X9,X11,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X11,X9)
=> ( c_Orderings_Oord__class_Oless(X8,X23,X11)
=> c_Orderings_Oord__class_Oless(X8,X23,X9) ) ) ),
c_0_507 ).
fof(c_0_1764,axiom,
! [X23,X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless(X8,X11,X23)
=> c_Orderings_Oord__class_Oless(X8,X9,X23) ) ) ),
c_0_508 ).
fof(c_0_1765,axiom,
! [X23,X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X23)
=> c_Orderings_Oord__class_Oless__eq(X8,X9,X23) ) ) ),
c_0_509 ).
fof(c_0_1766,axiom,
! [X23,X9,X11,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X11)
=> c_Orderings_Oord__class_Oless__eq(X8,X23,X9) ) ) ),
c_0_510 ).
fof(c_0_1767,axiom,
! [X27,X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X24)
=> ( c_Rings_Odvd__class_Odvd(X8,X24,X27)
=> c_Rings_Odvd__class_Odvd(X8,X7,X27) ) ) ),
c_0_511 ).
fof(c_0_1768,axiom,
! [X24,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Groups_Ouminus__class_Ouminus(X8,X24)) = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24)) ),
c_0_512 ).
fof(c_0_1769,axiom,
! [X24,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Groups_Ouminus__class_Ouminus(X8,X24)) ),
c_0_513 ).
fof(c_0_1770,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X24),c_Groups_Ouminus__class_Ouminus(X8,X7)) ),
c_0_514 ).
fof(c_0_1771,axiom,
! [X6,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),X6) ) ),
c_0_515 ).
fof(c_0_1772,axiom,
! [X26,X25,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,X25) ) ),
c_0_516 ).
fof(c_0_1773,axiom,
! [X26,X25,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless(X8,X26,X25) ) ),
c_0_517 ).
fof(c_0_1774,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ) ),
c_0_518 ).
fof(c_0_1775,axiom,
! [X24,X7,X8] :
( class_Rings_Oring(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),X24) ),
c_0_519 ).
fof(c_0_1776,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),X24) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ),
c_0_520 ).
fof(c_0_1777,axiom,
! [X11,X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X9)),X11) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),X11)) ),
c_0_521 ).
fof(c_0_1778,axiom,
! [X6,X7,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),X6) ),
c_0_522 ).
fof(c_0_1779,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X49,X48)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X18),X48) ) ),
c_0_523 ).
fof(c_0_1780,axiom,
! [X39,X7,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,X7,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X39)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39)) ),
c_0_524 ).
fof(c_0_1781,axiom,
! [X6,X48] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X48,X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X6) ) ),
c_0_525 ).
fof(c_0_1782,axiom,
! [X6,X23] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X23,X6)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X6) ) ),
c_0_526 ).
fof(c_0_1783,plain,
! [X27,X24,X7] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X7) )
=> ( X24 = X27
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X27)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X27,X7) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_527]) ).
fof(c_0_1784,plain,
! [X27,X24,X7] :
( X7 = X24
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X27)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X27,X24) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X27)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X27,X7) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_528]) ).
fof(c_0_1785,axiom,
! [X50,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X57) = X50
<=> X56 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X57) ) ),
c_0_529 ).
fof(c_0_1786,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X6 ),
c_0_530 ).
fof(c_0_1787,axiom,
! [X6,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Nat_OSuc(X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6),
c_0_531 ).
fof(c_0_1788,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
c_0_532 ).
fof(c_0_1789,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),X24)) = X24 ),
c_0_533 ).
fof(c_0_1790,axiom,
! [X6,X9,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9)),X6) ),
c_0_534 ).
fof(c_0_1791,axiom,
! [X23,X11,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X23)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X23) ) ),
c_0_535 ).
fof(c_0_1792,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X49)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,X48)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X48) ) ),
c_0_536 ).
fof(c_0_1793,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X49)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X49,X48)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X48) ) ),
c_0_537 ).
fof(c_0_1794,axiom,
! [X48,X49,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X49)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49,X48)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X48) ) ),
c_0_538 ).
fof(c_0_1795,axiom,
! [X6,X7,X8] :
( class_Power_Opower(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Nat_OSuc(X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ),
c_0_539 ).
fof(c_0_1796,axiom,
! [X38,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X38)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Nat_OSuc(X38)) ),
c_0_540 ).
fof(c_0_1797,axiom,
! [X38,X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Nat_OSuc(X38)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),X38)) ),
c_0_541 ).
fof(c_0_1798,axiom,
! [X38,X39,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Polynomial_Opos__poly(X8,X39)
=> ( c_Polynomial_Opos__poly(X8,X38)
=> c_Polynomial_Opos__poly(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),X38)) ) ) ),
c_0_542 ).
fof(c_0_1799,axiom,
! [X9,X39,X8] :
( class_Rings_Ocomm__ring(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X39)),X9) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(c_Polynomial_Opoly(X8,X39),X9)) ),
c_0_543 ).
fof(c_0_1800,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X25)
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),X26) ) ),
c_0_544 ).
fof(c_0_1801,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ouminus__class_Ouminus(X8,X25))
<=> c_Orderings_Oord__class_Oless__eq(X8,X25,c_Groups_Ouminus__class_Ouminus(X8,X26)) ) ),
c_0_545 ).
fof(c_0_1802,axiom,
! [X22,X23] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X22)),
c_0_546 ).
fof(c_0_1803,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ouminus__class_Ouminus(X8,X25))
<=> c_Orderings_Oord__class_Oless(X8,X25,c_Groups_Ouminus__class_Ouminus(X8,X26)) ) ),
c_0_547 ).
fof(c_0_1804,axiom,
! [X25,X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X25)
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),X26) ) ),
c_0_548 ).
fof(c_0_1805,axiom,
! [X6,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_Omonom(X8,X7,X6)) = c_Polynomial_Omonom(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),X6) ),
c_0_549 ).
fof(c_0_1806,axiom,
! [X39,X7,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),X39) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X7,X39)) ),
c_0_550 ).
fof(c_0_1807,plain,
! [X6,X17] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6)) = X17 ),
inference(fof_simplification,[status(thm)],[c_0_551]) ).
fof(c_0_1808,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X7))
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7) ) ) ),
c_0_552 ).
fof(c_0_1809,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Groups_Ozero__class_Ozero(X8))
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8)) ) ) ),
c_0_553 ).
fof(c_0_1810,axiom,
! [X26,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_554 ).
fof(c_0_1811,axiom,
! [X26,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X26))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
c_0_555 ).
fof(c_0_1812,axiom,
! [X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_556 ).
fof(c_0_1813,axiom,
! [X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
c_0_557 ).
fof(c_0_1814,axiom,
! [X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_558 ).
fof(c_0_1815,axiom,
! [X26,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
c_0_559 ).
fof(c_0_1816,axiom,
! [X26,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X26))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
c_0_560 ).
fof(c_0_1817,axiom,
! [X26,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X26),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_561 ).
fof(c_0_1818,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X6 ),
c_0_562 ).
fof(c_0_1819,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> X6 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
c_0_563 ).
fof(c_0_1820,plain,
! [X35,X15,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
& ~ c_Orderings_Oord__class_Oless__eq(X8,X35,X15) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_564]) ).
fof(c_0_1821,axiom,
! [X24,X7,X8] :
( class_Rings_Oring(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ouminus__class_Ouminus(X8,X24)) ),
c_0_565 ).
fof(c_0_1822,axiom,
! [X24,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ouminus__class_Ouminus(X8,X24)) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ),
c_0_566 ).
fof(c_0_1823,axiom,
! [X9,X31,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),c_Groups_Ouminus__class_Ouminus(X8,X9)) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X9)) ),
c_0_567 ).
fof(c_0_1824,axiom,
! [X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X17)),X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)),
c_0_568 ).
fof(c_0_1825,axiom,
! [X24,X7,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X24),c_Groups_Ouminus__class_Ouminus(X8,X7)) ) ),
c_0_569 ).
fof(c_0_1826,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Oone__class_Oone(X8))) ),
c_0_570 ).
fof(c_0_1827,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),c_Groups_Oplus__class_Oplus(X8,X7,X24)) = X24 ),
c_0_571 ).
fof(c_0_1828,axiom,
! [X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),c_Nat_OSuc(X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)),
c_0_572 ).
fof(c_0_1829,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_573 ).
fof(c_0_1830,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X26)
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
c_0_574 ).
fof(c_0_1831,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X26)
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26) ) ),
c_0_575 ).
fof(c_0_1832,axiom,
! [X26,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ouminus__class_Ouminus(X8,X26))
<=> c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_576 ).
fof(c_0_1833,axiom,
! [X22,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23)),X22) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X22)),
c_0_577 ).
fof(c_0_1834,plain,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11) ),
inference(fof_simplification,[status(thm)],[c_0_578]) ).
fof(c_0_1835,plain,
! [X35,X15] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X15) )
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
& X15 != X35 ) ),
inference(fof_simplification,[status(thm)],[c_0_579]) ).
fof(c_0_1836,plain,
! [X35,X15] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
<=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X15) )
| X15 = X35 ) ),
inference(fof_simplification,[status(thm)],[c_0_580]) ).
fof(c_0_1837,axiom,
! [X7,X39,X27,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Polynomial_Osmult(X8,X27,X39) = c_Polynomial_OpCons(X8,X7,X39)
=> X39 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
c_0_581 ).
fof(c_0_1838,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ),
c_0_582 ).
fof(c_0_1839,axiom,
! [X7,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X7),c_Groups_Ozero__class_Ozero(X8)) ) ),
c_0_583 ).
fof(c_0_1840,axiom,
! [X24,X7,X8] :
( class_Rings_Oring(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ouminus__class_Ouminus(X8,X24)) ),
c_0_584 ).
fof(c_0_1841,axiom,
! [X24,X7,X8] :
( class_Rings_Oring(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),c_Groups_Ouminus__class_Ouminus(X8,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24) ),
c_0_585 ).
fof(c_0_1842,axiom,
! [X35,X15,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,c_Groups_Ouminus__class_Ouminus(X8,X15),X35)
<=> c_Rings_Odvd__class_Odvd(X8,X15,X35) ) ),
c_0_586 ).
fof(c_0_1843,axiom,
! [X35,X15,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X15,c_Groups_Ouminus__class_Ouminus(X8,X35))
<=> c_Rings_Odvd__class_Odvd(X8,X15,X35) ) ),
c_0_587 ).
fof(c_0_1844,axiom,
! [X25,X26,X8] :
( class_Rings_Oidom(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X25),X25)
<=> ( X26 = X25
| X26 = c_Groups_Ouminus__class_Ouminus(X8,X25) ) ) ),
c_0_588 ).
fof(c_0_1845,axiom,
! [X38,X39,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Polynomial_Opos__poly(X8,X39)
=> ( c_Polynomial_Opos__poly(X8,X38)
=> c_Polynomial_Opos__poly(X8,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,X38)) ) ) ),
c_0_589 ).
fof(c_0_1846,axiom,
! [X16,X36,X50] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X50)),X16)
<=> X36 = X16 ),
c_0_590 ).
fof(c_0_1847,axiom,
! [X45,X33,X25,X26,X8] :
( class_Groups_Oab__group__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X26,X25) = c_Groups_Ominus__class_Ominus(X8,X33,X45)
=> ( X26 = X25
<=> X33 = X45 ) ) ),
c_0_591 ).
fof(c_0_1848,plain,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> X15 = X35 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_592]) ).
fof(c_0_1849,axiom,
! [X24,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24)) = c_Groups_Ominus__class_Ominus(X8,X24,X7) ),
c_0_593 ).
fof(c_0_1850,axiom,
! [X35,X15,X8] :
( class_Orderings_Oorder(X8)
=> ( X15 = X35
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
& c_Orderings_Oord__class_Oless__eq(X8,X35,X15) ) ) ),
c_0_594 ).
fof(c_0_1851,axiom,
! [X15,X35,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X35,X15)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
<=> X15 = X35 ) ) ),
c_0_595 ).
fof(c_0_1852,axiom,
! [X11,X9,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> X9 = X11 ) ) ),
c_0_596 ).
fof(c_0_1853,axiom,
! [X9,X11,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> X9 = X11 ) ) ),
c_0_597 ).
fof(c_0_1854,axiom,
! [X7,X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless(X8,X7,c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oone__class_Oone(X8))) ),
c_0_598 ).
fof(c_0_1855,axiom,
! [X25,X16,X26,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_Omonom(X8,X26,X16) = c_Polynomial_Omonom(X8,X25,X16)
<=> X26 = X25 ) ),
c_0_599 ).
fof(c_0_1856,axiom,
! [X80,X25,X63,X26,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_OpCons(X8,X26,X63) = c_Polynomial_OpCons(X8,X25,X80)
<=> ( X26 = X25
& X63 = X80 ) ) ),
c_0_600 ).
fof(c_0_1857,axiom,
! [X27,X7,X24,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X24,X7) = c_Groups_Oplus__class_Oplus(X8,X27,X7)
=> X24 = X27 ) ),
c_0_601 ).
fof(c_0_1858,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Ocancel__ab__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X7,X24) = c_Groups_Oplus__class_Oplus(X8,X7,X27)
=> X24 = X27 ) ),
c_0_602 ).
fof(c_0_1859,axiom,
! [X27,X24,X7,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X7,X24) = c_Groups_Oplus__class_Oplus(X8,X7,X27)
=> X24 = X27 ) ),
c_0_603 ).
fof(c_0_1860,axiom,
! [X33,X26,X25,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X25,X26) = c_Groups_Oplus__class_Oplus(X8,X33,X26)
<=> X25 = X33 ) ),
c_0_604 ).
fof(c_0_1861,axiom,
! [X33,X25,X26,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X26,X25) = c_Groups_Oplus__class_Oplus(X8,X26,X33)
<=> X25 = X33 ) ),
c_0_605 ).
fof(c_0_1862,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
c_0_606 ).
fof(c_0_1863,plain,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> c_Orderings_Oord__class_Oless__eq(X8,X35,X15) ) ),
inference(fof_simplification,[status(thm)],[c_0_607]) ).
fof(c_0_1864,plain,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
<=> c_Orderings_Oord__class_Oless(X8,X35,X15) ) ),
inference(fof_simplification,[status(thm)],[c_0_608]) ).
fof(c_0_1865,plain,
! [X9,X11,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> ~ c_Orderings_Oord__class_Oless(X8,X9,X11) ) ),
inference(fof_simplification,[status(thm)],[c_0_609]) ).
fof(c_0_1866,plain,
! [X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ~ c_Orderings_Oord__class_Oless(X8,X11,X9) ) ),
inference(fof_simplification,[status(thm)],[c_0_610]) ).
fof(c_0_1867,plain,
! [X7,X24,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X7)
=> ~ c_Orderings_Oord__class_Oless(X8,X7,X24) ) ),
inference(fof_simplification,[status(thm)],[c_0_611]) ).
fof(c_0_1868,plain,
! [X24,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ~ c_Orderings_Oord__class_Oless(X8,X24,X7) ) ),
inference(fof_simplification,[status(thm)],[c_0_612]) ).
fof(c_0_1869,plain,
! [X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ~ c_Orderings_Oord__class_Oless(X8,X11,X9) ) ),
inference(fof_simplification,[status(thm)],[c_0_613]) ).
fof(c_0_1870,plain,
! [X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ~ c_Orderings_Oord__class_Oless(X8,X11,X9) ) ),
inference(fof_simplification,[status(thm)],[c_0_614]) ).
fof(c_0_1871,plain,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> ( c_Orderings_Oord__class_Oless(X8,X35,X15)
| X15 = X35 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_615]) ).
fof(c_0_1872,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(X36))
<=> X16 = X36 ) ),
c_0_616 ).
fof(c_0_1873,axiom,
! [X26,X63,X8] :
( class_Rings_Oidom(X8)
=> ( hAPP(c_Polynomial_Opoly(X8,X63),X26) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
| c_Polynomial_Oorder(X8,X26,X63) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
c_0_617 ).
fof(c_0_1874,plain,
! [X16,X36] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(X36)) ),
inference(fof_simplification,[status(thm)],[c_0_618]) ).
fof(c_0_1875,plain,
! [X16,X36] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X16),X36) ),
inference(fof_simplification,[status(thm)],[c_0_619]) ).
fof(c_0_1876,axiom,
! [X6,X17] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X17 = X6 ) ),
c_0_620 ).
fof(c_0_1877,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Nat_OSuc(X16))
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X72] :
( X36 = c_Nat_OSuc(X72)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X72,X16) ) ) ),
c_0_621 ).
fof(c_0_1878,axiom,
! [X83,X45] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X45,X83)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X45),X83) ),
c_0_622 ).
fof(c_0_1879,axiom,
! [X83,X45] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X45,X83)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X45,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X83)) ),
c_0_623 ).
fof(c_0_1880,axiom,
! [X24,X7] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X7,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X7)),c_Complex_Oexpi(X24)),
c_0_624 ).
fof(c_0_1881,axiom,
! [X7,X24,X8] :
( class_Divides_Osemiring__div(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Divides_Odiv__class_Odiv(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7),X24) = X7 ) ),
c_0_625 ).
fof(c_0_1882,axiom,
! [X7,X24,X8] :
( class_Divides_Osemiring__div(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> c_Divides_Odiv__class_Odiv(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24),X24) = X7 ) ),
c_0_626 ).
fof(c_0_1883,axiom,
! [X7,X8] :
( class_Rings_Olinordered__ring(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7)) ),
c_0_627 ).
fof(c_0_1884,axiom,
! [X11,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9)
=> X9 = X11 ) ),
c_0_628 ).
fof(c_0_1885,axiom,
! [X6,X17] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X6)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X6,X17)
=> X17 = X6 ) ),
c_0_629 ).
fof(c_0_1886,plain,
! [X24,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
=> ( X7 != X24
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X7) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_630]) ).
fof(c_0_1887,plain,
! [X11,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
| X9 = X11 ) ),
inference(fof_simplification,[status(thm)],[c_0_631]) ).
fof(c_0_1888,axiom,
! [X15,X35] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X15)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
<=> X15 = X35 ) ),
c_0_632 ).
fof(c_0_1889,plain,
! [X24,X7] :
( X7 != X24
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X7) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_633]) ).
fof(c_0_1890,axiom,
! [X35,X15] :
( X15 = X35
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X35)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X15) ) ),
c_0_634 ).
fof(c_0_1891,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X23)
=> X23 = X22 ) ),
c_0_635 ).
fof(c_0_1892,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X23)
=> X23 = X22 ) ),
c_0_636 ).
fof(c_0_1893,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17)
=> X17 = X6 ) ),
c_0_637 ).
fof(c_0_1894,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X7,X24),X24) = X7 ),
c_0_638 ).
fof(c_0_1895,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Oplus__class_Oplus(X8,X7,X24),X24) = X7 ),
c_0_639 ).
fof(c_0_1896,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X16) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X16 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
c_0_640 ).
fof(c_0_1897,axiom,
! [X16,X36,X50] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X16)
<=> X36 = X16 ),
c_0_641 ).
fof(c_0_1898,axiom,
! [X16,X50,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X50) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X50)
<=> X36 = X16 ),
c_0_642 ).
fof(c_0_1899,axiom,
~ ! [X76] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X76) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
=> ~ ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X76),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)) ),
c_0_643 ).
fof(c_0_1900,axiom,
? [X76] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X76) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X76),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)) ),
c_0_644 ).
fof(c_0_1901,axiom,
! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)),
c_0_645 ).
fof(c_0_1902,axiom,
! [X6,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Nat_OSuc(X6)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)),
c_0_646 ).
fof(c_0_1903,axiom,
! [X6,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X17),X6) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)),
c_0_647 ).
fof(c_0_1904,axiom,
! [X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24)) ),
c_0_648 ).
fof(c_0_1905,axiom,
! [X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7)) ),
c_0_649 ).
fof(c_0_1906,axiom,
! [X64,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X64)
<=> ? [X81] : X64 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X81) ),
c_0_650 ).
fof(c_0_1907,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
<=> ? [X71] : X16 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X71) ),
c_0_651 ).
fof(c_0_1908,axiom,
! [X6,X17] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),c_Nat_OSuc(X17)),
c_0_652 ).
fof(c_0_1909,axiom,
! [X17,X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X17)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_653 ).
fof(c_0_1910,axiom,
! [X6,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6),X6) = X17,
c_0_654 ).
fof(c_0_1911,axiom,
! [X17,X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X17),X6) = X17,
c_0_655 ).
fof(c_0_1912,axiom,
! [X6,X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),X17),
c_0_656 ).
fof(c_0_1913,axiom,
! [X17,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6)),
c_0_657 ).
fof(c_0_1914,axiom,
! [X17,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X17)),
c_0_658 ).
fof(c_0_1915,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X36),c_Nat_OSuc(X16))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ),
c_0_659 ).
fof(c_0_1916,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),c_Nat_OSuc(X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ),
c_0_660 ).
fof(c_0_1917,axiom,
! [X36,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X16),c_Nat_OSuc(X36))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X36) ),
c_0_661 ).
fof(c_0_1918,plain,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Nat_OSuc(X6))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> X17 = c_Nat_OSuc(X6) ) ),
inference(fof_simplification,[status(thm)],[c_0_662]) ).
fof(c_0_1919,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,c_Nat_OSuc(X16))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
| X36 = c_Nat_OSuc(X16) ) ),
c_0_663 ).
fof(c_0_1920,axiom,
! [X27,X7,X24,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X24,X7)
=> ( X24 = X27
=> c_Orderings_Oord__class_Oless(X8,X27,X7) ) ) ),
c_0_664 ).
fof(c_0_1921,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oord(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X24)
=> ( X24 = X27
=> c_Orderings_Oord__class_Oless(X8,X7,X27) ) ) ),
c_0_665 ).
fof(c_0_1922,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( X7 = X24
=> ( c_Orderings_Oord__class_Oless(X8,X27,X24)
=> c_Orderings_Oord__class_Oless(X8,X27,X7) ) ) ),
c_0_666 ).
fof(c_0_1923,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oord(X8)
=> ( X7 = X24
=> ( c_Orderings_Oord__class_Oless(X8,X24,X27)
=> c_Orderings_Oord__class_Oless(X8,X7,X27) ) ) ),
c_0_667 ).
fof(c_0_1924,plain,
! [X15,X35,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X35,X15)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> X15 = X35 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_668]) ).
fof(c_0_1925,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oord(X8)
=> ( X7 = X24
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X27)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X27) ) ) ),
c_0_669 ).
fof(c_0_1926,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( X7 = X24
=> ( c_Orderings_Oord__class_Oless__eq(X8,X27,X24)
=> c_Orderings_Oord__class_Oless__eq(X8,X27,X7) ) ) ),
c_0_670 ).
fof(c_0_1927,axiom,
! [X27,X24,X7,X8] :
( class_Orderings_Oord(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( X24 = X27
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X27) ) ) ),
c_0_671 ).
fof(c_0_1928,axiom,
! [X27,X7,X24,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> ( X24 = X27
=> c_Orderings_Oord__class_Oless__eq(X8,X27,X7) ) ) ),
c_0_672 ).
fof(c_0_1929,axiom,
! [X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> ? [X5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,X4) ) ),
c_0_673 ).
fof(c_0_1930,axiom,
! [X16,X50,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X50) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X50)
<=> ( X36 = X16
| X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_674 ).
fof(c_0_1931,axiom,
! [X16,X36,X50] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16)
<=> ( X36 = X16
| X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_675 ).
fof(c_0_1932,axiom,
! [X16,X36,X50] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X16)
<=> ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X36 = X16 ) ),
c_0_676 ).
fof(c_0_1933,axiom,
! [X25,X26,X33] :
( X33 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X33)
<=> X26 = X25 ) ),
c_0_677 ).
fof(c_0_1934,axiom,
! [X25,X26,X33] :
( X33 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X33),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X33),X25)
<=> X26 = X25 ) ),
c_0_678 ).
fof(c_0_1935,axiom,
! [X9,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X9)
=> c_Nat__Transfer_Otsub(X9,X11) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X11) ),
c_0_679 ).
fof(c_0_1936,plain,
! [X9,X11] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X9)
=> c_Nat__Transfer_Otsub(X9,X11) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X11) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X9)
=> c_Nat__Transfer_Otsub(X9,X11) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[c_0_680]) ).
fof(c_0_1937,axiom,
! [X35,X15,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X15,X35)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
& X15 != X35 ) ) ),
c_0_681 ).
fof(c_0_1938,axiom,
! [X35,X15,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
<=> ( c_Orderings_Oord__class_Oless(X8,X15,X35)
| X15 = X35 ) ) ),
c_0_682 ).
fof(c_0_1939,plain,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X15,X35)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X15,X35)
<=> X15 = X35 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_683]) ).
fof(c_0_1940,axiom,
! [X24,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( X7 != X24
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
c_0_684 ).
fof(c_0_1941,axiom,
! [X24,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( X7 != X24
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> c_Orderings_Oord__class_Oless(X8,X24,X7) ) ) ),
c_0_685 ).
fof(c_0_1942,axiom,
! [X11,X9,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
| X9 = X11 ) ) ),
c_0_686 ).
fof(c_0_1943,axiom,
! [X24,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X24)
=> ( X7 != X24
=> c_Orderings_Oord__class_Oless(X8,X7,X24) ) ) ),
c_0_687 ).
fof(c_0_1944,axiom,
! [X7,X24,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X24,X7)
=> ( X7 != X24
=> c_Orderings_Oord__class_Oless(X8,X24,X7) ) ) ),
c_0_688 ).
fof(c_0_1945,axiom,
! [X9,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8))),X9) ),
c_0_689 ).
fof(c_0_1946,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),c_Nat_OSuc(X6)) ),
c_0_690 ).
fof(c_0_1947,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Nat_OSuc(X16))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
| X36 = X16 ) ),
c_0_691 ).
fof(c_0_1948,plain,
! [X36,X16] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X36)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(X36))
<=> X16 = X36 ) ),
inference(fof_simplification,[status(thm)],[c_0_692]) ).
fof(c_0_1949,plain,
! [X17,X6] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X17)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(X17))
=> X17 = X6 ) ),
inference(fof_simplification,[status(thm)],[c_0_693]) ).
fof(c_0_1950,plain,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X6))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> X17 = X6 ) ),
inference(fof_simplification,[status(thm)],[c_0_694]) ).
fof(c_0_1951,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> ( c_Nat_OSuc(X17) != X6
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),X6) ) ),
c_0_695 ).
fof(c_0_1952,axiom,
! [X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(X8,X9,X11) ) ),
c_0_696 ).
fof(c_0_1953,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ),
c_0_697 ).
fof(c_0_1954,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ),
c_0_698 ).
fof(c_0_1955,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ),
c_0_699 ).
fof(c_0_1956,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X36),X16)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16) ),
c_0_700 ).
fof(c_0_1957,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Nat_OSuc(X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ),
c_0_701 ).
fof(c_0_1958,axiom,
! [X36,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X36)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X16),X36) ),
c_0_702 ).
fof(c_0_1959,axiom,
! [X48,X24,X7,X8] :
( class_Rings_Odvd(X8)
=> ( X7 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X48)
=> c_Rings_Odvd__class_Odvd(X8,X24,X7) ) ),
c_0_703 ).
fof(c_0_1960,axiom,
! [X37] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X37)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X37) ),
c_0_704 ).
fof(c_0_1961,axiom,
! [X15,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X15))
<=> X15 != c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_705 ).
fof(c_0_1962,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9)),
c_0_706 ).
fof(c_0_1963,axiom,
! [X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X9 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
c_0_707 ).
fof(c_0_1964,axiom,
! [X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X17)),
c_0_708 ).
fof(c_0_1965,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X6)) ),
c_0_709 ).
fof(c_0_1966,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Nat_OSuc(X6)) ),
c_0_710 ).
fof(c_0_1967,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X6) ),
c_0_711 ).
fof(c_0_1968,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X6)) ),
c_0_712 ).
fof(c_0_1969,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,X24) = c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ouminus__class_Ouminus(X8,X24)) ),
c_0_713 ).
fof(c_0_1970,axiom,
! [X24,X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,X24) = c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ouminus__class_Ouminus(X8,X24)) ),
c_0_714 ).
fof(c_0_1971,axiom,
! [X11,X9,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Ominus__class_Ominus(X8,X9,X11) = c_Groups_Oplus__class_Oplus(X8,X9,c_Groups_Ouminus__class_Ouminus(X8,X11)) ),
c_0_715 ).
fof(c_0_1972,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,c_Groups_Ouminus__class_Ouminus(X8,X24)) = c_Groups_Oplus__class_Oplus(X8,X7,X24) ),
c_0_716 ).
fof(c_0_1973,axiom,
! [X15,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X15 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_717 ).
fof(c_0_1974,plain,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> X11 != X9 ),
inference(fof_simplification,[status(thm)],[c_0_718]) ).
fof(c_0_1975,plain,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> X9 != X11 ),
inference(fof_simplification,[status(thm)],[c_0_719]) ).
fof(c_0_1976,plain,
! [X11,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X11,X9) )
=> X9 != X11 ),
inference(fof_simplification,[status(thm)],[c_0_720]) ).
fof(c_0_1977,axiom,
! [X27,X24,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X24)
=> ( X24 = X27
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X27) ) ),
c_0_721 ).
fof(c_0_1978,axiom,
! [X27,X24,X7] :
( X7 = X24
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X27)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X27) ) ),
c_0_722 ).
fof(c_0_1979,axiom,
! [X16,X36] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16) ),
c_0_723 ).
fof(c_0_1980,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_724 ).
fof(c_0_1981,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X35)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X35)
| X15 = X35 ) ),
c_0_725 ).
fof(c_0_1982,axiom,
! [X35,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X35)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X35)
& X15 != X35 ) ),
c_0_726 ).
fof(c_0_1983,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
& X36 != X16 ) ),
c_0_727 ).
fof(c_0_1984,axiom,
! [X16,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X16)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
| X36 = X16 ) ),
c_0_728 ).
fof(c_0_1985,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> ( X17 != X6
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6) ) ),
c_0_729 ).
fof(c_0_1986,axiom,
! [X46,X37] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,X46)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X37,X46)
& X37 != X46 ) ),
c_0_730 ).
fof(c_0_1987,axiom,
! [X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X9)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X9),
c_0_731 ).
fof(c_0_1988,axiom,
! [X7,X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_Omonom(X8,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X8,X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) ),
c_0_732 ).
fof(c_0_1989,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ),
c_0_733 ).
fof(c_0_1990,axiom,
! [X6,X17] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
| X17 = X6 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ),
c_0_734 ).
fof(c_0_1991,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X11) ),
c_0_735 ).
fof(c_0_1992,plain,
! [X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_simplification,[status(thm)],[c_0_736]) ).
fof(c_0_1993,axiom,
! [X38,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))),X38) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
c_0_737 ).
fof(c_0_1994,axiom,
! [X22,X23] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X22)),
c_0_738 ).
fof(c_0_1995,axiom,
! [X22,X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X22)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X22),
c_0_739 ).
fof(c_0_1996,axiom,
! [X11,X9] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X9,X11) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11)),
c_0_740 ).
fof(c_0_1997,axiom,
! [X13,X14] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,X13) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13)),
c_0_741 ).
fof(c_0_1998,axiom,
! [X11,X9] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X9,X11) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X9,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X11)),
c_0_742 ).
fof(c_0_1999,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
c_0_743 ).
fof(c_0_2000,axiom,
! [X63,X26,X8] :
( class_Rings_Oidom(X8)
=> ( c_Polynomial_Osmult(X8,X26,X63) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> ( X26 = c_Groups_Ozero__class_Ozero(X8)
| X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ) ),
c_0_744 ).
fof(c_0_2001,axiom,
! [X26,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X26)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X15 = X26 ),
c_0_745 ).
fof(c_0_2002,axiom,
! [X16,X26,X8] :
( ( class_Power_Opower(X8)
& class_Rings_Omult__zero(X8)
& class_Rings_Ono__zero__divisors(X8)
& class_Rings_Ozero__neq__one(X8) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X26),X16) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X26 = c_Groups_Ozero__class_Ozero(X8)
& X16 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
c_0_746 ).
fof(c_0_2003,axiom,
! [X15,X8] :
( class_Rings_Oring__1__no__zero__divisors(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X15),X15) = c_Groups_Oone__class_Oone(X8)
<=> ( X15 = c_Groups_Oone__class_Oone(X8)
| X15 = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8)) ) ) ),
c_0_747 ).
fof(c_0_2004,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),X7) = c_Groups_Oone__class_Oone(X8) ) ),
c_0_748 ).
fof(c_0_2005,axiom,
! [X7,X8] :
( class_Fields_Ofield(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),X7) = c_Groups_Oone__class_Oone(X8) ) ),
c_0_749 ).
fof(c_0_2006,axiom,
! [X63,X26,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_OpCons(X8,X26,X63) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> ( X26 = c_Groups_Ozero__class_Ozero(X8)
& X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ) ),
c_0_750 ).
fof(c_0_2007,plain,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X9,X11)
=> ( X9 != X11
=> c_Orderings_Oord__class_Oless(X8,X11,X9) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_751]) ).
fof(c_0_2008,plain,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( X9 != X11
=> ( ~ c_Orderings_Oord__class_Oless(X8,X9,X11)
=> c_Orderings_Oord__class_Oless(X8,X11,X9) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_752]) ).
fof(c_0_2009,axiom,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
| X9 = X11
| c_Orderings_Oord__class_Oless(X8,X11,X9) ) ),
c_0_753 ).
fof(c_0_2010,axiom,
! [X35,X15,X8] :
( class_Orderings_Olinorder(X8)
=> ( X15 != X35
<=> ( c_Orderings_Oord__class_Oless(X8,X15,X35)
| c_Orderings_Oord__class_Oless(X8,X35,X15) ) ) ),
c_0_754 ).
fof(c_0_2011,plain,
! [X11,X9,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( X9 != X11
=> ( ~ c_Orderings_Oord__class_Oless(X8,X9,X11)
=> c_Orderings_Oord__class_Oless(X8,X11,X9) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_755]) ).
fof(c_0_2012,axiom,
! [X2,X77,X8] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X8,X77,X2)
<=> ! [X3,X62] : hAPP(X2,X3) = hAPP(X2,X62) ),
c_0_756 ).
fof(c_0_2013,axiom,
! [X6,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X17),c_Nat_OSuc(X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X6),
c_0_757 ).
fof(c_0_2014,axiom,
! [X6,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X17),X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Nat_OSuc(X6)),
c_0_758 ).
fof(c_0_2015,axiom,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
| c_Orderings_Oord__class_Oless(X8,X11,X9) ) ),
c_0_759 ).
fof(c_0_2016,plain,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(X8,X11,X9) ) ),
inference(fof_simplification,[status(thm)],[c_0_760]) ).
fof(c_0_2017,plain,
! [X9,X11,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X11,X9)
=> c_Orderings_Oord__class_Oless(X8,X9,X11) ) ),
inference(fof_simplification,[status(thm)],[c_0_761]) ).
fof(c_0_2018,axiom,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
| c_Orderings_Oord__class_Oless__eq(X8,X11,X9) ) ),
c_0_762 ).
fof(c_0_2019,plain,
! [X11,X9,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X9,X11)
=> c_Orderings_Oord__class_Oless__eq(X8,X11,X9) ) ),
inference(fof_simplification,[status(thm)],[c_0_763]) ).
fof(c_0_2020,axiom,
! [X27,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,X27) = c_Groups_Oplus__class_Oplus(X8,X27,X7) ),
c_0_764 ).
fof(c_0_2021,axiom,
! [X25,X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( X26 = c_Groups_Ouminus__class_Ouminus(X8,X25)
<=> c_Groups_Oplus__class_Oplus(X8,X26,X25) = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_765 ).
fof(c_0_2022,axiom,
! [X24,X7,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X7,X24) = c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,X7) = X24 ) ),
c_0_766 ).
fof(c_0_2023,axiom,
! [X35,X15,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X15,X35) = c_Groups_Ozero__class_Ozero(X8)
<=> X35 = c_Groups_Ouminus__class_Ouminus(X8,X15) ) ),
c_0_767 ).
fof(c_0_2024,axiom,
! [X16,X26,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_Omonom(X8,X26,X16) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_768 ).
fof(c_0_2025,plain,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> ~ c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(X8)) ),
inference(fof_simplification,[status(thm)],[c_0_769]) ).
fof(c_0_2026,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(fof_simplification,[status(thm)],[c_0_770]) ).
fof(c_0_2027,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(fof_simplification,[status(thm)],[c_0_771]) ).
fof(c_0_2028,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
inference(fof_simplification,[status(thm)],[c_0_772]) ).
fof(c_0_2029,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
inference(fof_simplification,[status(thm)],[c_0_773]) ).
fof(c_0_2030,plain,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(X8)) ),
inference(fof_simplification,[status(thm)],[c_0_774]) ).
fof(c_0_2031,axiom,
! [X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X39),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
c_0_775 ).
fof(c_0_2032,axiom,
! [X24,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X7) ),
c_0_776 ).
fof(c_0_2033,axiom,
! [X36] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_777 ).
fof(c_0_2034,axiom,
! [X16,X36] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16)
<=> ( ( X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X16 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
c_0_778 ).
fof(c_0_2035,axiom,
! [X16,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X16 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
c_0_779 ).
fof(c_0_2036,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24) = c_Groups_Oone__class_Oone(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,X7) = X24 ) ),
c_0_780 ).
fof(c_0_2037,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X11)
| X9 = X11
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,X9) ),
c_0_781 ).
fof(c_0_2038,axiom,
! [X16,X36] :
( X36 != X16
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X16)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X36) ) ),
c_0_782 ).
fof(c_0_2039,plain,
! [X11,X9] :
( X9 != X11
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X11)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9) ) ),
inference(fof_simplification,[status(thm)],[c_0_783]) ).
fof(c_0_2040,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> X7 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_784 ).
fof(c_0_2041,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_785 ).
fof(c_0_2042,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X22)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X23) ),
c_0_786 ).
fof(c_0_2043,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X23) ),
c_0_787 ).
fof(c_0_2044,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X17) ),
c_0_788 ).
fof(c_0_2045,axiom,
! [X25,X26,X8] :
( class_Rings_Oring__no__zero__divisors(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X25) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X26 = c_Groups_Ozero__class_Ozero(X8)
| X25 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
c_0_789 ).
fof(c_0_2046,axiom,
! [X24,X7,X8] :
( class_Rings_Ono__zero__divisors(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24) != c_Groups_Ozero__class_Ozero(X8) ) ) ),
c_0_790 ).
fof(c_0_2047,axiom,
! [X24,X7,X8] :
( class_Rings_Ono__zero__divisors(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X24) = c_Groups_Ozero__class_Ozero(X8)
=> ( X7 = c_Groups_Ozero__class_Ozero(X8)
| X24 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
c_0_791 ).
fof(c_0_2048,axiom,
! [X38,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X38) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X38) ),
c_0_792 ).
fof(c_0_2049,axiom,
! [X22,X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X23),
c_0_793 ).
fof(c_0_2050,axiom,
! [X6,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X17),
c_0_794 ).
fof(c_0_2051,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X26,X26) = c_Groups_Ozero__class_Ozero(X8)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_795 ).
fof(c_0_2052,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = c_Groups_Oplus__class_Oplus(X8,X26,X26)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_796 ).
fof(c_0_2053,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
c_0_797 ).
fof(c_0_2054,axiom,
! [X25,X26,X8] :
( class_Groups_Oab__group__add(X8)
=> ( X26 = X25
<=> c_Groups_Ominus__class_Ominus(X8,X26,X25) = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_798 ).
fof(c_0_2055,axiom,
! [X25,X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X26,X25) = c_Groups_Ozero__class_Ozero(X8)
<=> X26 = X25 ) ),
c_0_799 ).
fof(c_0_2056,axiom,
! [X35,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X35) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X35 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15) ),
c_0_800 ).
fof(c_0_2057,axiom,
! [X6,X7,X8] :
( class_Rings_Oring__1__no__zero__divisors(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6) != c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_801 ).
fof(c_0_2058,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16)
<=> ? [X73] : X16 = c_Nat_OSuc(X73) ),
c_0_802 ).
fof(c_0_2059,axiom,
! [X26,X25,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( X25 = c_Groups_Oplus__class_Oplus(X8,X25,X26)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_803 ).
fof(c_0_2060,axiom,
! [X63,X8] :
( ( class_Int_Oring__char__0(X8)
& class_Rings_Oidom(X8) )
=> ( c_Polynomial_Opoly(X8,X63) = c_Polynomial_Opoly(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))
<=> X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
c_0_804 ).
fof(c_0_2061,axiom,
! [X9] :
( X9 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X9)),X9) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
c_0_805 ).
fof(c_0_2062,axiom,
! [X11,X9,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> X11 != X9 ) ),
c_0_806 ).
fof(c_0_2063,axiom,
! [X11,X9,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> X9 != X11 ) ),
c_0_807 ).
fof(c_0_2064,axiom,
! [X11,X9,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X11)
=> X9 != X11 ) ),
c_0_808 ).
fof(c_0_2065,axiom,
! [X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X8)) = c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) ),
c_0_809 ).
fof(c_0_2066,axiom,
! [X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
c_0_810 ).
fof(c_0_2067,axiom,
! [X36,X15] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X36) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X15 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
c_0_811 ).
fof(c_0_2068,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Rings_Oinverse__class_Oinverse(X8,X7)) = c_Groups_Oone__class_Oone(X8) ) ),
c_0_812 ).
fof(c_0_2069,axiom,
! [X16] :
( X16 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16) ),
c_0_813 ).
fof(c_0_2070,plain,
! [X9,X8] :
( class_Orderings_Opreorder(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,X9,X9) ),
inference(fof_simplification,[status(thm)],[c_0_814]) ).
fof(c_0_2071,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X6),X6),
inference(fof_simplification,[status(thm)],[c_0_815]) ).
fof(c_0_2072,axiom,
! [X7,X8] :
( ( class_RealVector_Oreal__normed__div__algebra(X8)
& class_Rings_Odivision__ring__inverse__zero(X8) )
=> c_RealVector_Onorm__class_Onorm(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7)) ),
c_0_816 ).
fof(c_0_2073,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ouminus__class_Ouminus(X8,X7)) = c_Groups_Ouminus__class_Ouminus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ),
c_0_817 ).
fof(c_0_2074,axiom,
! [X36] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
c_0_818 ).
fof(c_0_2075,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_819 ).
fof(c_0_2076,axiom,
! [X16,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X16 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
c_0_820 ).
fof(c_0_2077,axiom,
! [X22,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X22) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X23),
c_0_821 ).
fof(c_0_2078,axiom,
! [X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X17),
c_0_822 ).
fof(c_0_2079,axiom,
! [X22,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X22) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X23),
c_0_823 ).
fof(c_0_2080,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ouminus__class_Ouminus(X8,X7)) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_824 ).
fof(c_0_2081,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),X7) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_825 ).
fof(c_0_2082,axiom,
! [X7,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7),X7) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_826 ).
fof(c_0_2083,axiom,
! [X16,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_827 ).
fof(c_0_2084,axiom,
! [X7,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7)) ) ),
c_0_828 ).
fof(c_0_2085,axiom,
! [X38,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Opcompose(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X38) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
c_0_829 ).
fof(c_0_2086,axiom,
! [X27,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osynthetic__div(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X27) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
c_0_830 ).
fof(c_0_2087,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
c_0_831 ).
fof(c_0_2088,axiom,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ? [X55] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X55) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_832 ).
fof(c_0_2089,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X6)
=> X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_833 ).
fof(c_0_2090,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9)) ),
c_0_834 ).
fof(c_0_2091,axiom,
! [X6,X8] :
( ( class_Power_Opower(X8)
& class_Rings_Osemiring__0(X8) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),c_Nat_OSuc(X6)) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_835 ).
fof(c_0_2092,axiom,
! [X6,X8] :
( ( class_Power_Opower(X8)
& class_Rings_Osemiring__0(X8) )
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),X6) = c_Groups_Oone__class_Oone(X8) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),X6) = c_Groups_Ozero__class_Ozero(X8) ) ) ),
c_0_836 ).
fof(c_0_2093,axiom,
! [X6,X17] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X6) = X17
=> X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_837 ).
fof(c_0_2094,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[c_0_838]) ).
fof(c_0_2095,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[c_0_839]) ).
fof(c_0_2096,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[c_0_840]) ).
fof(c_0_2097,axiom,
! [X9,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))),X9) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_841 ).
fof(c_0_2098,axiom,
! [X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X8))),X9) = c_Groups_Oone__class_Oone(X8) ),
c_0_842 ).
fof(c_0_2099,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X17)
=> X17 != X6 ),
c_0_843 ).
fof(c_0_2100,axiom,
! [X53,X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X53)
=> X13 != X53 ),
c_0_844 ).
fof(c_0_2101,axiom,
! [X38,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X38) = X38 ),
c_0_845 ).
fof(c_0_2102,axiom,
! [X39,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X39,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = X39 ),
c_0_846 ).
fof(c_0_2103,axiom,
! [X39,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X39,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = X39 ),
c_0_847 ).
fof(c_0_2104,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ouminus__class_Ouminus(X8,X7)) = c_Groups_Ouminus__class_Ouminus(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) ),
c_0_848 ).
fof(c_0_2105,axiom,
! [X16,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_849 ).
fof(c_0_2106,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X6),
inference(fof_simplification,[status(thm)],[c_0_850]) ).
fof(c_0_2107,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X6),
inference(fof_simplification,[status(thm)],[c_0_851]) ).
fof(c_0_2108,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Ozero__class_Ozero(X8),X7) = c_Groups_Ouminus__class_Ouminus(X8,X7) ),
c_0_852 ).
fof(c_0_2109,axiom,
! [X6,X17] :
( X17 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X6)
=> ( X6 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_853 ).
fof(c_0_2110,axiom,
! [X16,X36] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X16 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
c_0_854 ).
fof(c_0_2111,axiom,
! [X16,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X16) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X16 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
c_0_855 ).
fof(c_0_2112,axiom,
! [X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23),X23) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_856 ).
fof(c_0_2113,axiom,
! [X6,X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_Omonom(X8,c_Groups_Ozero__class_Ozero(X8),X6) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
c_0_857 ).
fof(c_0_2114,axiom,
! [X39,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Ozero__class_Ozero(X8),X39) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
c_0_858 ).
fof(c_0_2115,axiom,
! [X8] :
( class_Power_Opower(X8)
=> c_Power_Opower__class_Opower(X8) = c_Power_Opower_Opower(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Otimes__class_Otimes(X8)) ),
c_0_859 ).
fof(c_0_2116,axiom,
! [X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X6) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_860 ).
fof(c_0_2117,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X7) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_861 ).
fof(c_0_2118,axiom,
! [X6,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Oone__class_Oone(X8)),X6) = c_Groups_Oone__class_Oone(X8) ),
c_0_862 ).
fof(c_0_2119,axiom,
! [X7,X8] :
( class_Rings_Omult__zero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X7) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_863 ).
fof(c_0_2120,axiom,
! [X24,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X24) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_864 ).
fof(c_0_2121,axiom,
! [X11,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X11) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_865 ).
fof(c_0_2122,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oone__class_Oone(X8)) ),
c_0_866 ).
fof(c_0_2123,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oone__class_Oone(X8)) ),
c_0_867 ).
fof(c_0_2124,axiom,
! [X7,X8] :
( class_Groups_Ocomm__monoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X7) = X7 ),
c_0_868 ).
fof(c_0_2125,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X7) = X7 ),
c_0_869 ).
fof(c_0_2126,axiom,
! [X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X7) = X7 ),
c_0_870 ).
fof(c_0_2127,axiom,
! [X7,X8] :
( class_Divides_Osemiring__div(X8)
=> c_Divides_Odiv__class_Odiv(X8,c_Groups_Ozero__class_Ozero(X8),X7) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_871 ).
fof(c_0_2128,axiom,
! [X7,X8] :
( class_Divides_Osemiring__div(X8)
=> c_Divides_Odiv__class_Odiv(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_872 ).
fof(c_0_2129,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_873 ).
fof(c_0_2130,axiom,
! [X7,X8] :
( class_Rings_Omult__zero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_874 ).
fof(c_0_2131,axiom,
! [X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_875 ).
fof(c_0_2132,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X9),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_876 ).
fof(c_0_2133,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
c_0_877 ).
fof(c_0_2134,axiom,
! [X39,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Oone__class_Oone(X8),X39) = X39 ),
c_0_878 ).
fof(c_0_2135,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = X7 ),
c_0_879 ).
fof(c_0_2136,axiom,
! [X7,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = X7 ),
c_0_880 ).
fof(c_0_2137,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = X7 ),
c_0_881 ).
fof(c_0_2138,axiom,
! [X7,X8] :
( class_Groups_Omonoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = X7 ),
c_0_882 ).
fof(c_0_2139,axiom,
! [X7,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ozero__class_Ozero(X8),X7) = X7 ),
c_0_883 ).
fof(c_0_2140,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ozero__class_Ozero(X8),X7) = X7 ),
c_0_884 ).
fof(c_0_2141,axiom,
! [X7,X8] :
( class_Groups_Omonoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ozero__class_Ozero(X8),X7) = X7 ),
c_0_885 ).
fof(c_0_2142,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,c_Groups_Oone__class_Oone(X8),X7) ),
c_0_886 ).
fof(c_0_2143,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X7,c_Groups_Ozero__class_Ozero(X8)) ),
c_0_887 ).
fof(c_0_2144,axiom,
! [X7,X8] :
( class_Groups_Ocomm__monoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Oone__class_Oone(X8)) = X7 ),
c_0_888 ).
fof(c_0_2145,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Oone__class_Oone(X8)) = X7 ),
c_0_889 ).
fof(c_0_2146,axiom,
! [X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Oone__class_Oone(X8)) = X7 ),
c_0_890 ).
fof(c_0_2147,axiom,
! [X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X8) ),
c_0_891 ).
fof(c_0_2148,axiom,
! [X7,X8] :
( class_Power_Opower(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X8) ),
c_0_892 ).
fof(c_0_2149,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,X7) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_893 ).
fof(c_0_2150,axiom,
! [X11,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( X9 = X11
=> c_Orderings_Oord__class_Oless__eq(X8,X9,X11) ) ),
c_0_894 ).
fof(c_0_2151,axiom,
! [X48] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X48),
c_0_895 ).
fof(c_0_2152,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X7) = c_Rings_Oinverse__class_Oinverse(X8,X24)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( X24 != c_Groups_Ozero__class_Ozero(X8)
=> X7 = X24 ) ) ) ),
c_0_896 ).
fof(c_0_2153,axiom,
! [X9,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X9 ),
c_0_897 ).
fof(c_0_2154,axiom,
! [X7,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X7 ),
c_0_898 ).
fof(c_0_2155,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6,
c_0_899 ).
fof(c_0_2156,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X6)),
c_0_900 ).
fof(c_0_2157,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_901 ).
fof(c_0_2158,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X7,X7) ),
c_0_902 ).
fof(c_0_2159,axiom,
! [X9,X8] :
( class_Orderings_Opreorder(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,X9,X9) ),
c_0_903 ).
fof(c_0_2160,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ouminus__class_Ouminus(X8,X9)) = c_RealVector_Onorm__class_Onorm(X8,X9) ),
c_0_904 ).
fof(c_0_2161,axiom,
! [X80,X63,X8] :
( ( class_Int_Oring__char__0(X8)
& class_Rings_Oidom(X8) )
=> ( c_Polynomial_Opoly(X8,X63) = c_Polynomial_Opoly(X8,X80)
<=> X63 = X80 ) ),
c_0_905 ).
fof(c_0_2162,axiom,
! [X6] : c_Nat_OSuc(X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
c_0_906 ).
fof(c_0_2163,axiom,
! [X6] : c_Nat_OSuc(X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X6),
c_0_907 ).
fof(c_0_2164,axiom,
! [X6] :
( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) ),
c_0_908 ).
fof(c_0_2165,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
c_0_909 ).
fof(c_0_2166,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
c_0_910 ).
fof(c_0_2167,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)),
c_0_911 ).
fof(c_0_2168,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(X6)),
c_0_912 ).
fof(c_0_2169,axiom,
! [X24] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_913 ).
fof(c_0_2170,plain,
! [X8] :
( class_Rings_Olinordered__idom(X8)
=> ~ c_Polynomial_Opos__poly(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) ),
inference(fof_simplification,[status(thm)],[c_0_914]) ).
fof(c_0_2171,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_915 ).
fof(c_0_2172,axiom,
! [X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23) = X23,
c_0_916 ).
fof(c_0_2173,axiom,
! [X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X23,
c_0_917 ).
fof(c_0_2174,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
c_0_918 ).
fof(c_0_2175,axiom,
! [X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17,
c_0_919 ).
fof(c_0_2176,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) = X6,
c_0_920 ).
fof(c_0_2177,axiom,
! [X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17,
c_0_921 ).
fof(c_0_2178,axiom,
! [X11,X9] :
( X9 = X11
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X11) ),
c_0_922 ).
fof(c_0_2179,axiom,
! [X6,X17] :
( X17 = X6
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6) ),
c_0_923 ).
fof(c_0_2180,axiom,
! [X9] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9),
c_0_924 ).
fof(c_0_2181,axiom,
! [X9] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_925 ).
fof(c_0_2182,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6),
c_0_926 ).
fof(c_0_2183,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6),
c_0_927 ).
fof(c_0_2184,axiom,
! [X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
c_0_928 ).
fof(c_0_2185,axiom,
! [X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_929 ).
fof(c_0_2186,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_930 ).
fof(c_0_2187,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_931 ).
fof(c_0_2188,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
c_0_932 ).
fof(c_0_2189,axiom,
! [X25,X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X26) = c_Groups_Ouminus__class_Ouminus(X8,X25)
<=> X26 = X25 ) ),
c_0_933 ).
fof(c_0_2190,axiom,
! [X25,X26,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X26) = c_Rings_Oinverse__class_Oinverse(X8,X25)
<=> X26 = X25 ) ),
c_0_934 ).
fof(c_0_2191,axiom,
! [X24,X7,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X7) = c_Rings_Oinverse__class_Oinverse(X8,X24)
=> X7 = X24 ) ),
c_0_935 ).
fof(c_0_2192,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) = X7 ) ),
c_0_936 ).
fof(c_0_2193,axiom,
! [X9] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X9),
c_0_937 ).
fof(c_0_2194,axiom,
! [X22] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X22),
c_0_938 ).
fof(c_0_2195,axiom,
! [X22] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X22),
c_0_939 ).
fof(c_0_2196,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X6),
c_0_940 ).
fof(c_0_2197,axiom,
! [X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23) = X23,
c_0_941 ).
fof(c_0_2198,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6) = X6,
c_0_942 ).
fof(c_0_2199,axiom,
! [X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X23) = X23,
c_0_943 ).
fof(c_0_2200,axiom,
! [X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_944 ).
fof(c_0_2201,axiom,
! [X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X23,
c_0_945 ).
fof(c_0_2202,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6,
c_0_946 ).
fof(c_0_2203,axiom,
! [X7,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7)) = X7 ),
c_0_947 ).
fof(c_0_2204,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)) = X7 ),
c_0_948 ).
fof(c_0_2205,axiom,
! [X25,X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( X26 = c_Groups_Ouminus__class_Ouminus(X8,X25)
<=> X25 = c_Groups_Ouminus__class_Ouminus(X8,X26) ) ),
c_0_949 ).
fof(c_0_2206,axiom,
! [X25,X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X26) = X25
<=> c_Groups_Ouminus__class_Ouminus(X8,X25) = X26 ) ),
c_0_950 ).
fof(c_0_2207,axiom,
! [X63,X8] :
( class_Groups_Ozero(X8)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X8,X63) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X63 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
c_0_951 ).
fof(c_0_2208,axiom,
! [X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = c_Groups_Ouminus__class_Ouminus(X8,X26)
<=> c_Groups_Ozero__class_Ozero(X8) = X26 ) ),
c_0_952 ).
fof(c_0_2209,axiom,
! [X26,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X26) = c_Groups_Ozero__class_Ozero(X8)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_953 ).
fof(c_0_2210,axiom,
! [X15,X8] :
( class_Fields_Ofield__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X15) = c_Groups_Oone__class_Oone(X8)
<=> X15 = c_Groups_Oone__class_Oone(X8) ) ),
c_0_954 ).
fof(c_0_2211,axiom,
! [X26,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X26) = c_Groups_Ozero__class_Ozero(X8)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_955 ).
fof(c_0_2212,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,X7) != c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_956 ).
fof(c_0_2213,axiom,
! [X7,X8] :
( class_Rings_Odivision__ring(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X7) = c_Groups_Ozero__class_Ozero(X8)
=> X7 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_957 ).
fof(c_0_2214,axiom,
! [X15,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_RealVector_Onorm__class_Onorm(X8,X15) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X15 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_958 ).
fof(c_0_2215,axiom,
! [X90,X89] :
( class_Orderings_Oord(X89)
=> class_Orderings_Oord(tc_fun(X90,X89)) ),
c_0_959 ).
fof(c_0_2216,axiom,
! [X90,X89] :
( class_Orderings_Oorder(X89)
=> class_Orderings_Oorder(tc_fun(X90,X89)) ),
c_0_960 ).
fof(c_0_2217,axiom,
! [X90,X89] :
( class_Orderings_Opreorder(X89)
=> class_Orderings_Opreorder(tc_fun(X90,X89)) ),
c_0_961 ).
fof(c_0_2218,axiom,
! [X23] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23)) = X23,
c_0_962 ).
fof(c_0_2219,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( X26 = c_Groups_Ouminus__class_Ouminus(X8,X26)
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_963 ).
fof(c_0_2220,axiom,
! [X26,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X26) = X26
<=> X26 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_964 ).
fof(c_0_2221,axiom,
! [X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_965 ).
fof(c_0_2222,axiom,
! [X8] :
( class_Rings_Odivision__ring(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Oone__class_Oone(X8)) = c_Groups_Oone__class_Oone(X8) ),
c_0_966 ).
fof(c_0_2223,axiom,
! [X8] :
( class_Fields_Ofield__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_967 ).
fof(c_0_2224,axiom,
! [X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
c_0_968 ).
fof(c_0_2225,axiom,
! [X8] :
( class_RealVector_Oreal__normed__algebra__1(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oone__class_Oone(X8)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
c_0_969 ).
fof(c_0_2226,axiom,
! [X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_970 ).
fof(c_0_2227,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
c_0_971 ).
fof(c_0_2228,axiom,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
c_0_972 ).
fof(c_0_2229,axiom,
! [X15,X8] :
( class_Groups_Oone(X8)
=> ( c_Groups_Oone__class_Oone(X8) = X15
<=> X15 = c_Groups_Oone__class_Oone(X8) ) ),
c_0_973 ).
fof(c_0_2230,axiom,
! [X15,X8] :
( class_Groups_Ozero(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = X15
<=> X15 = c_Groups_Ozero__class_Ozero(X8) ) ),
c_0_974 ).
fof(c_0_2231,axiom,
! [X8] :
( class_Rings_Ozero__neq__one(X8)
=> c_Groups_Oone__class_Oone(X8) != c_Groups_Ozero__class_Ozero(X8) ),
c_0_975 ).
fof(c_0_2232,axiom,
! [X8] :
( class_Rings_Ozero__neq__one(X8)
=> c_Groups_Ozero__class_Ozero(X8) != c_Groups_Oone__class_Oone(X8) ),
c_0_976 ).
fof(c_0_2233,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_977 ).
fof(c_0_2234,axiom,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_978 ).
fof(c_0_2235,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X89)) ),
c_0_979 ).
fof(c_0_2236,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Oone(tc_Polynomial_Opoly(X89)) ),
c_0_980 ).
fof(c_0_2237,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X89)) ),
c_0_981 ).
fof(c_0_2238,axiom,
! [X89] :
( class_Rings_Ocomm__ring(X89)
=> class_Rings_Oring(tc_Polynomial_Opoly(X89)) ),
c_0_982 ).
fof(c_0_2239,axiom,
! [X89] :
( class_Groups_Ozero(X89)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X89)) ),
c_0_983 ).
fof(c_0_2240,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Power_Opower(tc_Polynomial_Opoly(X89)) ),
c_0_984 ).
fof(c_0_2241,axiom,
! [X89] :
( class_Rings_Ocomm__ring__1(X89)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X89)) ),
c_0_985 ).
fof(c_0_2242,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X89)) ),
c_0_986 ).
fof(c_0_2243,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X89)) ),
c_0_987 ).
fof(c_0_2244,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X89)) ),
c_0_988 ).
fof(c_0_2245,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X89)) ),
c_0_989 ).
fof(c_0_2246,axiom,
! [X89] :
( class_Rings_Ocomm__ring(X89)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X89)) ),
c_0_990 ).
fof(c_0_2247,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X89)) ),
c_0_991 ).
fof(c_0_2248,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X89)) ),
c_0_992 ).
fof(c_0_2249,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X89)) ),
c_0_993 ).
fof(c_0_2250,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X89)) ),
c_0_994 ).
fof(c_0_2251,axiom,
! [X89] :
( class_Rings_Ocomm__ring__1(X89)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X89)) ),
c_0_995 ).
fof(c_0_2252,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X89)) ),
c_0_996 ).
fof(c_0_2253,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X89)) ),
c_0_997 ).
fof(c_0_2254,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X89)) ),
c_0_998 ).
fof(c_0_2255,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X89)) ),
c_0_999 ).
fof(c_0_2256,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X89)) ),
c_0_1000 ).
fof(c_0_2257,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X89)) ),
c_0_1001 ).
fof(c_0_2258,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X89)) ),
c_0_1002 ).
fof(c_0_2259,axiom,
! [X89] :
( class_Fields_Ofield(X89)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X89)) ),
c_0_1003 ).
fof(c_0_2260,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X89)) ),
c_0_1004 ).
fof(c_0_2261,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X89)) ),
c_0_1005 ).
fof(c_0_2262,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X89)) ),
c_0_1006 ).
fof(c_0_2263,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X89)) ),
c_0_1007 ).
fof(c_0_2264,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X89)) ),
c_0_1008 ).
fof(c_0_2265,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X89)) ),
c_0_1009 ).
fof(c_0_2266,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X89)) ),
c_0_1010 ).
fof(c_0_2267,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
c_0_1011 ).
fof(c_0_2268,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X89)) ),
c_0_1012 ).
fof(c_0_2269,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X89)) ),
c_0_1013 ).
fof(c_0_2270,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X89)) ),
c_0_1014 ).
fof(c_0_2271,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X89)) ),
c_0_1015 ).
fof(c_0_2272,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X89)) ),
c_0_1016 ).
fof(c_0_2273,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X89)) ),
c_0_1017 ).
fof(c_0_2274,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X89)) ),
c_0_1018 ).
fof(c_0_2275,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X89)) ),
c_0_1019 ).
fof(c_0_2276,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X89)) ),
c_0_1020 ).
fof(c_0_2277,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X89)) ),
c_0_1021 ).
fof(c_0_2278,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X89)) ),
c_0_1022 ).
fof(c_0_2279,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X89)) ),
c_0_1023 ).
fof(c_0_2280,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
c_0_1024 ).
fof(c_0_2281,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X89)) ),
c_0_1025 ).
fof(c_0_2282,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X89)) ),
c_0_1026 ).
fof(c_0_2283,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
c_0_1027 ).
fof(c_0_2284,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X89)) ),
c_0_1028 ).
fof(c_0_2285,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X89)) ),
c_0_1029 ).
fof(c_0_2286,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X89)) ),
c_0_1030 ).
fof(c_0_2287,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X89)) ),
c_0_1031 ).
fof(c_0_2288,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
c_0_1032 ).
fof(c_0_2289,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X89)) ),
c_0_1033 ).
fof(c_0_2290,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X89)) ),
c_0_1034 ).
fof(c_0_2291,axiom,
! [X11,X9] :
( c_Nat_OSuc(X9) = c_Nat_OSuc(X11)
=> X9 = X11 ),
c_0_1035 ).
fof(c_0_2292,axiom,
! [X67,X68] :
( c_Nat_OSuc(X68) = c_Nat_OSuc(X67)
<=> X68 = X67 ),
c_0_1036 ).
fof(c_0_2293,axiom,
! [X17] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X17),
c_0_1037 ).
fof(c_0_2294,axiom,
! [X66] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X66),
c_0_1038 ).
fof(c_0_2295,axiom,
! [X17] : c_Nat_OSuc(X17) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_1039 ).
fof(c_0_2296,axiom,
! [X65] : c_Nat_OSuc(X65) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_1040 ).
fof(c_0_2297,axiom,
! [X17] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X17),
c_0_1041 ).
fof(c_0_2298,axiom,
! [X17] : c_Nat_OSuc(X17) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_1042 ).
fof(c_0_2299,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_1043 ).
fof(c_0_2300,axiom,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_1044 ).
fof(c_0_2301,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
c_0_1045 ).
fof(c_0_2302,axiom,
! [X6] : c_Nat_OSuc(X6) != X6,
c_0_1046 ).
fof(c_0_2303,axiom,
! [X6] : X6 != c_Nat_OSuc(X6),
c_0_1047 ).
fof(c_0_2304,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_1048 ).
fof(c_0_2305,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_1049 ).
fof(c_0_2306,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_1050 ).
fof(c_0_2307,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_1051 ).
fof(c_0_2308,axiom,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_1052 ).
fof(c_0_2309,axiom,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_1053 ).
fof(c_0_2310,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
c_0_1054 ).
fof(c_0_2311,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
c_0_1055 ).
fof(c_0_2312,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
c_0_1056 ).
fof(c_0_2313,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
c_0_1057 ).
fof(c_0_2314,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
c_0_1058 ).
fof(c_0_2315,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_1059 ).
fof(c_0_2316,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
c_0_1060 ).
fof(c_0_2317,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
c_0_1061 ).
fof(c_0_2318,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
c_0_1062 ).
fof(c_0_2319,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
c_0_1063 ).
fof(c_0_2320,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
c_0_1064 ).
fof(c_0_2321,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
c_0_1065 ).
fof(c_0_2322,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
c_0_1066 ).
fof(c_0_2323,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
c_0_1067 ).
fof(c_0_2324,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
c_0_1068 ).
fof(c_0_2325,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_1069 ).
fof(c_0_2326,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
c_0_1070 ).
fof(c_0_2327,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_1071 ).
fof(c_0_2328,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
c_0_1072 ).
fof(c_0_2329,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_1073 ).
fof(c_0_2330,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
c_0_1074 ).
fof(c_0_2331,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_1075 ).
fof(c_0_2332,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_1076 ).
fof(c_0_2333,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_1077 ).
fof(c_0_2334,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_1078 ).
fof(c_0_2335,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_1079 ).
fof(c_0_2336,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_1080 ).
fof(c_0_2337,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_1081 ).
fof(c_0_2338,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
c_0_1082 ).
fof(c_0_2339,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_1083 ).
fof(c_0_2340,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_1084 ).
fof(c_0_2341,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
c_0_1085 ).
fof(c_0_2342,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_1086 ).
fof(c_0_2343,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_1087 ).
fof(c_0_2344,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_1088 ).
fof(c_0_2345,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
c_0_1089 ).
fof(c_0_2346,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
c_0_1090 ).
fof(c_0_2347,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
c_0_1091 ).
fof(c_0_2348,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
c_0_1092 ).
fof(c_0_2349,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
c_0_1093 ).
fof(c_0_2350,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
c_0_1094 ).
fof(c_0_2351,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
c_0_1095 ).
fof(c_0_2352,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
c_0_1096 ).
fof(c_0_2353,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
c_0_1097 ).
fof(c_0_2354,axiom,
class_Power_Opower(tc_RealDef_Oreal),
c_0_1098 ).
fof(c_0_2355,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
c_0_1099 ).
fof(c_0_2356,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
c_0_1100 ).
fof(c_0_2357,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
c_0_1101 ).
fof(c_0_2358,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
c_0_1102 ).
fof(c_0_2359,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
c_0_1103 ).
fof(c_0_2360,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
c_0_1104 ).
fof(c_0_2361,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
c_0_1105 ).
fof(c_0_2362,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
c_0_1106 ).
fof(c_0_2363,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
c_0_1107 ).
fof(c_0_2364,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
c_0_1108 ).
fof(c_0_2365,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
c_0_1109 ).
fof(c_0_2366,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
c_0_1110 ).
fof(c_0_2367,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
c_0_1111 ).
fof(c_0_2368,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
c_0_1112 ).
fof(c_0_2369,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
c_0_1113 ).
fof(c_0_2370,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
c_0_1114 ).
fof(c_0_2371,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
c_0_1115 ).
fof(c_0_2372,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
c_0_1116 ).
fof(c_0_2373,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
c_0_1117 ).
fof(c_0_2374,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
c_0_1118 ).
fof(c_0_2375,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
c_0_1119 ).
fof(c_0_2376,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
c_0_1120 ).
fof(c_0_2377,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
c_0_1121 ).
fof(c_0_2378,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
c_0_1122 ).
fof(c_0_2379,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
c_0_1123 ).
fof(c_0_2380,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
c_0_1124 ).
fof(c_0_2381,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
c_0_1125 ).
fof(c_0_2382,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
c_0_1126 ).
fof(c_0_2383,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
c_0_1127 ).
fof(c_0_2384,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
c_0_1128 ).
fof(c_0_2385,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
c_0_1129 ).
fof(c_0_2386,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
c_0_1130 ).
fof(c_0_2387,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
c_0_1131 ).
fof(c_0_2388,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
c_0_1132 ).
fof(c_0_2389,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
c_0_1133 ).
fof(c_0_2390,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
c_0_1134 ).
fof(c_0_2391,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
c_0_1135 ).
fof(c_0_2392,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
c_0_1136 ).
fof(c_0_2393,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
c_0_1137 ).
fof(c_0_2394,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
c_0_1138 ).
fof(c_0_2395,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
c_0_1139 ).
fof(c_0_2396,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
c_0_1140 ).
fof(c_0_2397,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
c_0_1141 ).
fof(c_0_2398,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_1142 ).
fof(c_0_2399,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
c_0_1143 ).
fof(c_0_2400,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
c_0_1144 ).
fof(c_0_2401,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
c_0_1145 ).
fof(c_0_2402,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
c_0_1146 ).
fof(c_0_2403,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
c_0_1147 ).
fof(c_0_2404,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
c_0_1148 ).
fof(c_0_2405,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
c_0_1149 ).
fof(c_0_2406,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
c_0_1150 ).
fof(c_0_2407,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
c_0_1151 ).
fof(c_0_2408,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
c_0_1152 ).
fof(c_0_2409,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
c_0_1153 ).
fof(c_0_2410,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
c_0_1154 ).
fof(c_0_2411,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_1155 ).
fof(c_0_2412,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
c_0_1156 ).
fof(c_0_2413,axiom,
class_Orderings_Oord(tc_HOL_Obool),
c_0_1157 ).
fof(c_0_2414,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
c_0_1158 ).
fof(c_0_2415,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
c_0_1159 ).
fof(c_0_2416,axiom,
class_Rings_Odvd(tc_Nat_Onat),
c_0_1160 ).
fof(c_0_2417,axiom,
class_Groups_Oone(tc_Nat_Onat),
c_0_1161 ).
fof(c_0_2418,axiom,
class_Groups_Ozero(tc_Nat_Onat),
c_0_1162 ).
fof(c_0_2419,axiom,
class_Power_Opower(tc_Nat_Onat),
c_0_1163 ).
fof(c_0_2420,axiom,
class_Orderings_Oord(tc_Nat_Onat),
c_0_1164 ).
fof(c_0_2421,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
c_0_1165 ).
fof(c_0_2422,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
c_0_1166 ).
fof(c_0_2423,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
c_0_1167 ).
fof(c_0_2424,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
c_0_1168 ).
fof(c_0_2425,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
c_0_1169 ).
fof(c_0_2426,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
c_0_1170 ).
fof(c_0_2427,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
c_0_1171 ).
fof(c_0_2428,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
c_0_1172 ).
fof(c_0_2429,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
c_0_1173 ).
fof(c_0_2430,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
c_0_1174 ).
fof(c_0_2431,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
c_0_1175 ).
fof(c_0_2432,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
c_0_1176 ).
fof(c_0_2433,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
c_0_1177 ).
fof(c_0_2434,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
c_0_1178 ).
fof(c_0_2435,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
c_0_1179 ).
fof(c_0_2436,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
c_0_1180 ).
fof(c_0_2437,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
c_0_1181 ).
fof(c_0_2438,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
c_0_1182 ).
fof(c_0_2439,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
c_0_1183 ).
fof(c_0_2440,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
c_0_1184 ).
fof(c_0_2441,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
c_0_1185 ).
fof(c_0_2442,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
c_0_1186 ).
fof(c_0_2443,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
c_0_1187 ).
fof(c_0_2444,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
c_0_1188 ).
fof(c_0_2445,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
c_0_1189 ).
fof(c_0_2446,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
c_0_1190 ).
fof(c_0_2447,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
c_0_1191 ).
fof(c_0_2448,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
c_0_1192 ).
fof(c_0_2449,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
c_0_1193 ).
fof(c_0_2450,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
c_0_1194 ).
fof(c_0_2451,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
c_0_1195 ).
fof(c_0_2452,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
c_0_1196 ).
fof(c_0_2453,axiom,
class_Rings_Odvd(tc_Int_Oint),
c_0_1197 ).
fof(c_0_2454,axiom,
class_Groups_Oone(tc_Int_Oint),
c_0_1198 ).
fof(c_0_2455,axiom,
class_Rings_Oidom(tc_Int_Oint),
c_0_1199 ).
fof(c_0_2456,axiom,
class_Rings_Oring(tc_Int_Oint),
c_0_1200 ).
fof(c_0_2457,axiom,
class_Groups_Ozero(tc_Int_Oint),
c_0_1201 ).
fof(c_0_2458,axiom,
class_Power_Opower(tc_Int_Oint),
c_0_1202 ).
fof(c_0_2459,axiom,
class_Rings_Oring__1(tc_Int_Oint),
c_0_1203 ).
fof(c_0_2460,axiom,
class_Orderings_Oord(tc_Int_Oint),
c_0_1204 ).
fof(c_0_2461,axiom,
class_Rings_Osemiring(tc_Int_Oint),
c_0_1205 ).
fof(c_0_2462,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
c_0_1206 ).
fof(c_0_2463,axiom,
class_Orderings_Oorder(tc_Int_Oint),
c_0_1207 ).
fof(c_0_2464,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
c_0_1208 ).
fof(c_0_2465,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
c_0_1209 ).
fof(c_0_2466,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
c_0_1210 ).
fof(c_0_2467,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
c_0_1211 ).
fof(c_0_2468,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
c_0_1212 ).
fof(c_0_2469,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
c_0_1213 ).
fof(c_0_2470,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
c_0_1214 ).
fof(c_0_2471,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
c_0_1215 ).
fof(c_0_2472,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
c_0_1216 ).
fof(c_0_2473,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
c_0_1217 ).
fof(c_0_2474,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
c_0_1218 ).
fof(c_0_2475,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
c_0_1219 ).
fof(c_0_2476,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
c_0_1220 ).
fof(c_0_2477,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
c_0_1221 ).
fof(c_0_2478,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
c_0_1222 ).
fof(c_0_2479,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
c_0_1223 ).
fof(c_0_2480,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
c_0_1224 ).
fof(c_0_2481,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
c_0_1225 ).
fof(c_0_2482,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
c_0_1226 ).
fof(c_0_2483,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
c_0_1227 ).
fof(c_0_2484,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
c_0_1228 ).
fof(c_0_2485,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
c_0_1229 ).
fof(c_0_2486,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
c_0_1230 ).
fof(c_0_2487,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
c_0_1231 ).
fof(c_0_2488,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
c_0_1232 ).
fof(c_0_2489,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
c_0_1233 ).
fof(c_0_2490,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
c_0_1234 ).
fof(c_0_2491,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
c_0_1235 ).
fof(c_0_2492,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
c_0_1236 ).
fof(c_0_2493,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
c_0_1237 ).
fof(c_0_2494,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
c_0_1238 ).
fof(c_0_2495,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
c_0_1239 ).
fof(c_0_2496,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
c_0_1240 ).
fof(c_0_2497,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
c_0_1241 ).
fof(c_0_2498,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
c_0_1242 ).
fof(c_0_2499,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
c_0_1243 ).
fof(c_0_2500,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
c_0_1244 ).
fof(c_0_2501,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
c_0_1245 ).
fof(c_0_2502,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
c_0_1246 ).
fof(c_0_2503,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
c_0_1247 ).
fof(c_0_2504,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
c_0_1248 ).
fof(c_0_2505,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
c_0_1249 ).
fof(c_0_2506,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
c_0_1250 ).
fof(c_0_2507,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
c_0_1251 ).
fof(c_0_2508,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
c_0_1252 ).
fof(c_0_2509,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
c_0_1253 ).
fof(c_0_2510,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
c_0_1254 ).
fof(c_0_2511,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_1255 ).
fof(c_0_2512,plain,
! [X87,X88,X89,X90,X92] :
( ( c_Orderings_Oord__class_Oless__eq(X89,X88,esk31_4(X87,X88,X89,X90))
| ~ c_Orderings_Oord__class_Oless__eq(X89,X88,X92)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X90,hAPP(X87,X92)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X90,hAPP(X87,X88))))
| ~ class_RealVector_Oreal__normed__vector(X90)
| ~ class_Orderings_Oord(X89) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X90,c_Groups_Ominus__class_Ominus(X90,hAPP(X87,X88),hAPP(X87,esk31_4(X87,X88,X89,X90)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(X89,X88,X92)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X90,hAPP(X87,X92)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X90,hAPP(X87,X88))))
| ~ class_RealVector_Oreal__normed__vector(X90)
| ~ class_Orderings_Oord(X89) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1256])])])])]) ).
fof(c_0_2513,plain,
! [X47,X48] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X47)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X47)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X48)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X48)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1257])])])]) ).
fof(c_0_2514,plain,
! [X86] :
( esk26_0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& esk25_0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk27_0),esk25_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X86) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X86),esk25_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk26_0,esk27_0)),X86))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1258])])]) ).
fof(c_0_2515,plain,
! [X56] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X56) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X56),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X56))),
inference(variable_rename,[status(thm)],[c_0_1259]) ).
fof(c_0_2516,plain,
! [X40,X41,X42] :
( ~ class_Rings_Oidom(X42)
| X41 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X42))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X42),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X42)),c_Polynomial_OpCons(X42,c_Groups_Ouminus__class_Ouminus(X42,X40),c_Polynomial_OpCons(X42,c_Groups_Oone__class_Oone(X42),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X42))))),c_Nat_OSuc(c_Polynomial_Oorder(X42,X40,X41))),X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1260])]) ).
fof(c_0_2517,plain,
! [X40,X41,X42] :
( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X42),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X42)),c_Polynomial_OpCons(X42,c_Groups_Ouminus__class_Ouminus(X42,X40),c_Polynomial_OpCons(X42,c_Groups_Oone__class_Oone(X42),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X42))))),c_Polynomial_Oorder(X42,X40,X41)),X41)
| X41 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X42))
| ~ class_Rings_Oidom(X42) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X42),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X42)),c_Polynomial_OpCons(X42,c_Groups_Ouminus__class_Ouminus(X42,X40),c_Polynomial_OpCons(X42,c_Groups_Oone__class_Oone(X42),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X42))))),c_Nat_OSuc(c_Polynomial_Oorder(X42,X40,X41))),X41)
| X41 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X42))
| ~ class_Rings_Oidom(X42) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1261])])]) ).
fof(c_0_2518,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk18_0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1262])])]) ).
fof(c_0_2519,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
c_0_1263 ).
fof(c_0_2520,plain,
! [X56] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X56) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X56)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
inference(variable_rename,[status(thm)],[c_0_1264]) ).
fof(c_0_2521,plain,
! [X78,X79,X80,X81,X82] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X80,X81),X79,X78)
| c_Orderings_Oord__class_Oless__eq(X81,hAPP(X79,X82),hAPP(X78,X82))
| ~ class_Orderings_Oord(X81) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X81,hAPP(X79,esk28_4(X78,X79,X80,X81)),hAPP(X78,esk28_4(X78,X79,X80,X81)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X80,X81),X79,X78)
| ~ class_Orderings_Oord(X81) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1265])])])])]) ).
fof(c_0_2522,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
c_0_1266 ).
fof(c_0_2523,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_RealVector_Oreal__normed__algebra(X29)
| c_Groups_Ominus__class_Ominus(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X26),X25)) = c_Groups_Oplus__class_Oplus(X29,c_Groups_Oplus__class_Oplus(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),c_Groups_Ominus__class_Ominus(X29,X28,X26)),c_Groups_Ominus__class_Ominus(X29,X27,X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),c_Groups_Ominus__class_Ominus(X29,X28,X26)),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X26),c_Groups_Ominus__class_Ominus(X29,X27,X25))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1267])]) ).
fof(c_0_2524,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk21_0) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk22_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1268])])]) ).
fof(c_0_2525,plain,
! [X40,X41,X42] :
( ~ class_Rings_Ocomm__ring__1(X42)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X42)),c_Polynomial_OpCons(X42,c_Groups_Ouminus__class_Ouminus(X42,X41),c_Polynomial_OpCons(X42,c_Groups_Oone__class_Oone(X42),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X42))))),c_Polynomial_Osynthetic__div(X42,X40,X41)),c_Polynomial_OpCons(X42,hAPP(c_Polynomial_Opoly(X42,X40),X41),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X42)))) = X40 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1269])]) ).
fof(c_0_2526,plain,
! [X52,X53,X54,X55,X56,X57] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54),c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52))
| c_Orderings_Oord__class_Oless__eq(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X56,X53)),X55),X54),X52)
| ~ class_Rings_Oordered__ring(X57) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X56,X53)),X55),X54),X52)
| c_Orderings_Oord__class_Oless__eq(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54),c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52))
| ~ class_Rings_Oordered__ring(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1270])])]) ).
fof(c_0_2527,plain,
! [X52,X53,X54,X55,X56,X57] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54),c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52))
| c_Orderings_Oord__class_Oless__eq(X57,X54,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X53,X56)),X55),X52))
| ~ class_Rings_Oordered__ring(X57) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X57,X54,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X53,X56)),X55),X52))
| c_Orderings_Oord__class_Oless__eq(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54),c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52))
| ~ class_Rings_Oordered__ring(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1271])])]) ).
fof(c_0_2528,plain,
! [X52,X53,X54,X55,X56,X57] :
( ( ~ c_Orderings_Oord__class_Oless(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54),c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52))
| c_Orderings_Oord__class_Oless(X57,X54,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X53,X56)),X55),X52))
| ~ class_Rings_Oordered__ring(X57) )
& ( ~ c_Orderings_Oord__class_Oless(X57,X54,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X53,X56)),X55),X52))
| c_Orderings_Oord__class_Oless(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54),c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52))
| ~ class_Rings_Oordered__ring(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1272])])]) ).
fof(c_0_2529,plain,
! [X52,X53,X54,X55,X56,X57] :
( ( ~ c_Orderings_Oord__class_Oless(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54),c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52))
| c_Orderings_Oord__class_Oless(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X56,X53)),X55),X54),X52)
| ~ class_Rings_Oordered__ring(X57) )
& ( ~ c_Orderings_Oord__class_Oless(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X56,X53)),X55),X54),X52)
| c_Orderings_Oord__class_Oless(X57,c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54),c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52))
| ~ class_Rings_Oordered__ring(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1273])])]) ).
fof(c_0_2530,plain,
! [X75,X76,X77,X78,X79] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X76),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X75))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X76),X75)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X76),X75)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X76),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X75))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1274])])]) ).
fof(c_0_2531,plain,
! [X75,X76,X77,X78,X79] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X76),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X75))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X76,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X75))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X76,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X75))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X76),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X75))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1275])])]) ).
fof(c_0_2532,plain,
! [X75,X76,X77,X78,X79] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X76),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X75))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X76),X75)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X76),X75)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X76),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X75))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1276])])]) ).
fof(c_0_2533,plain,
! [X75,X76,X77,X78,X79] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X76),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X75))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X76,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X75))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X76,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X75))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X76),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X75))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1277])])]) ).
fof(c_0_2534,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
c_0_1278 ).
fof(c_0_2535,plain,
! [X40,X41,X42] :
( ~ class_Rings_Oidom(X42)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X42),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X42)),c_Polynomial_OpCons(X42,c_Groups_Ouminus__class_Ouminus(X42,X41),c_Polynomial_OpCons(X42,c_Groups_Oone__class_Oone(X42),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X42))))),c_Polynomial_Oorder(X42,X41,X40)),X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1279])]) ).
fof(c_0_2536,plain,
! [X56,X57] :
( X57 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X56 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X57),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk4_2(X56,X57)),X56)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1280])])]) ).
fof(c_0_2537,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_RealVector_Oreal__normed__vector(X45)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X45,c_Groups_Ominus__class_Ominus(X45,c_Groups_Oplus__class_Oplus(X45,X44,X43),c_Groups_Oplus__class_Oplus(X45,X42,X41))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X45,c_Groups_Ominus__class_Ominus(X45,X44,X42)),c_RealVector_Onorm__class_Onorm(X45,c_Groups_Ominus__class_Ominus(X45,X43,X41)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1281])]) ).
fof(c_0_2538,plain,
! [X25,X26,X27] :
( ~ class_Rings_Odivision__ring(X27)
| X26 = c_Groups_Ozero__class_Ozero(X27)
| X25 = c_Groups_Ozero__class_Ozero(X27)
| c_Groups_Ominus__class_Ominus(X27,c_Rings_Oinverse__class_Oinverse(X27,X26),c_Rings_Oinverse__class_Oinverse(X27,X25)) = c_Groups_Ouminus__class_Ouminus(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Rings_Oinverse__class_Oinverse(X27,X26)),c_Groups_Ominus__class_Ominus(X27,X26,X25))),c_Rings_Oinverse__class_Oinverse(X27,X25))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1282])]) ).
fof(c_0_2539,plain,
! [X50,X51,X52,X53,X54] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54,X53)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),X51),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X54),X52),X50)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X54)),X52),X51),X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1283])]) ).
fof(c_0_2540,plain,
! [X50,X51,X52,X53,X54] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54,X53)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X54),X52),X51),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),X50)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X54)),X52),X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1284])]) ).
fof(c_0_2541,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__ring__1(X43)
| hAPP(c_Polynomial_Opoly(X43,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),c_Polynomial_Omonom(X43,c_Groups_Oone__class_Oone(X43),X42)),X41)),X40) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X43),hAPP(hAPP(c_Power_Opower__class_Opower(X43),X40),X42)),hAPP(c_Polynomial_Opoly(X43,X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1285])]) ).
fof(c_0_2542,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),esk13_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1286])]) ).
fof(c_0_2543,plain,
! [X85,X86,X87,X88,X89,X90,X91,X92] :
( ( ~ c_Rings_Odvd__class_Odvd(X88,X87,c_Groups_Oplus__class_Oplus(X88,X89,X85))
| c_Rings_Odvd__class_Odvd(X88,X87,c_Groups_Oplus__class_Oplus(X88,c_Groups_Ominus__class_Ominus(X88,X89,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X88),X90),X86)),X85))
| ~ c_Rings_Odvd__class_Odvd(X88,X87,X86)
| ~ class_Rings_Ocomm__ring(X88)
| ~ class_Rings_Odvd(X88) )
& ( ~ c_Rings_Odvd__class_Odvd(X88,X87,c_Groups_Oplus__class_Oplus(X88,c_Groups_Ominus__class_Ominus(X88,X91,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X88),X92),X86)),X85))
| c_Rings_Odvd__class_Odvd(X88,X87,c_Groups_Oplus__class_Oplus(X88,X91,X85))
| ~ c_Rings_Odvd__class_Odvd(X88,X87,X86)
| ~ class_Rings_Ocomm__ring(X88)
| ~ class_Rings_Odvd(X88) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1287])])])])]) ).
fof(c_0_2544,plain,
! [X85,X86,X87,X88,X89,X90,X91,X92] :
( ( ~ c_Rings_Odvd__class_Odvd(X88,X87,c_Groups_Oplus__class_Oplus(X88,X89,X85))
| c_Rings_Odvd__class_Odvd(X88,X87,c_Groups_Oplus__class_Oplus(X88,c_Groups_Ominus__class_Ominus(X88,X89,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X88),X90),X86)),X85))
| ~ c_Rings_Odvd__class_Odvd(X88,X87,X86)
| ~ class_Rings_Ocomm__ring(X88)
| ~ class_Rings_Odvd(X88) )
& ( ~ c_Rings_Odvd__class_Odvd(X88,X87,c_Groups_Oplus__class_Oplus(X88,c_Groups_Ominus__class_Ominus(X88,X91,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X88),X92),X86)),X85))
| c_Rings_Odvd__class_Odvd(X88,X87,c_Groups_Oplus__class_Oplus(X88,X91,X85))
| ~ c_Rings_Odvd__class_Odvd(X88,X87,X86)
| ~ class_Rings_Ocomm__ring(X88)
| ~ class_Rings_Odvd(X88) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1288])])])])]) ).
fof(c_0_2545,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
c_0_1289 ).
fof(c_0_2546,plain,
! [X80,X81,X82,X83,X84,X85] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X85),X84),X83) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X82),X81),X80)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X82),X81),X80))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X80,X82)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X83)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X82)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X82,X85)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X84,X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1290])]) ).
fof(c_0_2547,plain,
! [X80,X81,X82,X83,X84,X85] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X85),X84),X83) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X82),X81),X80)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X82),X81),X80),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X83,X85)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X82)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X82,X85)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1291])]) ).
fof(c_0_2548,plain,
! [X84,X85,X86,X87,X88] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X88,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X86,X85))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X88,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X86,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X87)),X85))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X88,X87) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X88,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X86,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X87)),X85))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X88,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X86,X85))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X88,X87) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1292])])]) ).
fof(c_0_2549,plain,
! [X89,X91,X92] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_1(X89))
| ~ class_RealVector_Oreal__normed__algebra(X89) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X89,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X89),X91),X92)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X89,X91)),c_RealVector_Onorm__class_Onorm(X89,X92))),esk35_1(X89)))
| ~ class_RealVector_Oreal__normed__algebra(X89) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1293])])])])]) ).
fof(c_0_2550,plain,
! [X25,X26,X27] :
( ~ class_Fields_Ofield(X27)
| X26 = c_Groups_Ozero__class_Ozero(X27)
| X25 = c_Groups_Ozero__class_Ozero(X27)
| c_Groups_Oplus__class_Oplus(X27,c_Rings_Oinverse__class_Oinverse(X27,X26),c_Rings_Oinverse__class_Oinverse(X27,X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Oplus__class_Oplus(X27,X26,X25)),c_Rings_Oinverse__class_Oinverse(X27,X26))),c_Rings_Oinverse__class_Oinverse(X27,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1294])]) ).
fof(c_0_2551,plain,
! [X80,X81,X82,X83,X84] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X83),X82),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X81),X80))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X82)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X82,X84)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X80,X84)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X83,X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1295])]) ).
fof(c_0_2552,plain,
! [X80,X81,X82,X83,X84] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X83),X82),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X81),X80))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X80,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X84,X80)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X84,X82)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1296])]) ).
fof(c_0_2553,plain,
! [X75,X76,X77,X78,X79] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X76) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X75)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X76) = X75
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X76) != X75
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X76) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X75)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1297])])]) ).
fof(c_0_2554,plain,
! [X75,X76,X77,X78,X79] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X76) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X75)
| X76 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X75)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) )
& ( X76 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X78,X79)),X77),X75)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X79),X77),X76) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X78),X77),X75)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X79,X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1298])])]) ).
fof(c_0_2555,plain,
! [X52,X53,X54,X55,X56,X57] :
( ( c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54) != c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52)
| X54 = c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X53,X56)),X55),X52)
| ~ class_Rings_Oring(X57) )
& ( X54 != c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X53,X56)),X55),X52)
| c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54) = c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52)
| ~ class_Rings_Oring(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1299])])]) ).
fof(c_0_2556,plain,
! [X52,X53,X54,X55,X56,X57] :
( ( c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54) != c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52)
| c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X56,X53)),X55),X54) = X52
| ~ class_Rings_Oring(X57) )
& ( c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),c_Groups_Ominus__class_Ominus(X57,X56,X53)),X55),X54) != X52
| c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X55),X54) = c_Groups_Oplus__class_Oplus(X57,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X53),X55),X52)
| ~ class_Rings_Oring(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1300])])]) ).
fof(c_0_2557,plain,
! [X24] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X24) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X24,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X24,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X24,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X24,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1301])]) ).
fof(c_0_2558,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Rings_Oring(X29)
| c_Groups_Ominus__class_Ominus(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X26),X25)) = c_Groups_Oplus__class_Oplus(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),c_Groups_Ominus__class_Ominus(X29,X27,X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),c_Groups_Ominus__class_Ominus(X29,X28,X26)),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1302])]) ).
fof(c_0_2559,plain,
! [X29,X30,X31,X32,X33] :
( ~ class_Rings_Osemiring(X33)
| c_Groups_Oplus__class_Oplus(X33,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X32),X31),c_Groups_Oplus__class_Oplus(X33,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X30),X31),X29)) = c_Groups_Oplus__class_Oplus(X33,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),c_Groups_Oplus__class_Oplus(X33,X32,X30)),X31),X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1303])]) ).
fof(c_0_2560,axiom,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
c_0_1304 ).
fof(c_0_2561,plain,
! [X25,X26,X27] :
( ~ class_Rings_Odivision__ring(X27)
| X26 = c_Groups_Ozero__class_Ozero(X27)
| X25 = c_Groups_Ozero__class_Ozero(X27)
| c_Groups_Ominus__class_Ominus(X27,c_Rings_Oinverse__class_Oinverse(X27,X26),c_Rings_Oinverse__class_Oinverse(X27,X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Rings_Oinverse__class_Oinverse(X27,X26)),c_Groups_Ominus__class_Ominus(X27,X25,X26))),c_Rings_Oinverse__class_Oinverse(X27,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1305])]) ).
fof(c_0_2562,plain,
! [X25,X26,X27] :
( ~ class_Rings_Odivision__ring(X27)
| X26 = c_Groups_Ozero__class_Ozero(X27)
| X25 = c_Groups_Ozero__class_Ozero(X27)
| c_Groups_Oplus__class_Oplus(X27,c_Rings_Oinverse__class_Oinverse(X27,X26),c_Rings_Oinverse__class_Oinverse(X27,X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Rings_Oinverse__class_Oinverse(X27,X26)),c_Groups_Oplus__class_Oplus(X27,X26,X25))),c_Rings_Oinverse__class_Oinverse(X27,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1306])]) ).
fof(c_0_2563,plain,
! [X76,X77,X78,X79,X80,X81] :
( ~ class_Rings_Olinordered__semiring__1__strict(X81)
| ~ c_Orderings_Oord__class_Oless(X81,X80,X79)
| ~ c_Orderings_Oord__class_Oless(X81,X78,X79)
| ~ c_Orderings_Oord__class_Oless__eq(X81,c_Groups_Ozero__class_Ozero(X81),X77)
| ~ c_Orderings_Oord__class_Oless__eq(X81,c_Groups_Ozero__class_Ozero(X81),X76)
| c_Groups_Oplus__class_Oplus(X81,X77,X76) != c_Groups_Oone__class_Oone(X81)
| c_Orderings_Oord__class_Oless(X81,c_Groups_Oplus__class_Oplus(X81,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X81),X77),X80),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X81),X76),X78)),X79) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1307])]) ).
fof(c_0_2564,plain,
! [X76,X77,X78,X79,X80,X81] :
( ~ class_Rings_Olinordered__semiring__1(X81)
| ~ c_Orderings_Oord__class_Oless__eq(X81,X80,X79)
| ~ c_Orderings_Oord__class_Oless__eq(X81,X78,X79)
| ~ c_Orderings_Oord__class_Oless__eq(X81,c_Groups_Ozero__class_Ozero(X81),X77)
| ~ c_Orderings_Oord__class_Oless__eq(X81,c_Groups_Ozero__class_Ozero(X81),X76)
| c_Groups_Oplus__class_Oplus(X81,X77,X76) != c_Groups_Oone__class_Oone(X81)
| c_Orderings_Oord__class_Oless__eq(X81,c_Groups_Oplus__class_Oplus(X81,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X81),X77),X80),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X81),X76),X78)),X79) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1308])]) ).
fof(c_0_2565,plain,
! [X65,X66,X67,X68,X70] :
( ( c_Rings_Odvd__class_Odvd(X67,X65,c_Groups_Oplus__class_Oplus(X67,esk29_3(X65,X66,X67),c_Groups_Ozero__class_Ozero(X67)))
| ~ hBOOL(hAPP(X66,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X67),X65),X68)))
| ~ class_Rings_Odvd(X67)
| ~ class_Rings_Osemiring__0(X67) )
& ( hBOOL(hAPP(X66,esk29_3(X65,X66,X67)))
| ~ hBOOL(hAPP(X66,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X67),X65),X68)))
| ~ class_Rings_Odvd(X67)
| ~ class_Rings_Osemiring__0(X67) )
& ( ~ c_Rings_Odvd__class_Odvd(X67,X65,c_Groups_Oplus__class_Oplus(X67,X70,c_Groups_Ozero__class_Ozero(X67)))
| ~ hBOOL(hAPP(X66,X70))
| hBOOL(hAPP(X66,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X67),X65),esk30_3(X65,X66,X67))))
| ~ class_Rings_Odvd(X67)
| ~ class_Rings_Osemiring__0(X67) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1309])])])])]) ).
fof(c_0_2566,plain,
! [X50,X51,X52,X53] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X52),X50)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51)),X52),X50),
inference(variable_rename,[status(thm)],[c_0_1310]) ).
fof(c_0_2567,plain,
! [X13,X14,X15,X16] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X16)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X15)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X13))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X16)),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X15)),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1311])]) ).
fof(c_0_2568,plain,
! [X40,X41,X42,X43] :
( ~ class_Groups_Omonoid__mult(X43)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41)
| hAPP(hAPP(c_Power_Opower__class_Opower(X43),X40),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X41),X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X43),hAPP(hAPP(c_Power_Opower__class_Opower(X43),X40),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,X42))),X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1312])]) ).
fof(c_0_2569,plain,
! [X36,X37,X38] :
( ( ~ c_Orderings_Oord__class_Oless(X38,c_Groups_Ozero__class_Ozero(X38),c_Groups_Oplus__class_Oplus(X38,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X36),X36)))
| X37 != c_Groups_Ozero__class_Ozero(X38)
| X36 != c_Groups_Ozero__class_Ozero(X38)
| ~ class_Rings_Olinordered__ring__strict(X38) )
& ( X37 = c_Groups_Ozero__class_Ozero(X38)
| c_Orderings_Oord__class_Oless(X38,c_Groups_Ozero__class_Ozero(X38),c_Groups_Oplus__class_Oplus(X38,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X36),X36)))
| ~ class_Rings_Olinordered__ring__strict(X38) )
& ( X36 = c_Groups_Ozero__class_Ozero(X38)
| c_Orderings_Oord__class_Oless(X38,c_Groups_Ozero__class_Ozero(X38),c_Groups_Oplus__class_Oplus(X38,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X36),X36)))
| ~ class_Rings_Olinordered__ring__strict(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1313])])]) ).
fof(c_0_2570,plain,
! [X45,X46,X47,X48,X49] :
( ~ class_Rings_Ocomm__semiring__1(X49)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X48),X47)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X46),X45)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X46),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X48),X47)),X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1314])]) ).
fof(c_0_2571,plain,
! [X36,X37,X38] :
( ( X37 = c_Groups_Ozero__class_Ozero(X38)
| ~ c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Oplus__class_Oplus(X38,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X36),X36)),c_Groups_Ozero__class_Ozero(X38))
| ~ class_Rings_Olinordered__ring__strict(X38) )
& ( X36 = c_Groups_Ozero__class_Ozero(X38)
| ~ c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Oplus__class_Oplus(X38,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X36),X36)),c_Groups_Ozero__class_Ozero(X38))
| ~ class_Rings_Olinordered__ring__strict(X38) )
& ( X37 != c_Groups_Ozero__class_Ozero(X38)
| X36 != c_Groups_Ozero__class_Ozero(X38)
| c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Oplus__class_Oplus(X38,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X36),X36)),c_Groups_Ozero__class_Ozero(X38))
| ~ class_Rings_Olinordered__ring__strict(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1315])])]) ).
fof(c_0_2572,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__ring(X14)
| ~ c_Orderings_Oord__class_Oless(X14,c_Groups_Oplus__class_Oplus(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X12),X12)),c_Groups_Ozero__class_Ozero(X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1316])]) ).
fof(c_0_2573,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_1317 ).
fof(c_0_2574,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),c_Polynomial_OpCons(X43,X42,X41)),X40) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X43),c_Polynomial_Osmult(X43,X42,X40),c_Polynomial_OpCons(X43,c_Groups_Ozero__class_Ozero(X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),X41),X40))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1318])]) ).
fof(c_0_2575,plain,
! [X64,X65,X66] :
( ( hAPP(c_Polynomial_Opoly(X66,X65),X64) != c_Groups_Ozero__class_Ozero(X66)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X66),c_Polynomial_OpCons(X66,c_Groups_Ouminus__class_Ouminus(X66,X64),c_Polynomial_OpCons(X66,c_Groups_Oone__class_Oone(X66),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66)))),X65)
| ~ class_Rings_Oidom(X66) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X66),c_Polynomial_OpCons(X66,c_Groups_Ouminus__class_Ouminus(X66,X64),c_Polynomial_OpCons(X66,c_Groups_Oone__class_Oone(X66),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66)))),X65)
| hAPP(c_Polynomial_Opoly(X66,X65),X64) = c_Groups_Ozero__class_Ozero(X66)
| ~ class_Rings_Oidom(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1319])])]) ).
fof(c_0_2576,plain,
! [X13,X14,X15,X16] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X16)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X15)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X13))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X15))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1320])]) ).
fof(c_0_2577,plain,
! [X10,X11,X12] :
( ~ class_Groups_Omonoid__mult(X12)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(c_Power_Opower__class_Opower(X12),X10),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X10) = hAPP(hAPP(c_Power_Opower__class_Opower(X12),X10),X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1321])]) ).
fof(c_0_2578,plain,
! [X64,X65,X66] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X66),c_Polynomial_OpCons(X66,X65,c_Polynomial_OpCons(X66,c_Groups_Oone__class_Oone(X66),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66)))),X64)
| hAPP(c_Polynomial_Opoly(X66,X64),c_Groups_Ouminus__class_Ouminus(X66,X65)) = c_Groups_Ozero__class_Ozero(X66)
| ~ class_Rings_Oidom(X66) )
& ( hAPP(c_Polynomial_Opoly(X66,X64),c_Groups_Ouminus__class_Ouminus(X66,X65)) != c_Groups_Ozero__class_Ozero(X66)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X66),c_Polynomial_OpCons(X66,X65,c_Polynomial_OpCons(X66,c_Groups_Oone__class_Oone(X66),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66)))),X64)
| ~ class_Rings_Oidom(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1322])])]) ).
fof(c_0_2579,plain,
! [X47,X48,X49,X50,X51] :
( ( c_Groups_Oplus__class_Oplus(X51,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X50),X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X48),X47)) != c_Groups_Oplus__class_Oplus(X51,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X50),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X48),X49))
| X50 = X48
| X49 = X47
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X51) )
& ( X50 != X48
| c_Groups_Oplus__class_Oplus(X51,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X50),X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X48),X47)) = c_Groups_Oplus__class_Oplus(X51,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X50),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X48),X49))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X51) )
& ( X49 != X47
| c_Groups_Oplus__class_Oplus(X51,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X50),X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X48),X47)) = c_Groups_Oplus__class_Oplus(X51,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X50),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X48),X49))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X51) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1323])])]) ).
fof(c_0_2580,plain,
! [X46,X47,X48,X49,X50] :
( ( X49 = X48
| X47 = X46
| c_Groups_Oplus__class_Oplus(X50,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X49),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X48),X46)) != c_Groups_Oplus__class_Oplus(X50,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X49),X46),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X48),X47))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X50) )
& ( X49 != X48
| c_Groups_Oplus__class_Oplus(X50,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X49),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X48),X46)) = c_Groups_Oplus__class_Oplus(X50,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X49),X46),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X48),X47))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X50) )
& ( X47 != X46
| c_Groups_Oplus__class_Oplus(X50,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X49),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X48),X46)) = c_Groups_Oplus__class_Oplus(X50,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X49),X46),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X50),X48),X47))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X50) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1324])])]) ).
fof(c_0_2581,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
c_0_1325 ).
fof(c_0_2582,plain,
! [X61,X62,X63,X64,X65] : hAPP(hAPP(c_Power_Opower_Opower(X65,X64,X63),X62),c_Nat_OSuc(X61)) = hAPP(hAPP(X63,X62),hAPP(hAPP(c_Power_Opower_Opower(X65,X64,X63),X62),X61)),
inference(variable_rename,[status(thm)],[c_0_1326]) ).
fof(c_0_2583,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),X42),c_Polynomial_OpCons(X43,X41,X40)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X43),c_Polynomial_Osmult(X43,X41,X42),c_Polynomial_OpCons(X43,c_Groups_Ozero__class_Ozero(X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),X42),X40))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1327])]) ).
fof(c_0_2584,plain,
! [X9,X10,X11] :
( ~ class_Rings_Oring__1(X11)
| hAPP(hAPP(c_Power_Opower__class_Opower(X11),c_Groups_Ouminus__class_Ouminus(X11,X10)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),hAPP(hAPP(c_Power_Opower__class_Opower(X11),c_Groups_Ouminus__class_Ouminus(X11,c_Groups_Oone__class_Oone(X11))),X9)),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1328])]) ).
fof(c_0_2585,plain,
! [X80,X81,X82] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X82),X81),X80),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X82)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1329])]) ).
fof(c_0_2586,plain,
! [X80,X81,X82] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X82),X81),X80))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X80,X82)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X82)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1330])]) ).
fof(c_0_2587,plain,
! [X12,X13,X14] :
( ~ class_Rings_Ocomm__ring__1(X14)
| c_Groups_Ominus__class_Ominus(X14,hAPP(hAPP(c_Power_Opower__class_Opower(X14),X13),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X14),X12),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),c_Groups_Ominus__class_Ominus(X14,X13,X12)),c_Groups_Oplus__class_Oplus(X14,X13,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1331])]) ).
fof(c_0_2588,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| c_Polynomial_Opcompose(X43,c_Polynomial_OpCons(X43,X42,X41),X40) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X43),c_Polynomial_OpCons(X43,X42,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X43))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),X40),c_Polynomial_Opcompose(X43,X41,X40))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1332])]) ).
fof(c_0_2589,plain,
! [X45,X46,X47,X48,X49] :
( ~ class_Rings_Ocomm__semiring__1(X49)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X48),X47)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X46),X45)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X48),X46)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X47),X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1333])]) ).
fof(c_0_2590,plain,
! [X45,X46,X47,X48,X49] :
( ~ class_Rings_Ocomm__semiring__1(X49)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X48),X47)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X46),X45)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),X46),X45))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1334])]) ).
fof(c_0_2591,plain,
! [X25,X26] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X26,X25)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X26)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X25)),
inference(variable_rename,[status(thm)],[c_0_1335]) ).
fof(c_0_2592,plain,
! [X24,X25] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X25),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X25,X24)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X24))),
inference(variable_rename,[status(thm)],[c_0_1336]) ).
fof(c_0_2593,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X43),X42,X41)),X40) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),X42),X40),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1337])]) ).
fof(c_0_2594,plain,
! [X59,X60,X61,X62,X63,X64,X65] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X60,X59)
| hBOOL(hAPP(X61,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X61,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X60,X59))) )
& ( X60 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X59,X62)
| hBOOL(hAPP(X61,X62))
| ~ hBOOL(hAPP(X61,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X60,X59))) )
& ( X64 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,esk6_3(X63,X64,X65))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X64,X63)
| hBOOL(hAPP(X65,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X64,X63))) )
& ( ~ hBOOL(hAPP(X65,esk6_3(X63,X64,X65)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X64,X63)
| hBOOL(hAPP(X65,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X64,X63))) )
& ( X64 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,esk6_3(X63,X64,X65))
| ~ hBOOL(hAPP(X65,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X65,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X64,X63))) )
& ( ~ hBOOL(hAPP(X65,esk6_3(X63,X64,X65)))
| ~ hBOOL(hAPP(X65,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X65,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X64,X63))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1338])])])])])]) ).
fof(c_0_2595,plain,
! [X59,X60,X61,X62,X63,X64,X65] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X60,X59)
| hBOOL(hAPP(X61,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X61,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X60,X59))) )
& ( X60 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X59,X62)
| hBOOL(hAPP(X61,X62))
| ~ hBOOL(hAPP(X61,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X60,X59))) )
& ( X64 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,esk5_3(X63,X64,X65))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X64,X63)
| hBOOL(hAPP(X65,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X64,X63))) )
& ( ~ hBOOL(hAPP(X65,esk5_3(X63,X64,X65)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X64,X63)
| hBOOL(hAPP(X65,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X64,X63))) )
& ( X64 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,esk5_3(X63,X64,X65))
| ~ hBOOL(hAPP(X65,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X65,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X64,X63))) )
& ( ~ hBOOL(hAPP(X65,esk5_3(X63,X64,X65)))
| ~ hBOOL(hAPP(X65,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X65,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X64,X63))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1339])])])])])]) ).
fof(c_0_2596,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Rings_Ocomm__semiring__0(X29)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X29)),c_Polynomial_Omonom(X29,X28,X27)),c_Polynomial_Omonom(X29,X26,X25)) = c_Polynomial_Omonom(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X26),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1340])]) ).
fof(c_0_2597,plain,
! [X9,X10,X11] :
( ~ class_Rings_Olinordered__semidom(X11)
| ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Ozero__class_Ozero(X11),X10)
| ~ c_Orderings_Oord__class_Oless(X11,X10,c_Groups_Oone__class_Oone(X11))
| c_Orderings_Oord__class_Oless(X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1341])]) ).
fof(c_0_2598,plain,
! [X38,X39] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X38),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X38,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X39,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X39),X39),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1342])])])]) ).
fof(c_0_2599,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_RealVector_Oreal__normed__vector(X19)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X18),X17)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X16),X15)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,c_Groups_Oplus__class_Oplus(X19,X18,X16)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X17,X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1343])]) ).
fof(c_0_2600,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
c_0_1344 ).
fof(c_0_2601,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| hAPP(c_Polynomial_Opoly(X43,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),X42),X41)),X40) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X43),hAPP(c_Polynomial_Opoly(X43,X42),X40)),hAPP(c_Polynomial_Opoly(X43,X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1345])]) ).
fof(c_0_2602,plain,
! [X18,X19,X20,X21] :
( ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X18) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1346])])])]) ).
fof(c_0_2603,plain,
! [X51,X52,X53] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X53),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X53))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X53),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X53))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1347])])]) ).
fof(c_0_2604,plain,
! [X51,X52,X53] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X53),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X53))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X53),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X53))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1348])])]) ).
fof(c_0_2605,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Rings_Olinordered__semiring__strict(X45)
| ~ c_Orderings_Oord__class_Oless__eq(X45,X44,X43)
| ~ c_Orderings_Oord__class_Oless(X45,X42,X41)
| ~ c_Orderings_Oord__class_Oless(X45,c_Groups_Ozero__class_Ozero(X45),X44)
| ~ c_Orderings_Oord__class_Oless__eq(X45,c_Groups_Ozero__class_Ozero(X45),X42)
| c_Orderings_Oord__class_Oless(X45,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X44),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X43),X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1349])]) ).
fof(c_0_2606,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Rings_Olinordered__semiring__strict(X45)
| ~ c_Orderings_Oord__class_Oless(X45,X44,X43)
| ~ c_Orderings_Oord__class_Oless__eq(X45,X42,X41)
| ~ c_Orderings_Oord__class_Oless__eq(X45,c_Groups_Ozero__class_Ozero(X45),X44)
| ~ c_Orderings_Oord__class_Oless(X45,c_Groups_Ozero__class_Ozero(X45),X42)
| c_Orderings_Oord__class_Oless(X45,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X44),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X43),X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1350])]) ).
fof(c_0_2607,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Rings_Olinordered__semiring__strict(X45)
| ~ c_Orderings_Oord__class_Oless(X45,X44,X43)
| ~ c_Orderings_Oord__class_Oless(X45,X42,X41)
| ~ c_Orderings_Oord__class_Oless__eq(X45,c_Groups_Ozero__class_Ozero(X45),X44)
| ~ c_Orderings_Oord__class_Oless__eq(X45,c_Groups_Ozero__class_Ozero(X45),X42)
| c_Orderings_Oord__class_Oless(X45,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X44),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X43),X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1351])]) ).
fof(c_0_2608,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Rings_Olinordered__semiring__strict(X45)
| ~ c_Orderings_Oord__class_Oless(X45,X44,X43)
| ~ c_Orderings_Oord__class_Oless(X45,X42,X41)
| ~ c_Orderings_Oord__class_Oless(X45,c_Groups_Ozero__class_Ozero(X45),X43)
| ~ c_Orderings_Oord__class_Oless__eq(X45,c_Groups_Ozero__class_Ozero(X45),X42)
| c_Orderings_Oord__class_Oless(X45,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X44),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X43),X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1352])]) ).
fof(c_0_2609,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Rings_Oordered__semiring(X45)
| ~ c_Orderings_Oord__class_Oless__eq(X45,X44,X43)
| ~ c_Orderings_Oord__class_Oless__eq(X45,X42,X41)
| ~ c_Orderings_Oord__class_Oless__eq(X45,c_Groups_Ozero__class_Ozero(X45),X43)
| ~ c_Orderings_Oord__class_Oless__eq(X45,c_Groups_Ozero__class_Ozero(X45),X42)
| c_Orderings_Oord__class_Oless__eq(X45,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X44),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X43),X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1353])]) ).
fof(c_0_2610,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Rings_Oordered__semiring(X45)
| ~ c_Orderings_Oord__class_Oless__eq(X45,X44,X43)
| ~ c_Orderings_Oord__class_Oless__eq(X45,X42,X41)
| ~ c_Orderings_Oord__class_Oless__eq(X45,c_Groups_Ozero__class_Ozero(X45),X44)
| ~ c_Orderings_Oord__class_Oless__eq(X45,c_Groups_Ozero__class_Ozero(X45),X42)
| c_Orderings_Oord__class_Oless__eq(X45,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X44),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X43),X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1354])]) ).
fof(c_0_2611,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_RealVector_Oreal__normed__algebra(X19)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X18),X17)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X16),X15)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1355])]) ).
fof(c_0_2612,plain,
! [X40,X41,X42] :
( ~ class_Rings_Ocomm__semiring__0(X42)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X42),X41,c_Polynomial_Osmult(X42,X40,c_Polynomial_Osynthetic__div(X42,X41,X40))) = c_Polynomial_OpCons(X42,hAPP(c_Polynomial_Opoly(X42,X41),X40),c_Polynomial_Osynthetic__div(X42,X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1356])]) ).
fof(c_0_2613,plain,
! [X39,X40,X41,X42] :
( ~ class_Rings_Ocomm__semiring__1(X42)
| hAPP(hAPP(c_Power_Opower__class_Opower(X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X42),X41),X40)),X39) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X42),hAPP(hAPP(c_Power_Opower__class_Opower(X42),X41),X39)),hAPP(hAPP(c_Power_Opower__class_Opower(X42),X40),X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1357])]) ).
fof(c_0_2614,plain,
! [X25,X26,X27,X28] :
( ~ class_Groups_Ocomm__monoid__mult(X28)
| hAPP(hAPP(c_Power_Opower__class_Opower(X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28),X27),X26)),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28),hAPP(hAPP(c_Power_Opower__class_Opower(X28),X27),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X28),X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1358])]) ).
fof(c_0_2615,plain,
! [X25,X26,X27,X28] :
( ~ class_Rings_Olinordered__semidom(X28)
| ~ c_Orderings_Oord__class_Oless__eq(X28,hAPP(hAPP(c_Power_Opower__class_Opower(X28),X27),c_Nat_OSuc(X26)),hAPP(hAPP(c_Power_Opower__class_Opower(X28),X25),c_Nat_OSuc(X26)))
| ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X25)
| c_Orderings_Oord__class_Oless__eq(X28,X27,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1359])]) ).
fof(c_0_2616,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__ring(X14)
| c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14),c_Groups_Oplus__class_Oplus(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X12),X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1360])]) ).
fof(c_0_2617,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X53,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X52,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X51)))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X53,X52) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X56,X55)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X56,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X56),X54))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1361])])])]) ).
fof(c_0_2618,plain,
! [X10,X11] :
( ~ class_Rings_Oring__1(X11)
| c_Groups_Ominus__class_Ominus(X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),X10),c_Groups_Oone__class_Oone(X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),c_Groups_Oplus__class_Oplus(X11,X10,c_Groups_Oone__class_Oone(X11))),c_Groups_Ominus__class_Ominus(X11,X10,c_Groups_Oone__class_Oone(X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1362])]) ).
fof(c_0_2619,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| hAPP(c_Polynomial_Opoly(X43,c_Polynomial_OpCons(X43,X42,X41)),X40) = c_Groups_Oplus__class_Oplus(X43,X42,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X43),X40),hAPP(c_Polynomial_Opoly(X43,X41),X40))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1363])]) ).
fof(c_0_2620,plain,
! [X9,X10,X11] :
( ~ class_Rings_Olinordered__semidom(X11)
| ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Oone__class_Oone(X11),X10)
| c_Orderings_Oord__class_Oless(X11,hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1364])]) ).
fof(c_0_2621,plain,
! [X25,X26,X27,X28] :
( ~ class_Rings_Olinordered__semidom(X28)
| ~ c_Orderings_Oord__class_Oless(X28,hAPP(hAPP(c_Power_Opower__class_Opower(X28),X27),X26),hAPP(hAPP(c_Power_Opower__class_Opower(X28),X25),X26))
| ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X25)
| c_Orderings_Oord__class_Oless(X28,X27,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1365])]) ).
fof(c_0_2622,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring__strict(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28))
| ~ c_Orderings_Oord__class_Oless(X31,c_Groups_Ozero__class_Ozero(X31),X30)
| c_Orderings_Oord__class_Oless__eq(X31,X29,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1366])]) ).
fof(c_0_2623,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring__strict(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X29))
| ~ c_Orderings_Oord__class_Oless(X31,c_Groups_Ozero__class_Ozero(X31),X29)
| c_Orderings_Oord__class_Oless__eq(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1367])]) ).
fof(c_0_2624,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring__strict(X31)
| ~ c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28))
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31),X30)
| c_Orderings_Oord__class_Oless(X31,X29,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1368])]) ).
fof(c_0_2625,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring(X31)
| ~ c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28))
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31),X30)
| c_Orderings_Oord__class_Oless(X31,X29,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1369])]) ).
fof(c_0_2626,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring__strict(X31)
| ~ c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X29))
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31),X29)
| c_Orderings_Oord__class_Oless(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1370])]) ).
fof(c_0_2627,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring(X31)
| ~ c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X29))
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31),X29)
| c_Orderings_Oord__class_Oless(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1371])]) ).
fof(c_0_2628,plain,
! [X34,X35,X36,X37] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| c_Orderings_Oord__class_Oless__eq(X37,X34,X35)
| ~ c_Orderings_Oord__class_Oless(X37,X36,c_Groups_Ozero__class_Ozero(X37))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X37,X34,X35)
| c_Orderings_Oord__class_Oless__eq(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ c_Orderings_Oord__class_Oless(X37,X36,c_Groups_Ozero__class_Ozero(X37))
| ~ class_Rings_Olinordered__ring__strict(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1372])])]) ).
fof(c_0_2629,plain,
! [X34,X35,X36,X37] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| c_Orderings_Oord__class_Oless__eq(X37,X35,X34)
| ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X36)
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X37,X35,X34)
| c_Orderings_Oord__class_Oless__eq(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X36)
| ~ class_Rings_Olinordered__ring__strict(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1373])])]) ).
fof(c_0_2630,plain,
! [X34,X35,X36,X37] :
( ( ~ c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| c_Orderings_Oord__class_Oless(X37,X35,X34)
| ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X36)
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( ~ c_Orderings_Oord__class_Oless(X37,X35,X34)
| c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X36)
| ~ class_Rings_Olinordered__ring__strict(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1374])])]) ).
fof(c_0_2631,plain,
! [X34,X35,X36,X37] :
( ( ~ c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| c_Orderings_Oord__class_Oless(X37,X34,X35)
| ~ c_Orderings_Oord__class_Oless(X37,X36,c_Groups_Ozero__class_Ozero(X37))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( ~ c_Orderings_Oord__class_Oless(X37,X34,X35)
| c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ c_Orderings_Oord__class_Oless(X37,X36,c_Groups_Ozero__class_Ozero(X37))
| ~ class_Rings_Olinordered__ring__strict(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1375])])]) ).
fof(c_0_2632,plain,
! [X18,X19,X20,X21] :
( ~ class_Rings_Olinordered__semidom(X21)
| ~ c_Orderings_Oord__class_Oless(X21,c_Groups_Oone__class_Oone(X21),X20)
| ~ c_Orderings_Oord__class_Oless__eq(X21,hAPP(hAPP(c_Power_Opower__class_Opower(X21),X20),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X21),X20),X18))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1376])]) ).
fof(c_0_2633,plain,
! [X36,X37,X38,X39] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X39,hAPP(hAPP(c_Power_Opower__class_Opower(X39),X38),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X39),X38),X36))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X36)
| ~ c_Orderings_Oord__class_Oless(X39,c_Groups_Oone__class_Oone(X39),X38)
| ~ class_Rings_Olinordered__semidom(X39) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X36)
| c_Orderings_Oord__class_Oless__eq(X39,hAPP(hAPP(c_Power_Opower__class_Opower(X39),X38),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X39),X38),X36))
| ~ c_Orderings_Oord__class_Oless(X39,c_Groups_Oone__class_Oone(X39),X38)
| ~ class_Rings_Olinordered__semidom(X39) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1377])])]) ).
fof(c_0_2634,plain,
! [X36,X37,X38,X39] :
( ( ~ c_Orderings_Oord__class_Oless(X39,hAPP(hAPP(c_Power_Opower__class_Opower(X39),X38),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X39),X38),X36))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X36)
| ~ c_Orderings_Oord__class_Oless(X39,c_Groups_Oone__class_Oone(X39),X38)
| ~ class_Rings_Olinordered__semidom(X39) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X36)
| c_Orderings_Oord__class_Oless(X39,hAPP(hAPP(c_Power_Opower__class_Opower(X39),X38),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X39),X38),X36))
| ~ c_Orderings_Oord__class_Oless(X39,c_Groups_Oone__class_Oone(X39),X38)
| ~ class_Rings_Olinordered__semidom(X39) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1378])])]) ).
fof(c_0_2635,plain,
! [X18,X19,X20,X21] :
( ~ class_Rings_Olinordered__semidom(X21)
| ~ c_Orderings_Oord__class_Oless(X21,c_Groups_Oone__class_Oone(X21),X20)
| ~ c_Orderings_Oord__class_Oless(X21,hAPP(hAPP(c_Power_Opower__class_Opower(X21),X20),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X21),X20),X18))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1379])]) ).
fof(c_0_2636,plain,
! [X40,X41,X42,X43,X44] :
( ~ class_Groups_Ocomm__monoid__add(X44)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X44),c_Polynomial_OpCons(X44,X43,X42),c_Polynomial_OpCons(X44,X41,X40)) = c_Polynomial_OpCons(X44,c_Groups_Oplus__class_Oplus(X44,X43,X41),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X44),X42,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1380])]) ).
fof(c_0_2637,plain,
! [X40,X41,X42,X43,X44] :
( ~ class_Groups_Oab__group__add(X44)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X44),c_Polynomial_OpCons(X44,X43,X42),c_Polynomial_OpCons(X44,X41,X40)) = c_Polynomial_OpCons(X44,c_Groups_Ominus__class_Ominus(X44,X43,X41),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X44),X42,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1381])]) ).
fof(c_0_2638,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__1(X43)
| hAPP(c_Polynomial_Opoly(X43,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X43)),X42),X41)),X40) = hAPP(hAPP(c_Power_Opower__class_Opower(X43),hAPP(c_Polynomial_Opoly(X43,X42),X40)),X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1382])]) ).
fof(c_0_2639,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Groups_Oab__group__add(X45)
| c_Groups_Ominus__class_Ominus(X45,c_Groups_Oplus__class_Oplus(X45,X44,X43),c_Groups_Oplus__class_Oplus(X45,X42,X41)) = c_Groups_Oplus__class_Oplus(X45,c_Groups_Ominus__class_Ominus(X45,X44,X42),c_Groups_Ominus__class_Ominus(X45,X43,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1383])]) ).
fof(c_0_2640,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Rings_Ocomm__semiring__1(X45)
| c_Groups_Oplus__class_Oplus(X45,c_Groups_Oplus__class_Oplus(X45,X44,X43),c_Groups_Oplus__class_Oplus(X45,X42,X41)) = c_Groups_Oplus__class_Oplus(X45,c_Groups_Oplus__class_Oplus(X45,X44,X42),c_Groups_Oplus__class_Oplus(X45,X43,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1384])]) ).
fof(c_0_2641,plain,
! [X35,X36,X37,X38] :
( ~ class_Rings_Olinordered__semidom(X38)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X36)
| ~ c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Ozero__class_Ozero(X38),X35)
| ~ c_Orderings_Oord__class_Oless__eq(X38,X35,c_Groups_Oone__class_Oone(X38))
| c_Orderings_Oord__class_Oless__eq(X38,hAPP(hAPP(c_Power_Opower__class_Opower(X38),X35),X36),hAPP(hAPP(c_Power_Opower__class_Opower(X38),X35),X37)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1385])]) ).
fof(c_0_2642,plain,
! [X35,X36,X37,X38] :
( ~ class_Rings_Olinordered__semidom(X38)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X36)
| ~ c_Orderings_Oord__class_Oless(X38,c_Groups_Ozero__class_Ozero(X38),X35)
| ~ c_Orderings_Oord__class_Oless(X38,X35,c_Groups_Oone__class_Oone(X38))
| c_Orderings_Oord__class_Oless(X38,hAPP(hAPP(c_Power_Opower__class_Opower(X38),X35),X36),hAPP(hAPP(c_Power_Opower__class_Opower(X38),X35),X37)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1386])]) ).
fof(c_0_2643,plain,
! [X25,X26,X27,X28] :
( ~ class_Rings_Olinordered__semidom(X28)
| ~ c_Orderings_Oord__class_Oless(X28,X27,X26)
| ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25)
| c_Orderings_Oord__class_Oless(X28,hAPP(hAPP(c_Power_Opower__class_Opower(X28),X27),X25),hAPP(hAPP(c_Power_Opower__class_Opower(X28),X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1387])]) ).
fof(c_0_2644,plain,
! [X34,X35,X36,X37] :
( ( c_Orderings_Oord__class_Oless(X37,X35,c_Groups_Ozero__class_Ozero(X37))
| c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X35)
| ~ c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X34),X35))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( c_Orderings_Oord__class_Oless(X37,X34,X36)
| c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X35)
| ~ c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X34),X35))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( c_Orderings_Oord__class_Oless(X37,X35,c_Groups_Ozero__class_Ozero(X37))
| c_Orderings_Oord__class_Oless(X37,X36,X34)
| ~ c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X34),X35))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( c_Orderings_Oord__class_Oless(X37,X34,X36)
| c_Orderings_Oord__class_Oless(X37,X36,X34)
| ~ c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X34),X35))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X35)
| ~ c_Orderings_Oord__class_Oless(X37,X36,X34)
| c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X34),X35))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( ~ c_Orderings_Oord__class_Oless(X37,X35,c_Groups_Ozero__class_Ozero(X37))
| ~ c_Orderings_Oord__class_Oless(X37,X34,X36)
| c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X34),X35))
| ~ class_Rings_Olinordered__ring__strict(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1388])])]) ).
fof(c_0_2645,plain,
! [X34,X35,X36,X37] :
( ( c_Orderings_Oord__class_Oless(X37,X36,c_Groups_Ozero__class_Ozero(X37))
| c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X36)
| ~ c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( c_Orderings_Oord__class_Oless(X37,X34,X35)
| c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X36)
| ~ c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( c_Orderings_Oord__class_Oless(X37,X36,c_Groups_Ozero__class_Ozero(X37))
| c_Orderings_Oord__class_Oless(X37,X35,X34)
| ~ c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( c_Orderings_Oord__class_Oless(X37,X34,X35)
| c_Orderings_Oord__class_Oless(X37,X35,X34)
| ~ c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X36)
| ~ c_Orderings_Oord__class_Oless(X37,X35,X34)
| c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ class_Rings_Olinordered__ring__strict(X37) )
& ( ~ c_Orderings_Oord__class_Oless(X37,X36,c_Groups_Ozero__class_Ozero(X37))
| ~ c_Orderings_Oord__class_Oless(X37,X34,X35)
| c_Orderings_Oord__class_Oless(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ class_Rings_Olinordered__ring__strict(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1389])])]) ).
fof(c_0_2646,plain,
! [X88,X89,X91] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk34_2(X88,X89))
| ~ class_RealVector_Oreal__normed__algebra(X89) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X89,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X89),X88),X91)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X89,X91)),esk34_2(X88,X89)))
| ~ class_RealVector_Oreal__normed__algebra(X89) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1390])])])])]) ).
fof(c_0_2647,plain,
! [X88,X89,X91] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_2(X88,X89))
| ~ class_RealVector_Oreal__normed__algebra(X89) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X89,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X89),X91),X88)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X89,X91)),esk33_2(X88,X89)))
| ~ class_RealVector_Oreal__normed__algebra(X89) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1391])])])])]) ).
fof(c_0_2648,plain,
! [X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__algebra(X14)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X14,X13)),c_RealVector_Onorm__class_Onorm(X14,X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1392])]) ).
fof(c_0_2649,plain,
! [X31,X32,X33,X34] :
( ~ class_RealVector_Oreal__normed__algebra(X34)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),c_Groups_Ominus__class_Ominus(X34,X33,X32)),X31) = c_Groups_Ominus__class_Ominus(X34,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),X33),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1393])]) ).
fof(c_0_2650,plain,
! [X30,X31,X32,X33] :
( ~ class_RealVector_Oreal__normed__algebra(X33)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),c_Groups_Ominus__class_Ominus(X33,X32,X31)),X30) = c_Groups_Ominus__class_Ominus(X33,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X32),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X31),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1394])]) ).
fof(c_0_2651,plain,
! [X25,X26,X27,X28] :
( ~ class_Rings_Ocomm__semiring__1(X28)
| c_Groups_Oplus__class_Oplus(X28,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28),X27),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28),X25),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28),c_Groups_Oplus__class_Oplus(X28,X27,X25)),X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1395])]) ).
fof(c_0_2652,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring__1(X31)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),c_Groups_Oplus__class_Oplus(X31,X30,X29)),X28) = c_Groups_Oplus__class_Oplus(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X29),X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1396])]) ).
fof(c_0_2653,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring(X31)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),c_Groups_Oplus__class_Oplus(X31,X30,X29)),X28) = c_Groups_Oplus__class_Oplus(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X29),X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1397])]) ).
fof(c_0_2654,plain,
! [X31,X32,X33,X34] :
( ~ class_RealVector_Oreal__normed__algebra(X34)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),c_Groups_Oplus__class_Oplus(X34,X33,X32)),X31) = c_Groups_Oplus__class_Oplus(X34,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),X33),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1398])]) ).
fof(c_0_2655,plain,
! [X30,X31,X32,X33] :
( ~ class_RealVector_Oreal__normed__algebra(X33)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),c_Groups_Oplus__class_Oplus(X33,X32,X31)),X30) = c_Groups_Oplus__class_Oplus(X33,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X32),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X31),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1399])]) ).
fof(c_0_2656,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__1(X43)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X43),hAPP(hAPP(c_Power_Opower__class_Opower(X43),X42),X41)),hAPP(hAPP(c_Power_Opower__class_Opower(X43),X42),X40)) = hAPP(hAPP(c_Power_Opower__class_Opower(X43),X42),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1400])]) ).
fof(c_0_2657,plain,
! [X18,X19,X20,X21] :
( ~ class_Groups_Omonoid__mult(X21)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21),X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21),hAPP(hAPP(c_Power_Opower__class_Opower(X21),X20),X19)),hAPP(hAPP(c_Power_Opower__class_Opower(X21),X20),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1401])]) ).
fof(c_0_2658,plain,
! [X45,X46,X47,X48] :
( ~ class_Rings_Ocomm__semiring__1(X48)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X48),X47),X46)),X45) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X48),X47),X45)),X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1402])]) ).
fof(c_0_2659,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X52))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X52),c_Nat_OSuc(X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1403])]) ).
fof(c_0_2660,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X52)),X50) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X51),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X52,X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1404])]) ).
fof(c_0_2661,plain,
! [X41,X42,X43,X44,X45,X46] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X46)
| X45 = c_Groups_Ozero__class_Ozero(X46)
| X44 != X43
| X42 = X41
| c_Groups_Oplus__class_Oplus(X46,X44,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X46),X45),X42)) != c_Groups_Oplus__class_Oplus(X46,X43,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X46),X45),X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1405])]) ).
fof(c_0_2662,plain,
! [X19,X20,X21] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X20),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X19))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X21)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1406])]) ).
fof(c_0_2663,plain,
! [X49,X50,X51] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X49))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X51)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X50,X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1407])]) ).
fof(c_0_2664,plain,
! [X51,X52,X53] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X52,X51)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X52,X51)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1408])])]) ).
fof(c_0_2665,plain,
! [X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X40),X39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X40),X38))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X40) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X40),X39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X40),X38))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X40) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1409])])]) ).
fof(c_0_2666,plain,
! [X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X39),X40),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X38),X40))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X40) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X39),X40),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X38),X40))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X40) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1410])])]) ).
fof(c_0_2667,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X56)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X54)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X55,X54)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X54)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1411])])])])]) ).
fof(c_0_2668,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X52))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X52)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X55)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X54),X55)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X54)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X54),X55)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1412])])])])]) ).
fof(c_0_2669,plain,
! [X51,X52,X53] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1413])])]) ).
fof(c_0_2670,plain,
! [X51,X52,X53] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1414])])]) ).
fof(c_0_2671,plain,
! [X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X39),X40),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X38),X40))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X39,X38)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X40) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X39,X38)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X39),X40),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X38),X40))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X40) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1415])])]) ).
fof(c_0_2672,plain,
! [X19,X20,X21] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X20),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X19))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1416])]) ).
fof(c_0_2673,plain,
! [X25,X26,X27] :
( ~ class_RealVector_Oreal__normed__vector(X27)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X27,X26),c_RealVector_Onorm__class_Onorm(X27,X25)),c_RealVector_Onorm__class_Onorm(X27,c_Groups_Ominus__class_Ominus(X27,X26,X25))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1417])]) ).
fof(c_0_2674,plain,
! [X25,X26,X27] :
( ~ class_RealVector_Oreal__normed__vector(X27)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X27,X26),c_RealVector_Onorm__class_Onorm(X27,X25)),c_RealVector_Onorm__class_Onorm(X27,c_Groups_Oplus__class_Oplus(X27,X26,X25))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1418])]) ).
fof(c_0_2675,plain,
! [X25,X26,X27] :
( ~ class_RealVector_Oreal__normed__vector(X27)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X27,c_Groups_Ominus__class_Ominus(X27,X26,X25)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X27,X26),c_RealVector_Onorm__class_Onorm(X27,X25))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1419])]) ).
fof(c_0_2676,plain,
! [X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__vector(X14)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,c_Groups_Oplus__class_Oplus(X14,X13,X12)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,X13),c_RealVector_Onorm__class_Onorm(X14,X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1420])]) ).
fof(c_0_2677,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),c_Polynomial_Osmult(X43,X42,X41)),X40) = c_Polynomial_Osmult(X43,X42,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1421])]) ).
fof(c_0_2678,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X53)),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X53)),X51))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X56)),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X56)),X54)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1422])])])]) ).
fof(c_0_2679,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X53)),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X53)),X51))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X55,X54)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X56)),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X56)),X54)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1423])])])]) ).
fof(c_0_2680,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| hAPP(c_Polynomial_Opoly(X43,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X43),X42,X41)),X40) = c_Groups_Oplus__class_Oplus(X43,hAPP(c_Polynomial_Opoly(X43,X42),X40),hAPP(c_Polynomial_Opoly(X43,X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1424])]) ).
fof(c_0_2681,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__ring(X43)
| hAPP(c_Polynomial_Opoly(X43,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X43),X42,X41)),X40) = c_Groups_Ominus__class_Ominus(X43,hAPP(c_Polynomial_Opoly(X43,X42),X40),hAPP(c_Polynomial_Opoly(X43,X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1425])]) ).
fof(c_0_2682,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Rings_Ocomm__semiring__1(X29)
| ~ c_Rings_Odvd__class_Odvd(X29,hAPP(hAPP(c_Power_Opower__class_Opower(X29),X28),X27),X26)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X27)
| c_Rings_Odvd__class_Odvd(X29,hAPP(hAPP(c_Power_Opower__class_Opower(X29),X28),X25),X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1426])]) ).
fof(c_0_2683,plain,
! [X49,X50] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X49)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X49),X50),X49) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X49),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1427])]) ).
fof(c_0_2684,plain,
! [X58,X59,X60] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X58,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X59,X60))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X58,X60),X59)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,X59) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X58,X60),X59)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X58,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X59,X60))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,X59) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1428])])]) ).
fof(c_0_2685,plain,
! [X23,X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X25,X24)),X23) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X23)),
inference(variable_rename,[status(thm)],[c_0_1429]) ).
fof(c_0_2686,plain,
! [X23,X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24)),X23) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X23)),
inference(variable_rename,[status(thm)],[c_0_1430]) ).
fof(c_0_2687,plain,
! [X49,X50,X51] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X50)),X49) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X49)),
inference(variable_rename,[status(thm)],[c_0_1431]) ).
fof(c_0_2688,plain,
! [X49,X50,X51] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50)),X49) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X49)),
inference(variable_rename,[status(thm)],[c_0_1432]) ).
fof(c_0_2689,plain,
! [X23,X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X25,X24)),X23) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X23)),
inference(variable_rename,[status(thm)],[c_0_1433]) ).
fof(c_0_2690,plain,
! [X10,X11,X12] :
( ~ class_RealVector_Oreal__normed__algebra__1(X12)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X12,hAPP(hAPP(c_Power_Opower__class_Opower(X12),X11),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X12,X11)),X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1434])]) ).
fof(c_0_2691,plain,
! [X34,X35,X36,X37] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X34,X35))
| c_Orderings_Oord__class_Oless__eq(X37,X36,X34)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X37,X36,X34)
| c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X34,X35))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1435])])]) ).
fof(c_0_2692,plain,
! [X34,X35,X36,X37] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X36,X34))
| c_Orderings_Oord__class_Oless__eq(X37,X35,X34)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X37,X35,X34)
| c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X36,X34))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1436])])]) ).
fof(c_0_2693,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Oplus__class_Oplus(X31,X30,X29),c_Groups_Oplus__class_Oplus(X31,X28,X29))
| c_Orderings_Oord__class_Oless__eq(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1437])]) ).
fof(c_0_2694,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Oplus__class_Oplus(X31,X30,X29),c_Groups_Oplus__class_Oplus(X31,X30,X28))
| c_Orderings_Oord__class_Oless__eq(X31,X29,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1438])]) ).
fof(c_0_2695,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X31)
| ~ c_Orderings_Oord__class_Oless(X31,c_Groups_Oplus__class_Oplus(X31,X30,X29),c_Groups_Oplus__class_Oplus(X31,X30,X28))
| c_Orderings_Oord__class_Oless(X31,X29,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1439])]) ).
fof(c_0_2696,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X31)
| ~ c_Orderings_Oord__class_Oless(X31,c_Groups_Oplus__class_Oplus(X31,X30,X29),c_Groups_Oplus__class_Oplus(X31,X28,X29))
| c_Orderings_Oord__class_Oless(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1440])]) ).
fof(c_0_2697,plain,
! [X34,X35,X36,X37] :
( ( ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X36,X34))
| c_Orderings_Oord__class_Oless(X37,X35,X34)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37) )
& ( ~ c_Orderings_Oord__class_Oless(X37,X35,X34)
| c_Orderings_Oord__class_Oless(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X36,X34))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1441])])]) ).
fof(c_0_2698,plain,
! [X34,X35,X36,X37] :
( ( ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X34,X35))
| c_Orderings_Oord__class_Oless(X37,X36,X34)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37) )
& ( ~ c_Orderings_Oord__class_Oless(X37,X36,X34)
| c_Orderings_Oord__class_Oless(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X34,X35))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1442])])]) ).
fof(c_0_2699,plain,
! [X49,X50,X51] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X50)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X49)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,X51),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X51)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1443])]) ).
fof(c_0_2700,plain,
! [X34,X35,X36,X37] :
( ( ~ c_Rings_Odvd__class_Odvd(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X34),X35))
| X35 = c_Groups_Ozero__class_Ozero(X37)
| c_Rings_Odvd__class_Odvd(X37,X36,X34)
| ~ class_Rings_Oidom(X37) )
& ( X35 != c_Groups_Ozero__class_Ozero(X37)
| c_Rings_Odvd__class_Odvd(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X34),X35))
| ~ class_Rings_Oidom(X37) )
& ( ~ c_Rings_Odvd__class_Odvd(X37,X36,X34)
| c_Rings_Odvd__class_Odvd(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X34),X35))
| ~ class_Rings_Oidom(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1444])])]) ).
fof(c_0_2701,plain,
! [X34,X35,X36,X37] :
( ( ~ c_Rings_Odvd__class_Odvd(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| X36 = c_Groups_Ozero__class_Ozero(X37)
| c_Rings_Odvd__class_Odvd(X37,X35,X34)
| ~ class_Rings_Oidom(X37) )
& ( X36 != c_Groups_Ozero__class_Ozero(X37)
| c_Rings_Odvd__class_Odvd(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ class_Rings_Oidom(X37) )
& ( ~ c_Rings_Odvd__class_Odvd(X37,X35,X34)
| c_Rings_Odvd__class_Odvd(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X37),X36),X34))
| ~ class_Rings_Oidom(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1445])])]) ).
fof(c_0_2702,plain,
! [X53,X54,X55] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X54,X55)
| hBOOL(hAPP(hAPP(X53,X54),X55))
| X55 = X54
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54) )
& ( ~ hBOOL(hAPP(hAPP(X53,X54),X55))
| hBOOL(hAPP(hAPP(X53,X54),X55))
| X55 = X54
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X54,X55)
| hBOOL(hAPP(hAPP(X53,X54),X55))
| ~ hBOOL(hAPP(hAPP(X53,X54),X55))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54) )
& ( ~ hBOOL(hAPP(hAPP(X53,X54),X55))
| hBOOL(hAPP(hAPP(X53,X54),X55))
| ~ hBOOL(hAPP(hAPP(X53,X54),X55))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X54,X55)
| hBOOL(hAPP(hAPP(X53,X54),X55))
| X55 = X54
| ~ hBOOL(hAPP(hAPP(X53,X54),X55)) )
& ( ~ hBOOL(hAPP(hAPP(X53,X54),X55))
| hBOOL(hAPP(hAPP(X53,X54),X55))
| X55 = X54
| ~ hBOOL(hAPP(hAPP(X53,X54),X55)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X54,X55)
| hBOOL(hAPP(hAPP(X53,X54),X55))
| ~ hBOOL(hAPP(hAPP(X53,X54),X55))
| ~ hBOOL(hAPP(hAPP(X53,X54),X55)) )
& ( ~ hBOOL(hAPP(hAPP(X53,X54),X55))
| hBOOL(hAPP(hAPP(X53,X54),X55))
| ~ hBOOL(hAPP(hAPP(X53,X54),X55))
| ~ hBOOL(hAPP(hAPP(X53,X54),X55)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1446])])]) ).
fof(c_0_2703,plain,
! [X9,X10,X11] :
( ~ class_Rings_Olinordered__semidom(X11)
| ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Oone__class_Oone(X11),X10)
| c_Orderings_Oord__class_Oless(X11,c_Groups_Oone__class_Oone(X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1447])]) ).
fof(c_0_2704,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk3_0),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1448])])]) ).
fof(c_0_2705,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_1449 ).
fof(c_0_2706,plain,
! [X49,X50,X51] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X51,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,X49))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X51,X50)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49,X50)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X51,X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1450])]) ).
fof(c_0_2707,plain,
! [X49,X50,X51] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X51,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,X49))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X51,X49)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49,X50)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X51,X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1451])]) ).
fof(c_0_2708,plain,
! [X24,X25,X26] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X24)),
inference(variable_rename,[status(thm)],[c_0_1452]) ).
fof(c_0_2709,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X43),c_Polynomial_Osmult(X43,X42,X41),c_Polynomial_OpCons(X43,X40,X41)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X43))
| X41 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1453])]) ).
fof(c_0_2710,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X52),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X55,X54)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X55),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X54)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1454])])])]) ).
fof(c_0_2711,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X52),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X55),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X54)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1455])])])]) ).
fof(c_0_2712,plain,
! [X39,X40,X41] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X41)
| X41 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X40,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X41),X39))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X40)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1456])]) ).
fof(c_0_2713,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
c_0_1457 ).
fof(c_0_2714,plain,
! [X39,X40,X41] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X41)
| X41 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X40,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X41),X39))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X40,X41)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X39) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1458])]) ).
fof(c_0_2715,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| c_Polynomial_Osmult(X43,X42,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X43),X41,X40)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X43),c_Polynomial_Osmult(X43,X42,X41),c_Polynomial_Osmult(X43,X42,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1459])]) ).
fof(c_0_2716,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__ring(X43)
| c_Polynomial_Osmult(X43,X42,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X43),X41,X40)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X43),c_Polynomial_Osmult(X43,X42,X41),c_Polynomial_Osmult(X43,X42,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1460])]) ).
fof(c_0_2717,plain,
! [X25,X26,X27,X28] :
( ~ class_Rings_Olinordered__semidom(X28)
| hAPP(hAPP(c_Power_Opower__class_Opower(X28),X27),X26) != hAPP(hAPP(c_Power_Opower__class_Opower(X28),X25),X26)
| ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X25)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)
| X27 = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1461])]) ).
fof(c_0_2718,plain,
! [X18,X19,X20] :
( ~ class_Rings_Ocomm__semiring__1(X20)
| c_Groups_Oplus__class_Oplus(X20,X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X18),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),c_Groups_Oplus__class_Oplus(X20,X18,c_Groups_Oone__class_Oone(X20))),X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1462])]) ).
fof(c_0_2719,plain,
! [X18,X19,X20] :
( ~ class_Rings_Ocomm__semiring__1(X20)
| c_Groups_Oplus__class_Oplus(X20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X19),X18),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),c_Groups_Oplus__class_Oplus(X20,X19,c_Groups_Oone__class_Oone(X20))),X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1463])]) ).
fof(c_0_2720,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__idom(X14)
| ~ c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14),X13)
| ~ c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14),X12)
| ~ c_Orderings_Oord__class_Oless__eq(X14,X12,c_Groups_Oone__class_Oone(X14))
| c_Orderings_Oord__class_Oless__eq(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X12),X13),X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1464])]) ).
fof(c_0_2721,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__idom(X14)
| ~ c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14),X13)
| ~ c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14),X12)
| ~ c_Orderings_Oord__class_Oless__eq(X14,X12,c_Groups_Oone__class_Oone(X14))
| c_Orderings_Oord__class_Oless__eq(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12),X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1465])]) ).
fof(c_0_2722,plain,
! [X28,X29,X30,X31] :
( ~ class_RealVector_Oreal__normed__vector(X31)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X30,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X31,X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),c_RealVector_Onorm__class_Onorm(X31,X28)))
| X29 = c_Groups_Ozero__class_Ozero(X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1466])]) ).
fof(c_0_2723,plain,
! [X25,X26,X27,X28] :
( ~ class_Rings_Olinordered__semidom(X28)
| ~ c_Orderings_Oord__class_Oless__eq(X28,X27,X26)
| ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| c_Orderings_Oord__class_Oless__eq(X28,hAPP(hAPP(c_Power_Opower__class_Opower(X28),X27),X25),hAPP(hAPP(c_Power_Opower__class_Opower(X28),X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1467])]) ).
fof(c_0_2724,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Oordered__ring(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X30,X29)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X28,c_Groups_Ozero__class_Ozero(X31))
| c_Orderings_Oord__class_Oless__eq(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1468])]) ).
fof(c_0_2725,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Oordered__ring(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X30,X29)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X28,c_Groups_Ozero__class_Ozero(X31))
| c_Orderings_Oord__class_Oless__eq(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X29),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1469])]) ).
fof(c_0_2726,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Oordered__comm__semiring(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X30,X29)
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31),X28)
| c_Orderings_Oord__class_Oless__eq(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1470])]) ).
fof(c_0_2727,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Oordered__semiring(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X30,X29)
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31),X28)
| c_Orderings_Oord__class_Oless__eq(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1471])]) ).
fof(c_0_2728,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Oordered__semiring(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X30,X29)
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31),X28)
| c_Orderings_Oord__class_Oless__eq(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X29),X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1472])]) ).
fof(c_0_2729,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring__strict(X31)
| ~ c_Orderings_Oord__class_Oless(X31,X30,X29)
| ~ c_Orderings_Oord__class_Oless(X31,c_Groups_Ozero__class_Ozero(X31),X28)
| c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X29),X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1473])]) ).
fof(c_0_2730,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring__strict(X31)
| ~ c_Orderings_Oord__class_Oless(X31,X30,X29)
| ~ c_Orderings_Oord__class_Oless(X31,c_Groups_Ozero__class_Ozero(X31),X28)
| c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1474])]) ).
fof(c_0_2731,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X31)
| ~ c_Orderings_Oord__class_Oless(X31,X30,X29)
| ~ c_Orderings_Oord__class_Oless(X31,c_Groups_Ozero__class_Ozero(X31),X28)
| c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1475])]) ).
fof(c_0_2732,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__ring__strict(X31)
| ~ c_Orderings_Oord__class_Oless(X31,X30,X29)
| ~ c_Orderings_Oord__class_Oless(X31,X28,c_Groups_Ozero__class_Ozero(X31))
| c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X29),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1476])]) ).
fof(c_0_2733,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__ring__strict(X31)
| ~ c_Orderings_Oord__class_Oless(X31,X30,X29)
| ~ c_Orderings_Oord__class_Oless(X31,X28,c_Groups_Ozero__class_Ozero(X31))
| c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1477])]) ).
fof(c_0_2734,plain,
! [X49,X50,X51] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X50)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X49),X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1478])]) ).
fof(c_0_2735,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X45)
| ~ c_Orderings_Oord__class_Oless__eq(X45,X44,X43)
| ~ c_Orderings_Oord__class_Oless(X45,X42,X41)
| c_Orderings_Oord__class_Oless(X45,c_Groups_Oplus__class_Oplus(X45,X44,X42),c_Groups_Oplus__class_Oplus(X45,X43,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1479])]) ).
fof(c_0_2736,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X45)
| ~ c_Orderings_Oord__class_Oless(X45,X44,X43)
| ~ c_Orderings_Oord__class_Oless__eq(X45,X42,X41)
| c_Orderings_Oord__class_Oless(X45,c_Groups_Oplus__class_Oplus(X45,X44,X42),c_Groups_Oplus__class_Oplus(X45,X43,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1480])]) ).
fof(c_0_2737,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Groups_Oordered__ab__semigroup__add(X45)
| ~ c_Orderings_Oord__class_Oless__eq(X45,X44,X43)
| ~ c_Orderings_Oord__class_Oless__eq(X45,X42,X41)
| c_Orderings_Oord__class_Oless__eq(X45,c_Groups_Oplus__class_Oplus(X45,X44,X42),c_Groups_Oplus__class_Oplus(X45,X43,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1481])]) ).
fof(c_0_2738,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X45)
| ~ c_Orderings_Oord__class_Oless(X45,X44,X43)
| ~ c_Orderings_Oord__class_Oless(X45,X42,X41)
| c_Orderings_Oord__class_Oless(X45,c_Groups_Oplus__class_Oplus(X45,X44,X42),c_Groups_Oplus__class_Oplus(X45,X43,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1482])]) ).
fof(c_0_2739,plain,
! [X35,X36,X37,X38] :
( ~ class_Rings_Olinordered__semidom(X38)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X36)
| ~ c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Oone__class_Oone(X38),X35)
| c_Orderings_Oord__class_Oless__eq(X38,hAPP(hAPP(c_Power_Opower__class_Opower(X38),X35),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X38),X35),X36)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1483])]) ).
fof(c_0_2740,plain,
! [X35,X36,X37,X38] :
( ~ class_Rings_Olinordered__semidom(X38)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X36)
| ~ c_Orderings_Oord__class_Oless(X38,c_Groups_Oone__class_Oone(X38),X35)
| c_Orderings_Oord__class_Oless(X38,hAPP(hAPP(c_Power_Opower__class_Opower(X38),X35),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X38),X35),X36)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1484])]) ).
fof(c_0_2741,plain,
! [X25,X26,X27,X28] :
( ~ class_Groups_Ocomm__monoid__add(X28)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X28),c_Polynomial_Omonom(X28,X27,X26),c_Polynomial_Omonom(X28,X25,X26)) = c_Polynomial_Omonom(X28,c_Groups_Oplus__class_Oplus(X28,X27,X25),X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1485])]) ).
fof(c_0_2742,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| c_Polynomial_Osmult(X43,c_Groups_Oplus__class_Oplus(X43,X42,X41),X40) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X43),c_Polynomial_Osmult(X43,X42,X40),c_Polynomial_Osmult(X43,X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1486])]) ).
fof(c_0_2743,plain,
! [X25,X26,X27,X28] :
( ~ class_Groups_Oab__group__add(X28)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X28),c_Polynomial_Omonom(X28,X27,X26),c_Polynomial_Omonom(X28,X25,X26)) = c_Polynomial_Omonom(X28,c_Groups_Ominus__class_Ominus(X28,X27,X25),X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1487])]) ).
fof(c_0_2744,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__ring(X43)
| c_Polynomial_Osmult(X43,c_Groups_Ominus__class_Ominus(X43,X42,X41),X40) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X43),c_Polynomial_Osmult(X43,X42,X40),c_Polynomial_Osmult(X43,X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1488])]) ).
fof(c_0_2745,plain,
! [X41,X42,X43,X44,X45] :
( ~ class_Rings_Ocomm__semiring__1(X45)
| ~ c_Rings_Odvd__class_Odvd(X45,X44,X43)
| ~ c_Rings_Odvd__class_Odvd(X45,X42,X41)
| c_Rings_Odvd__class_Odvd(X45,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X44),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X45),X43),X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1489])]) ).
fof(c_0_2746,plain,
! [X18,X19,X20] :
( ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20),X18),X19) = c_Groups_Oone__class_Oone(X20)
| ~ class_Power_Opower(X20) )
& ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20),X18),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X20),X18),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1490])])]) ).
fof(c_0_2747,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Rings_Ocomm__semiring__1(X22)
| ~ c_Rings_Odvd__class_Odvd(X22,X21,X20)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| c_Rings_Odvd__class_Odvd(X22,hAPP(hAPP(c_Power_Opower__class_Opower(X22),X21),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X22),X20),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1491])]) ).
fof(c_0_2748,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| c_Polynomial_Osmult(X43,X42,c_Polynomial_OpCons(X43,X41,X40)) = c_Polynomial_OpCons(X43,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X43),X42),X41),c_Polynomial_Osmult(X43,X42,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1492])]) ).
fof(c_0_2749,plain,
! [X28,X29,X30] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X29)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X30)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X28),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1493])]) ).
fof(c_0_2750,plain,
! [X55,X56,X57,X58] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X58,X57)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X58,X56),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X55)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1494])]) ).
fof(c_0_2751,plain,
! [X71,X72,X73,X74] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X74,X73)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X72,X71)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X74,X72),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X73,X71)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1495])]) ).
fof(c_0_2752,plain,
! [X55,X56,X57] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,X56)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,X55)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X56),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X57)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1496])]) ).
fof(c_0_2753,plain,
! [X55,X56,X57,X58] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X57)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X55)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X58,X56),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X55)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1497])]) ).
fof(c_0_2754,plain,
! [X36,X37,X38] :
( ( X37 = c_Groups_Ozero__class_Ozero(X38)
| c_Groups_Oplus__class_Oplus(X38,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X36),X36)) != c_Groups_Ozero__class_Ozero(X38)
| ~ class_Rings_Olinordered__ring__strict(X38) )
& ( X36 = c_Groups_Ozero__class_Ozero(X38)
| c_Groups_Oplus__class_Oplus(X38,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X36),X36)) != c_Groups_Ozero__class_Ozero(X38)
| ~ class_Rings_Olinordered__ring__strict(X38) )
& ( X37 != c_Groups_Ozero__class_Ozero(X38)
| X36 != c_Groups_Ozero__class_Ozero(X38)
| c_Groups_Oplus__class_Oplus(X38,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X36),X36)) = c_Groups_Ozero__class_Ozero(X38)
| ~ class_Rings_Olinordered__ring__strict(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1498])])]) ).
fof(c_0_2755,plain,
! [X33,X34,X35,X36] :
( ~ class_RealVector_Oreal__normed__algebra(X36)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X36),X35),c_Groups_Ominus__class_Ominus(X36,X34,X33)) = c_Groups_Ominus__class_Ominus(X36,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X36),X35),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X36),X35),X33)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1499])]) ).
fof(c_0_2756,plain,
! [X32,X33,X34,X35] :
( ~ class_RealVector_Oreal__normed__algebra(X35)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X35),X34),c_Groups_Ominus__class_Ominus(X35,X33,X32)) = c_Groups_Ominus__class_Ominus(X35,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X35),X34),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X35),X34),X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1500])]) ).
fof(c_0_2757,plain,
! [X24,X25,X26,X27] :
( ~ class_Rings_Ocomm__semiring__1(X27)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),c_Groups_Oplus__class_Oplus(X27,X25,X24)) = c_Groups_Oplus__class_Oplus(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1501])]) ).
fof(c_0_2758,plain,
! [X33,X34,X35,X36] :
( ~ class_RealVector_Oreal__normed__algebra(X36)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X36),X35),c_Groups_Oplus__class_Oplus(X36,X34,X33)) = c_Groups_Oplus__class_Oplus(X36,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X36),X35),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X36),X35),X33)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1502])]) ).
fof(c_0_2759,plain,
! [X32,X33,X34,X35] :
( ~ class_RealVector_Oreal__normed__algebra(X35)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X35),X34),c_Groups_Oplus__class_Oplus(X35,X33,X32)) = c_Groups_Oplus__class_Oplus(X35,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X35),X34),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X35),X34),X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1503])]) ).
fof(c_0_2760,plain,
! [X25,X26,X27] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X27),X26),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X25),X26))
| X26 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X27,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1504])]) ).
fof(c_0_2761,plain,
! [X27,X28,X29] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X28),X29),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X27),X29))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X28,X27)
| X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X28,X27)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X28),X29),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X27),X29))
| X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1505])])]) ).
fof(c_0_2762,plain,
! [X27,X28,X29] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X29),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X27),X29))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X28,X27)
| X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X28,X27)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X29),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X27),X29))
| X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1506])])]) ).
fof(c_0_2763,plain,
! [X25,X26,X27] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X27),X26),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X26))
| X26 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X27,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1507])]) ).
fof(c_0_2764,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51))
| X53 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X52,X51) )
& ( X56 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X54)) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X55,X54)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X54)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1508])])])])]) ).
fof(c_0_2765,plain,
! [X49,X50,X51] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),X49))
| X51 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X50,X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1509])]) ).
fof(c_0_2766,plain,
! [X84,X85,X86] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X85,X84)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X86),X85),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X86),X84))
| X86 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X86),X85),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X86),X84))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X85,X84)
| X86 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1510])])]) ).
fof(c_0_2767,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X52)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X52)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X52)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X55)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X54)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X54),X55)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1511])])])])]) ).
fof(c_0_2768,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X56)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X54)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1512])])])])]) ).
fof(c_0_2769,plain,
! [X25,X26,X27] :
( ~ class_Rings_Olinordered__semiring__strict(X27)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25))
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1513])]) ).
fof(c_0_2770,plain,
! [X25,X26,X27] :
( ~ class_Rings_Olinordered__semiring__strict(X27)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25))
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1514])]) ).
fof(c_0_2771,plain,
! [X45,X46,X47,X48] :
( ~ class_Rings_Ocomm__semiring__1(X48)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X48),X47),X46)),X45) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X48),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X48),X46),X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1515])]) ).
fof(c_0_2772,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oab__semigroup__mult(X31)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29)),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X29),X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1516])]) ).
fof(c_0_2773,plain,
! [X44,X45,X46,X47] :
( ~ class_Rings_Ocomm__semiring__1(X47)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X47),X46),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X47),X45),X44)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X47),X46),X45)),X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1517])]) ).
fof(c_0_2774,plain,
! [X9,X10,X11] :
( ~ class_Groups_Omonoid__mult(X11)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1518])]) ).
fof(c_0_2775,plain,
! [X10,X11,X12,X13] :
( ~ class_Rings_Ocomm__semiring__1(X13)
| hAPP(c_Polynomial_Opoly(X13,c_Polynomial_Omonom(X13,X12,X11)),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X13),X10),X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1519])]) ).
fof(c_0_2776,plain,
! [X40,X41,X42,X43,X44] :
( ( X40 = hAPP(c_Polynomial_Opoly(X44,X43),X42)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X44),X43,c_Polynomial_Osmult(X44,X42,X41)) != c_Polynomial_OpCons(X44,X40,X41)
| ~ class_Rings_Ocomm__semiring__0(X44) )
& ( X41 = c_Polynomial_Osynthetic__div(X44,X43,X42)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X44),X43,c_Polynomial_Osmult(X44,X42,X41)) != c_Polynomial_OpCons(X44,X40,X41)
| ~ class_Rings_Ocomm__semiring__0(X44) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1520])])]) ).
fof(c_0_2777,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| c_Polynomial_Osynthetic__div(X43,c_Polynomial_OpCons(X43,X42,X41),X40) = c_Polynomial_OpCons(X43,hAPP(c_Polynomial_Opoly(X43,X41),X40),c_Polynomial_Osynthetic__div(X43,X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1521])]) ).
fof(c_0_2778,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__1(X43)
| hAPP(hAPP(c_Power_Opower__class_Opower(X43),hAPP(hAPP(c_Power_Opower__class_Opower(X43),X42),X41)),X40) = hAPP(hAPP(c_Power_Opower__class_Opower(X43),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1522])]) ).
fof(c_0_2779,plain,
! [X18,X19,X20,X21] :
( ~ class_Groups_Omonoid__mult(X21)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X18)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21),hAPP(hAPP(c_Power_Opower__class_Opower(X21),X20),X19)),X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1523])]) ).
fof(c_0_2780,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X52,X51)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1524])]) ).
fof(c_0_2781,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X52),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1525])]) ).
fof(c_0_2782,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1526])]) ).
fof(c_0_2783,plain,
! [X24,X25,X26] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X26)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X25,X24)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1527])]) ).
fof(c_0_2784,plain,
! [X40,X41,X42,X43] :
( ( X41 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X40),X41) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X43 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X42),X43) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X42),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1528])])])]) ).
fof(c_0_2785,plain,
! [X58,X59,X60,X61,X62,X63] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X60,X59),X58)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X58,X59)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X63,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X61,X62))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X63,X62),X61) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1529])])])]) ).
fof(c_0_2786,plain,
! [X58,X59,X60,X61,X62,X63] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X60,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X59,X58))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X60,X58),X59) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,X61),X62)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X63,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X62,X61)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1530])])])]) ).
fof(c_0_2787,plain,
! [X55,X56,X57,X58] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X58,X57)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X58),X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X55)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1531])]) ).
fof(c_0_2788,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X52)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X52),X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1532])]) ).
fof(c_0_2789,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X52)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X51),X52) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1533])]) ).
fof(c_0_2790,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X51),X52) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X52)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1534])]) ).
fof(c_0_2791,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X52),X50) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),X52) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1535])]) ).
fof(c_0_2792,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),X52) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X52),X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1536])]) ).
fof(c_0_2793,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),X42),c_Polynomial_Osmult(X43,X41,X40)) = c_Polynomial_Osmult(X43,X41,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X43)),X42),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1537])]) ).
fof(c_0_2794,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| hAPP(c_Polynomial_Opoly(X43,c_Polynomial_Osmult(X43,X42,X41)),X40) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X43),X42),hAPP(c_Polynomial_Opoly(X43,X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1538])]) ).
fof(c_0_2795,plain,
! [X27,X28,X29] :
( ( c_Orderings_Oord__class_Oless__eq(X29,X28,c_Groups_Ozero__class_Ozero(X29))
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X28)
| ~ c_Orderings_Oord__class_Oless__eq(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27),c_Groups_Ozero__class_Ozero(X29))
| ~ class_Rings_Olinordered__ring__strict(X29) )
& ( c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X27)
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X28)
| ~ c_Orderings_Oord__class_Oless__eq(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27),c_Groups_Ozero__class_Ozero(X29))
| ~ class_Rings_Olinordered__ring__strict(X29) )
& ( c_Orderings_Oord__class_Oless__eq(X29,X28,c_Groups_Ozero__class_Ozero(X29))
| c_Orderings_Oord__class_Oless__eq(X29,X27,c_Groups_Ozero__class_Ozero(X29))
| ~ c_Orderings_Oord__class_Oless__eq(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27),c_Groups_Ozero__class_Ozero(X29))
| ~ class_Rings_Olinordered__ring__strict(X29) )
& ( c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X27)
| c_Orderings_Oord__class_Oless__eq(X29,X27,c_Groups_Ozero__class_Ozero(X29))
| ~ c_Orderings_Oord__class_Oless__eq(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27),c_Groups_Ozero__class_Ozero(X29))
| ~ class_Rings_Olinordered__ring__strict(X29) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X28)
| ~ c_Orderings_Oord__class_Oless__eq(X29,X27,c_Groups_Ozero__class_Ozero(X29))
| c_Orderings_Oord__class_Oless__eq(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27),c_Groups_Ozero__class_Ozero(X29))
| ~ class_Rings_Olinordered__ring__strict(X29) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X29,X28,c_Groups_Ozero__class_Ozero(X29))
| ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X27)
| c_Orderings_Oord__class_Oless__eq(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27),c_Groups_Ozero__class_Ozero(X29))
| ~ class_Rings_Olinordered__ring__strict(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1539])])]) ).
fof(c_0_2796,plain,
! [X27,X28,X29] :
( ( c_Orderings_Oord__class_Oless__eq(X29,X28,c_Groups_Ozero__class_Ozero(X29))
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X28)
| ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27))
| ~ class_Rings_Olinordered__ring__strict(X29) )
& ( c_Orderings_Oord__class_Oless__eq(X29,X27,c_Groups_Ozero__class_Ozero(X29))
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X28)
| ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27))
| ~ class_Rings_Olinordered__ring__strict(X29) )
& ( c_Orderings_Oord__class_Oless__eq(X29,X28,c_Groups_Ozero__class_Ozero(X29))
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X27)
| ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27))
| ~ class_Rings_Olinordered__ring__strict(X29) )
& ( c_Orderings_Oord__class_Oless__eq(X29,X27,c_Groups_Ozero__class_Ozero(X29))
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X27)
| ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27))
| ~ class_Rings_Olinordered__ring__strict(X29) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X28)
| ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),X27)
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27))
| ~ class_Rings_Olinordered__ring__strict(X29) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X29,X28,c_Groups_Ozero__class_Ozero(X29))
| ~ c_Orderings_Oord__class_Oless__eq(X29,X27,c_Groups_Ozero__class_Ozero(X29))
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ozero__class_Ozero(X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27))
| ~ class_Rings_Olinordered__ring__strict(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1540])])]) ).
fof(c_0_2797,plain,
! [X25,X26,X27,X28] :
( ~ class_Rings_Olinordered__semidom(X28)
| hAPP(hAPP(c_Power_Opower__class_Opower(X28),X27),c_Nat_OSuc(X26)) != hAPP(hAPP(c_Power_Opower__class_Opower(X28),X25),c_Nat_OSuc(X26))
| ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X25)
| X27 = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1541])]) ).
fof(c_0_2798,plain,
! [X18,X19,X20,X21] :
( ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18) = X18 )
& ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X20) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1542])])])]) ).
fof(c_0_2799,plain,
! [X49,X50,X51] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X51,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X50,X49))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X51,X49)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X51,X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1543])]) ).
fof(c_0_2800,plain,
! [X23,X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X24,X23)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X23)),
inference(variable_rename,[status(thm)],[c_0_1544]) ).
fof(c_0_2801,plain,
! [X23,X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,X23)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X23)),
inference(variable_rename,[status(thm)],[c_0_1545]) ).
fof(c_0_2802,plain,
! [X49,X50,X51] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,X49)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X49)),
inference(variable_rename,[status(thm)],[c_0_1546]) ).
fof(c_0_2803,plain,
! [X49,X50,X51] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X49)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X49)),
inference(variable_rename,[status(thm)],[c_0_1547]) ).
fof(c_0_2804,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| hAPP(c_Polynomial_Opoly(X43,c_Polynomial_Opcompose(X43,X42,X41)),X40) = hAPP(c_Polynomial_Opoly(X43,X42),hAPP(c_Polynomial_Opoly(X43,X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1548])]) ).
fof(c_0_2805,plain,
! [X18,X19] :
( ~ class_Rings_Ocomm__semiring__1(X19)
| c_Groups_Oplus__class_Oplus(X19,X18,X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oplus__class_Oplus(X19,c_Groups_Oone__class_Oone(X19),c_Groups_Oone__class_Oone(X19))),X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1549])]) ).
fof(c_0_2806,plain,
! [X15,X16,X17] :
( ~ class_RealVector_Oreal__normed__div__algebra(X17)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,c_RealVector_Onorm__class_Onorm(X17,X15))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X16)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X17,c_Rings_Oinverse__class_Oinverse(X17,X15)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1550])]) ).
fof(c_0_2807,plain,
! [X9,X10,X11] :
( ~ class_Rings_Olinordered__semidom(X11)
| ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Ozero__class_Ozero(X11),X10)
| ~ c_Orderings_Oord__class_Oless(X11,X10,c_Groups_Oone__class_Oone(X11))
| c_Orderings_Oord__class_Oless(X11,hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),c_Nat_OSuc(X9)),c_Groups_Oone__class_Oone(X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1551])]) ).
fof(c_0_2808,plain,
! [X36,X37,X38,X39] :
( ( X37 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X36)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X36 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X37),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X36)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X39 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X38 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X39),X39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X38),X38)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1552])])])])]) ).
fof(c_0_2809,plain,
! [X48] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X48))),
inference(variable_rename,[status(thm)],[c_0_1553]) ).
fof(c_0_2810,plain,
! [X15,X16,X17] :
( ~ class_Rings_Olinordered__semidom(X17)
| ~ c_Orderings_Oord__class_Oless__eq(X17,c_Groups_Ozero__class_Ozero(X17),X16)
| ~ c_Orderings_Oord__class_Oless__eq(X17,X16,c_Groups_Oone__class_Oone(X17))
| c_Orderings_Oord__class_Oless__eq(X17,hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),c_Nat_OSuc(X15)),X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1554])]) ).
fof(c_0_2811,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oordered__comm__monoid__add(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,c_Groups_Ozero__class_Ozero(X27))
| ~ c_Orderings_Oord__class_Oless(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless(X27,c_Groups_Oplus__class_Oplus(X27,X26,X25),c_Groups_Ozero__class_Ozero(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1555])]) ).
fof(c_0_2812,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oordered__comm__monoid__add(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,c_Groups_Ozero__class_Ozero(X27))
| ~ c_Orderings_Oord__class_Oless__eq(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless(X27,c_Groups_Oplus__class_Oplus(X27,X26,X25),c_Groups_Ozero__class_Ozero(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1556])]) ).
fof(c_0_2813,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oordered__comm__monoid__add(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),c_Groups_Oplus__class_Oplus(X27,X26,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1557])]) ).
fof(c_0_2814,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oordered__comm__monoid__add(X27)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),c_Groups_Oplus__class_Oplus(X27,X26,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1558])]) ).
fof(c_0_2815,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oordered__comm__monoid__add(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,c_Groups_Ozero__class_Ozero(X27))
| ~ c_Orderings_Oord__class_Oless__eq(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Oplus__class_Oplus(X27,X26,X25),c_Groups_Ozero__class_Ozero(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1559])]) ).
fof(c_0_2816,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oordered__comm__monoid__add(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),c_Groups_Oplus__class_Oplus(X27,X26,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1560])]) ).
fof(c_0_2817,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oordered__comm__monoid__add(X27)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),c_Groups_Oplus__class_Oplus(X27,X26,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1561])]) ).
fof(c_0_2818,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oordered__comm__monoid__add(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,c_Groups_Ozero__class_Ozero(X27))
| ~ c_Orderings_Oord__class_Oless(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless(X27,c_Groups_Oplus__class_Oplus(X27,X26,X25),c_Groups_Ozero__class_Ozero(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1562])]) ).
fof(c_0_2819,plain,
! [X37,X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X38)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X37) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X40)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X39)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1563])])])])]) ).
fof(c_0_2820,plain,
! [X22,X23,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X23)),X22) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X22)),
inference(variable_rename,[status(thm)],[c_0_1564]) ).
fof(c_0_2821,plain,
! [X24,X25,X26] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X25)),X24) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X24)),
inference(variable_rename,[status(thm)],[c_0_1565]) ).
fof(c_0_2822,plain,
! [X49,X50,X51] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X50)),X49) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X49)),
inference(variable_rename,[status(thm)],[c_0_1566]) ).
fof(c_0_2823,plain,
! [X22,X23,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X23)),X22) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X22)),
inference(variable_rename,[status(thm)],[c_0_1567]) ).
fof(c_0_2824,plain,
! [X25,X26,X27] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless__eq(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25),c_Groups_Ozero__class_Ozero(X27))
| ~ class_Rings_Oordered__cancel__semiring(X27) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X27,X26,c_Groups_Ozero__class_Ozero(X27))
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless__eq(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25),c_Groups_Ozero__class_Ozero(X27))
| ~ class_Rings_Oordered__cancel__semiring(X27) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1568])])]) ).
fof(c_0_2825,plain,
! [X25,X26,X27] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25))
| ~ class_Rings_Oordered__ring(X27) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X27,X26,c_Groups_Ozero__class_Ozero(X27))
| ~ c_Orderings_Oord__class_Oless__eq(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25))
| ~ class_Rings_Oordered__ring(X27) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1569])])]) ).
fof(c_0_2826,plain,
! [X25,X26,X27] :
( ~ class_Rings_Oordered__ring(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,c_Groups_Ozero__class_Ozero(X27))
| ~ c_Orderings_Oord__class_Oless__eq(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1570])]) ).
fof(c_0_2827,plain,
! [X25,X26,X27] :
( ~ class_Rings_Oordered__cancel__semiring(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,c_Groups_Ozero__class_Ozero(X27))
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless__eq(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25),c_Groups_Ozero__class_Ozero(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1571])]) ).
fof(c_0_2828,plain,
! [X25,X26,X27] :
( ~ class_Rings_Oordered__cancel__semiring(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless__eq(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X25),X26),c_Groups_Ozero__class_Ozero(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1572])]) ).
fof(c_0_2829,plain,
! [X25,X26,X27] :
( ~ class_Rings_Oordered__cancel__semiring(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless__eq(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25),c_Groups_Ozero__class_Ozero(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1573])]) ).
fof(c_0_2830,plain,
! [X25,X26,X27] :
( ~ class_Rings_Oordered__cancel__semiring(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1574])]) ).
fof(c_0_2831,plain,
! [X18,X19,X20] :
( ~ class_Rings_Olinordered__semidom(X20)
| ~ c_Orderings_Oord__class_Oless(X20,c_Groups_Oone__class_Oone(X20),X19)
| ~ c_Orderings_Oord__class_Oless(X20,c_Groups_Oone__class_Oone(X20),X18)
| c_Orderings_Oord__class_Oless(X20,c_Groups_Oone__class_Oone(X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X19),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1575])]) ).
fof(c_0_2832,plain,
! [X25,X26,X27] :
( ~ class_Rings_Olinordered__semiring__strict(X27)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1576])]) ).
fof(c_0_2833,plain,
! [X25,X26,X27] :
( ~ class_Rings_Olinordered__semiring__strict(X27)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25),c_Groups_Ozero__class_Ozero(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1577])]) ).
fof(c_0_2834,plain,
! [X25,X26,X27] :
( ~ class_Rings_Olinordered__semiring__strict(X27)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| ~ c_Orderings_Oord__class_Oless(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X25),X26),c_Groups_Ozero__class_Ozero(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1578])]) ).
fof(c_0_2835,plain,
! [X25,X26,X27] :
( ~ class_Rings_Olinordered__semiring__strict(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,c_Groups_Ozero__class_Ozero(X27))
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X25)
| c_Orderings_Oord__class_Oless(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25),c_Groups_Ozero__class_Ozero(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1579])]) ).
fof(c_0_2836,plain,
! [X25,X26,X27] :
( ~ class_Rings_Olinordered__ring__strict(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,c_Groups_Ozero__class_Ozero(X27))
| ~ c_Orderings_Oord__class_Oless(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1580])]) ).
fof(c_0_2837,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__ab__semigroup__add(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X30,X29)
| c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Oplus__class_Oplus(X31,X30,X28),c_Groups_Oplus__class_Oplus(X31,X29,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1581])]) ).
fof(c_0_2838,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__ab__semigroup__add(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X30,X29)
| c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Oplus__class_Oplus(X31,X28,X30),c_Groups_Oplus__class_Oplus(X31,X28,X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1582])]) ).
fof(c_0_2839,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X31)
| ~ c_Orderings_Oord__class_Oless(X31,X30,X29)
| c_Orderings_Oord__class_Oless(X31,c_Groups_Oplus__class_Oplus(X31,X28,X30),c_Groups_Oplus__class_Oplus(X31,X28,X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1583])]) ).
fof(c_0_2840,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X31)
| ~ c_Orderings_Oord__class_Oless(X31,X30,X29)
| c_Orderings_Oord__class_Oless(X31,c_Groups_Oplus__class_Oplus(X31,X30,X28),c_Groups_Oplus__class_Oplus(X31,X29,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1584])]) ).
fof(c_0_2841,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1585])]) ).
fof(c_0_2842,plain,
! [X37,X38,X39,X40] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X38)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X37)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X37)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X37)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X40)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X39)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X39)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1586])])])])]) ).
fof(c_0_2843,plain,
! [X24,X25,X26] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X24)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X26)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1587])])]) ).
fof(c_0_2844,plain,
! [X75] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk24_0)
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X75),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X75)),esk24_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1588])])])]) ).
fof(c_0_2845,plain,
! [X75] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk19_0)
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X75),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X75)),esk19_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1589])])])]) ).
fof(c_0_2846,plain,
! [X56] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X56),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X56)),v_m____) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1590])]) ).
fof(c_0_2847,plain,
! [X63,X64,X66] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk8_2(X63,X64))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X63)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X64) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk8_2(X63,X64)),X64) = X63
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X63)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X64) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X66)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X66),X64) != X63
| X66 = esk8_2(X63,X64)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X63)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X64) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1591])])])])]) ).
fof(c_0_2848,plain,
! [X48] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X48))),
inference(variable_rename,[status(thm)],[c_0_1592]) ).
fof(c_0_2849,plain,
! [X9,X10,X11] :
( ~ class_Rings_Olinordered__semidom(X11)
| ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Oone__class_Oone(X11),X10)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9)
| c_Orderings_Oord__class_Oless(X11,c_Groups_Oone__class_Oone(X11),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1593])]) ).
fof(c_0_2850,plain,
! [X12,X13,X14,X15] :
( ~ class_Rings_Ocomm__semiring__1(X15)
| ~ c_Rings_Odvd__class_Odvd(X15,X14,X13)
| c_Rings_Odvd__class_Odvd(X15,hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1594])]) ).
fof(c_0_2851,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__comm__monoid__add(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31),X30)
| ~ c_Orderings_Oord__class_Oless(X31,X29,X28)
| c_Orderings_Oord__class_Oless(X31,X29,c_Groups_Oplus__class_Oplus(X31,X30,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1595])]) ).
fof(c_0_2852,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__comm__monoid__add(X31)
| ~ c_Orderings_Oord__class_Oless(X31,c_Groups_Ozero__class_Ozero(X31),X30)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X29,X28)
| c_Orderings_Oord__class_Oless(X31,X29,c_Groups_Oplus__class_Oplus(X31,X30,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1596])]) ).
fof(c_0_2853,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__comm__monoid__add(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31),X30)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X29,X28)
| c_Orderings_Oord__class_Oless__eq(X31,X29,c_Groups_Oplus__class_Oplus(X31,X28,X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1597])]) ).
fof(c_0_2854,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oordered__comm__monoid__add(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31),X30)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X29,X28)
| c_Orderings_Oord__class_Oless__eq(X31,X29,c_Groups_Oplus__class_Oplus(X31,X30,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1598])]) ).
fof(c_0_2855,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semidom(X31)
| ~ c_Orderings_Oord__class_Oless(X31,c_Groups_Ozero__class_Ozero(X31),X30)
| ~ c_Orderings_Oord__class_Oless(X31,X29,X28)
| c_Orderings_Oord__class_Oless(X31,X29,c_Groups_Oplus__class_Oplus(X31,X30,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1599])]) ).
fof(c_0_2856,plain,
! [X18,X19,X20,X21] :
( ~ class_Rings_Ocomm__semiring__1(X21)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
| c_Rings_Odvd__class_Odvd(X21,hAPP(hAPP(c_Power_Opower__class_Opower(X21),X18),X20),hAPP(hAPP(c_Power_Opower__class_Opower(X21),X18),X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1600])]) ).
fof(c_0_2857,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1601])]) ).
fof(c_0_2858,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1602])]) ).
fof(c_0_2859,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X19,X18)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X18,X19)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1603])]) ).
fof(c_0_2860,plain,
! [X11,X12] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X11)),
inference(variable_rename,[status(thm)],[c_0_1604]) ).
fof(c_0_2861,plain,
! [X24,X25,X26] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X25)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X24,X26),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X24,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1605])]) ).
fof(c_0_2862,plain,
! [X55,X56,X57] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X56),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X57)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1606])]) ).
fof(c_0_2863,plain,
! [X55,X56,X57] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X57,X55),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X55)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1607])]) ).
fof(c_0_2864,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X52,X50),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1608])]) ).
fof(c_0_2865,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X52,X51)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X52,X50),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1609])]) ).
fof(c_0_2866,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X51)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X50,X52),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X50,X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1610])]) ).
fof(c_0_2867,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X52,X50),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1611])]) ).
fof(c_0_2868,plain,
! [X24,X25,X26,X27] :
( ~ class_Rings_Ocomm__ring__1(X27)
| ~ c_Rings_Odvd__class_Odvd(X27,X26,X25)
| ~ c_Rings_Odvd__class_Odvd(X27,X26,X24)
| c_Rings_Odvd__class_Odvd(X27,X26,c_Groups_Ominus__class_Ominus(X27,X25,X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1612])]) ).
fof(c_0_2869,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring__1(X31)
| ~ c_Rings_Odvd__class_Odvd(X31,X30,X29)
| ~ c_Rings_Odvd__class_Odvd(X31,X30,X28)
| c_Rings_Odvd__class_Odvd(X31,X30,c_Groups_Oplus__class_Oplus(X31,X29,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1613])]) ).
fof(c_0_2870,plain,
! [X12,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1614])]) ).
fof(c_0_2871,plain,
! [X12,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1615])]) ).
fof(c_0_2872,plain,
! [X81,X82,X83,X84] :
( ( X83 != c_Groups_Ozero__class_Ozero(X84)
| X81 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X84))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),c_Polynomial_Osmult(X84,X83,X82),X81)
| ~ class_Fields_Ofield(X84) )
& ( X83 = c_Groups_Ozero__class_Ozero(X84)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),X82,X81)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),c_Polynomial_Osmult(X84,X83,X82),X81)
| ~ class_Fields_Ofield(X84) )
& ( X83 != c_Groups_Ozero__class_Ozero(X84)
| X83 = c_Groups_Ozero__class_Ozero(X84)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),c_Polynomial_Osmult(X84,X83,X82),X81)
| ~ class_Fields_Ofield(X84) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),X82,X81)
| X83 = c_Groups_Ozero__class_Ozero(X84)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),c_Polynomial_Osmult(X84,X83,X82),X81)
| ~ class_Fields_Ofield(X84) )
& ( X83 != c_Groups_Ozero__class_Ozero(X84)
| X81 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X84))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),c_Polynomial_Osmult(X84,X83,X82),X81)
| ~ class_Fields_Ofield(X84) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),X82,X81)
| X81 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X84))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),c_Polynomial_Osmult(X84,X83,X82),X81)
| ~ class_Fields_Ofield(X84) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1616])])]) ).
fof(c_0_2873,plain,
! [X81,X82,X83,X84] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),X82,c_Polynomial_Osmult(X84,X83,X81))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),X82,X81)
| X83 = c_Groups_Ozero__class_Ozero(X84)
| ~ class_Fields_Ofield(X84) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),X82,X81)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X84),X82,c_Polynomial_Osmult(X84,X83,X81))
| X83 = c_Groups_Ozero__class_Ozero(X84)
| ~ class_Fields_Ofield(X84) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1617])])]) ).
fof(c_0_2874,plain,
! [X40,X41,X42,X43] :
( ~ class_Fields_Ofield(X43)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X43),X42,c_Polynomial_Osmult(X43,X41,X40))
| X41 = c_Groups_Ozero__class_Ozero(X43)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X43),X42,X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1618])]) ).
fof(c_0_2875,plain,
! [X51,X52,X53] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X53) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X53)
| X52 = X51
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52) )
& ( X52 != X51
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X53) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X53)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1619])])]) ).
fof(c_0_2876,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X19),X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1620])]) ).
fof(c_0_2877,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__1(X43)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X43),c_Polynomial_Osmult(X43,X42,X41),X40)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X43),X41,X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1621])]) ).
fof(c_0_2878,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Oplus__class_Oplus(X28,X27,X27),c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Oplus__class_Oplus(X28,X27,X27),c_Groups_Ozero__class_Ozero(X28))
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1622])])]) ).
fof(c_0_2879,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Oplus__class_Oplus(X28,X27,X27))
| c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Oplus__class_Oplus(X28,X27,X27))
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1623])])]) ).
fof(c_0_2880,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Oplus__class_Oplus(X28,X27,X27),c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| ~ class_Rings_Olinordered__idom(X28) )
& ( ~ c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless(X28,c_Groups_Oplus__class_Oplus(X28,X27,X27),c_Groups_Ozero__class_Ozero(X28))
| ~ class_Rings_Olinordered__idom(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1624])])]) ).
fof(c_0_2881,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Oplus__class_Oplus(X28,X27,X27),c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless(X28,c_Groups_Oplus__class_Oplus(X28,X27,X27),c_Groups_Ozero__class_Ozero(X28))
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1625])])]) ).
fof(c_0_2882,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Oplus__class_Oplus(X28,X27,X27))
| c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Oplus__class_Oplus(X28,X27,X27))
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1626])])]) ).
fof(c_0_2883,plain,
! [X49,X50,X51] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X51),X50),c_Nat_OSuc(X49)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X50),X49),
inference(variable_rename,[status(thm)],[c_0_1627]) ).
fof(c_0_2884,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring__1(X31)
| c_Groups_Oplus__class_Oplus(X31,c_Groups_Oplus__class_Oplus(X31,X30,X29),X28) = c_Groups_Oplus__class_Oplus(X31,c_Groups_Oplus__class_Oplus(X31,X30,X28),X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1628])]) ).
fof(c_0_2885,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Oab__semigroup__add(X31)
| c_Groups_Oplus__class_Oplus(X31,c_Groups_Oplus__class_Oplus(X31,X30,X29),X28) = c_Groups_Oplus__class_Oplus(X31,X30,c_Groups_Oplus__class_Oplus(X31,X29,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1629])]) ).
fof(c_0_2886,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring__1(X31)
| c_Groups_Oplus__class_Oplus(X31,c_Groups_Oplus__class_Oplus(X31,X30,X29),X28) = c_Groups_Oplus__class_Oplus(X31,X30,c_Groups_Oplus__class_Oplus(X31,X29,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1630])]) ).
fof(c_0_2887,plain,
! [X41,X42,X43,X44] :
( ~ class_Rings_Ocomm__semiring__1(X44)
| c_Groups_Oplus__class_Oplus(X44,X43,c_Groups_Oplus__class_Oplus(X44,X42,X41)) = c_Groups_Oplus__class_Oplus(X44,c_Groups_Oplus__class_Oplus(X44,X43,X42),X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1631])]) ).
fof(c_0_2888,plain,
! [X41,X42,X43,X44] :
( ~ class_Rings_Ocomm__semiring__1(X44)
| c_Groups_Oplus__class_Oplus(X44,X43,c_Groups_Oplus__class_Oplus(X44,X42,X41)) = c_Groups_Oplus__class_Oplus(X44,X42,c_Groups_Oplus__class_Oplus(X44,X43,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1632])]) ).
fof(c_0_2889,plain,
! [X36,X37,X38,X39] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X37,X36),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X37)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X38,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X39))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X39,X38),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1633])])])]) ).
fof(c_0_2890,plain,
! [X36,X37,X38,X39] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X37,X36))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X37),X36) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X39),X38)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X39,X38)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1634])])])]) ).
fof(c_0_2891,plain,
! [X36,X37,X38,X39] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X37,X36),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X36,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X37)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X38,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X39))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X39,X38),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1635])])])]) ).
fof(c_0_2892,plain,
! [X36,X37,X38,X39] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X37,X36))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X37),X36) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X39),X38)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X39,X38)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1636])])])]) ).
fof(c_0_2893,plain,
! [X28,X29,X30,X31] :
( ~ class_Divides_Osemiring__div(X31)
| X30 = c_Groups_Ozero__class_Ozero(X31)
| c_Divides_Odiv__class_Odiv(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X29),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X30)) = c_Divides_Odiv__class_Odiv(X31,X29,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1637])]) ).
fof(c_0_2894,plain,
! [X28,X29,X30,X31] :
( ( X30 != c_Groups_Ozero__class_Ozero(X31)
| c_Divides_Odiv__class_Odiv(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28)) = c_Groups_Ozero__class_Ozero(X31)
| ~ class_Divides_Osemiring__div(X31) )
& ( X30 = c_Groups_Ozero__class_Ozero(X31)
| c_Divides_Odiv__class_Odiv(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X28)) = c_Divides_Odiv__class_Odiv(X31,X29,X28)
| ~ class_Divides_Osemiring__div(X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1638])])]) ).
fof(c_0_2895,plain,
! [X25,X26,X27] :
( ~ class_Fields_Olinordered__field(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Rings_Oinverse__class_Oinverse(X27,X26),c_Rings_Oinverse__class_Oinverse(X27,X25))
| ~ c_Orderings_Oord__class_Oless(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless__eq(X27,X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1639])]) ).
fof(c_0_2896,plain,
! [X25,X26,X27] :
( ~ class_Fields_Olinordered__field(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,c_Rings_Oinverse__class_Oinverse(X27,X26),c_Rings_Oinverse__class_Oinverse(X27,X25))
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| c_Orderings_Oord__class_Oless__eq(X27,X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1640])]) ).
fof(c_0_2897,plain,
! [X27,X28,X29] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X29,X28,X27)
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ominus__class_Ominus(X29,X28,X27),c_Groups_Ozero__class_Ozero(X29))
| ~ class_Groups_Oordered__ab__group__add(X29) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ominus__class_Ominus(X29,X28,X27),c_Groups_Ozero__class_Ozero(X29))
| c_Orderings_Oord__class_Oless__eq(X29,X28,X27)
| ~ class_Groups_Oordered__ab__group__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1641])])]) ).
fof(c_0_2898,plain,
! [X27,X28,X29] :
( ( ~ c_Orderings_Oord__class_Oless(X29,X28,X27)
| c_Orderings_Oord__class_Oless(X29,c_Groups_Ominus__class_Ominus(X29,X28,X27),c_Groups_Ozero__class_Ozero(X29))
| ~ class_Groups_Oordered__ab__group__add(X29) )
& ( ~ c_Orderings_Oord__class_Oless(X29,c_Groups_Ominus__class_Ominus(X29,X28,X27),c_Groups_Ozero__class_Ozero(X29))
| c_Orderings_Oord__class_Oless(X29,X28,X27)
| ~ class_Groups_Oordered__ab__group__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1642])])]) ).
fof(c_0_2899,plain,
! [X25,X26,X27] :
( ~ class_Fields_Olinordered__field(X27)
| ~ c_Orderings_Oord__class_Oless(X27,c_Rings_Oinverse__class_Oinverse(X27,X26),c_Rings_Oinverse__class_Oinverse(X27,X25))
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| c_Orderings_Oord__class_Oless(X27,X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1643])]) ).
fof(c_0_2900,plain,
! [X25,X26,X27] :
( ~ class_Fields_Olinordered__field(X27)
| ~ c_Orderings_Oord__class_Oless(X27,c_Rings_Oinverse__class_Oinverse(X27,X26),c_Rings_Oinverse__class_Oinverse(X27,X25))
| ~ c_Orderings_Oord__class_Oless(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless(X27,X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1644])]) ).
fof(c_0_2901,plain,
! [X25,X26,X27,X28] :
( ~ class_Rings_Ocomm__semiring__0(X28)
| c_Polynomial_Osmult(X28,X27,c_Polynomial_Omonom(X28,X26,X25)) = c_Polynomial_Omonom(X28,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28),X27),X26),X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1645])]) ).
fof(c_0_2902,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| c_Polynomial_Osmult(X43,X42,c_Polynomial_Osmult(X43,X41,X40)) = c_Polynomial_Osmult(X43,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X43),X42),X41),X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1646])]) ).
fof(c_0_2903,plain,
! [X49,X50,X51] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X51,X50)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X51,X49)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X51,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1647])]) ).
fof(c_0_2904,plain,
! [X12,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1648])]) ).
fof(c_0_2905,plain,
! [X37,X38,X39,X40] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X38)
| ~ 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),X38),X37)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X37)
| ~ 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),X38),X37)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X40)
| ~ 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X39)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1649])])])])]) ).
fof(c_0_2906,plain,
! [X12,X13] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1650])]) ).
fof(c_0_2907,plain,
! [X18] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X18))),
inference(variable_rename,[status(thm)],[c_0_1651]) ).
fof(c_0_2908,plain,
! [X9,X10,X11] :
( ~ class_Groups_Omonoid__mult(X11)
| hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),c_Nat_OSuc(X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)),X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1652])]) ).
fof(c_0_2909,plain,
! [X39,X40,X41] :
( ~ class_Rings_Ocomm__semiring__1(X41)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X41),hAPP(hAPP(c_Power_Opower__class_Opower(X41),X40),X39)),X40) = hAPP(hAPP(c_Power_Opower__class_Opower(X41),X40),c_Nat_OSuc(X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1653])]) ).
fof(c_0_2910,plain,
! [X46,X47,X48,X49,X50] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X50,X49,X48)
| c_Orderings_Oord__class_Oless__eq(X50,X47,X46)
| c_Groups_Ominus__class_Ominus(X50,X49,X48) != c_Groups_Ominus__class_Ominus(X50,X47,X46)
| ~ class_Groups_Oordered__ab__group__add(X50) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X50,X47,X46)
| c_Orderings_Oord__class_Oless__eq(X50,X49,X48)
| c_Groups_Ominus__class_Ominus(X50,X49,X48) != c_Groups_Ominus__class_Ominus(X50,X47,X46)
| ~ class_Groups_Oordered__ab__group__add(X50) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1654])])]) ).
fof(c_0_2911,plain,
! [X46,X47,X48,X49,X50] :
( ( ~ c_Orderings_Oord__class_Oless(X50,X49,X48)
| c_Orderings_Oord__class_Oless(X50,X47,X46)
| c_Groups_Ominus__class_Ominus(X50,X49,X48) != c_Groups_Ominus__class_Ominus(X50,X47,X46)
| ~ class_Groups_Oordered__ab__group__add(X50) )
& ( ~ c_Orderings_Oord__class_Oless(X50,X47,X46)
| c_Orderings_Oord__class_Oless(X50,X49,X48)
| c_Groups_Ominus__class_Ominus(X50,X49,X48) != c_Groups_Ominus__class_Ominus(X50,X47,X46)
| ~ class_Groups_Oordered__ab__group__add(X50) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1655])])]) ).
fof(c_0_2912,plain,
! [X37,X38] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),X38),X38)
| X37 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X38) )
& ( X37 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),X38),X38)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1656])])]) ).
fof(c_0_2913,plain,
! [X37,X38] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X37),X38)
| X37 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X38) )
& ( X37 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X37),X38)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1657])])]) ).
fof(c_0_2914,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1658])]) ).
fof(c_0_2915,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X52),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1659])]) ).
fof(c_0_2916,plain,
! [X44,X45,X46,X47] :
( ~ class_Rings_Ocomm__semiring__1(X47)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X47),X46),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X47),X45),X44)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X47),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X47),X46),X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1660])]) ).
fof(c_0_2917,plain,
! [X22,X23,X24] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,X23),X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)),
inference(variable_rename,[status(thm)],[c_0_1661]) ).
fof(c_0_2918,plain,
! [X24,X25,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X24)),
inference(variable_rename,[status(thm)],[c_0_1662]) ).
fof(c_0_2919,plain,
! [X50,X51,X52] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X51),X50) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X50),X51),
inference(variable_rename,[status(thm)],[c_0_1663]) ).
fof(c_0_2920,plain,
! [X50,X51,X52] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X51),X50) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50)),
inference(variable_rename,[status(thm)],[c_0_1664]) ).
fof(c_0_2921,plain,
! [X49,X50,X51] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X49)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,X49),
inference(variable_rename,[status(thm)],[c_0_1665]) ).
fof(c_0_2922,plain,
! [X49,X50,X51] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X49,X50)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X49),
inference(variable_rename,[status(thm)],[c_0_1666]) ).
fof(c_0_2923,plain,
! [X24,X25,X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X24)),
inference(variable_rename,[status(thm)],[c_0_1667]) ).
fof(c_0_2924,plain,
! [X49,X50,X51] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),X49) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X49)),
inference(variable_rename,[status(thm)],[c_0_1668]) ).
fof(c_0_2925,plain,
! [X47,X48,X49,X50] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X47,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47)
| X48 = X47 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( X50 != X49
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1669])])])])]) ).
fof(c_0_2926,plain,
! [X47,X48,X49,X50] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X47,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X47) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1670])])])]) ).
fof(c_0_2927,plain,
! [X47,X48,X49,X50] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint)),X47)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X50,c_Groups_Oone__class_Oone(tc_Int_Oint)),X49) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1671])])])]) ).
fof(c_0_2928,plain,
! [X47,X48,X49,X50] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X47,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X49,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1672])])])]) ).
fof(c_0_2929,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring__1(X31)
| ~ c_Rings_Odvd__class_Odvd(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29),X28)
| c_Rings_Odvd__class_Odvd(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1673])]) ).
fof(c_0_2930,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring__1(X31)
| ~ c_Rings_Odvd__class_Odvd(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X30),X29),X28)
| c_Rings_Odvd__class_Odvd(X31,X29,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1674])]) ).
fof(c_0_2931,plain,
! [X24,X25,X26] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X24)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X26)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1675])])]) ).
fof(c_0_2932,plain,
! [X24,X25,X26] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X24)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X26)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1676])])]) ).
fof(c_0_2933,plain,
! [X36,X37,X38,X39] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X37,X36)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X37,X36),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X39,X38),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1677])])])]) ).
fof(c_0_2934,plain,
! [X65,X66,X67,X68] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X66,X65)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X66,X65),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X68,X67),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,X67) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1678])])])]) ).
fof(c_0_2935,plain,
! [X37,X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X38,X37))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X38) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,X40)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X39)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1679])])])]) ).
fof(c_0_2936,plain,
! [X55,X56,X57,X58] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X57)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X57) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X58,X55)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X55) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1680])]) ).
fof(c_0_2937,plain,
! [X51,X52,X53,X54] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X52,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X52))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X52,X51) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X54,X53)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X54,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X54)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1681])])])]) ).
fof(c_0_2938,plain,
! [X49,X50,X51] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),X49)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1682])])])]) ).
fof(c_0_2939,plain,
! [X49,X50,X51] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),X49)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1683])]) ).
fof(c_0_2940,plain,
! [X49,X50,X51] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X49)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),X49) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X49)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),X49) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1684])])]) ).
fof(c_0_2941,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X52,X51),X50)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1685])]) ).
fof(c_0_2942,plain,
! [X36,X37,X38] :
( ( X37 = c_Groups_Ozero__class_Ozero(X38)
| c_Groups_Oplus__class_Oplus(X38,X37,X36) != c_Groups_Ozero__class_Ozero(X38)
| ~ c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Ozero__class_Ozero(X38),X36)
| ~ c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Ozero__class_Ozero(X38),X37)
| ~ class_Groups_Oordered__comm__monoid__add(X38) )
& ( X36 = c_Groups_Ozero__class_Ozero(X38)
| c_Groups_Oplus__class_Oplus(X38,X37,X36) != c_Groups_Ozero__class_Ozero(X38)
| ~ c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Ozero__class_Ozero(X38),X36)
| ~ c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Ozero__class_Ozero(X38),X37)
| ~ class_Groups_Oordered__comm__monoid__add(X38) )
& ( X37 != c_Groups_Ozero__class_Ozero(X38)
| X36 != c_Groups_Ozero__class_Ozero(X38)
| c_Groups_Oplus__class_Oplus(X38,X37,X36) = c_Groups_Ozero__class_Ozero(X38)
| ~ c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Ozero__class_Ozero(X38),X36)
| ~ c_Orderings_Oord__class_Oless__eq(X38,c_Groups_Ozero__class_Ozero(X38),X37)
| ~ class_Groups_Oordered__comm__monoid__add(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1686])])]) ).
fof(c_0_2943,plain,
! [X25,X26,X27] :
( ~ class_Fields_Olinordered__field(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless__eq(X27,c_Rings_Oinverse__class_Oinverse(X27,X25),c_Rings_Oinverse__class_Oinverse(X27,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1687])]) ).
fof(c_0_2944,plain,
! [X25,X26,X27] :
( ~ class_Fields_Olinordered__field(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| c_Orderings_Oord__class_Oless__eq(X27,c_Rings_Oinverse__class_Oinverse(X27,X25),c_Rings_Oinverse__class_Oinverse(X27,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1688])]) ).
fof(c_0_2945,plain,
! [X25,X26,X27] :
( ~ class_Fields_Olinordered__field(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
| c_Orderings_Oord__class_Oless(X27,c_Rings_Oinverse__class_Oinverse(X27,X25),c_Rings_Oinverse__class_Oinverse(X27,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1689])]) ).
fof(c_0_2946,plain,
! [X25,X26,X27] :
( ~ class_Fields_Olinordered__field(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless(X27,X25,c_Groups_Ozero__class_Ozero(X27))
| c_Orderings_Oord__class_Oless(X27,c_Rings_Oinverse__class_Oinverse(X27,X25),c_Rings_Oinverse__class_Oinverse(X27,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1690])]) ).
fof(c_0_2947,plain,
! [X78,X79,X80,X81] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X80,X81),X79,X78)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X80,X81),X79,X78)
| ~ class_Orderings_Oord(X81) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X80,X81),X78,X79)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X80,X81),X79,X78)
| ~ class_Orderings_Oord(X81) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X80,X81),X79,X78)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X80,X81),X78,X79)
| c_Orderings_Oord__class_Oless(tc_fun(X80,X81),X79,X78)
| ~ class_Orderings_Oord(X81) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1691])])]) ).
fof(c_0_2948,plain,
! [X17,X18,X19,X20] :
( ( ~ 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),X18),X17))
| X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) )
& ( X19 != 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),X20),X19)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
| 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),X20),X19)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1692])])])])]) ).
fof(c_0_2949,plain,
! [X17,X18,X19,X20] :
( ( ~ 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),X18),X17))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
| X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
| 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),X20),X19)) )
& ( X19 != 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),X20),X19)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1693])])])])]) ).
fof(c_0_2950,plain,
! [X9,X10] :
( ~ class_Fields_Olinordered__field(X10)
| ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
| ~ c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Oone__class_Oone(X10))
| c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Rings_Oinverse__class_Oinverse(X10,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1694])]) ).
fof(c_0_2951,plain,
! [X16,X17] :
( ( c_Orderings_Oord__class_Oless(X17,c_Groups_Ozero__class_Ozero(X17),X16)
| ~ c_Orderings_Oord__class_Oless__eq(X17,c_Groups_Oone__class_Oone(X17),c_Rings_Oinverse__class_Oinverse(X17,X16))
| ~ class_Fields_Olinordered__field__inverse__zero(X17) )
& ( c_Orderings_Oord__class_Oless__eq(X17,X16,c_Groups_Oone__class_Oone(X17))
| ~ c_Orderings_Oord__class_Oless__eq(X17,c_Groups_Oone__class_Oone(X17),c_Rings_Oinverse__class_Oinverse(X17,X16))
| ~ class_Fields_Olinordered__field__inverse__zero(X17) )
& ( ~ c_Orderings_Oord__class_Oless(X17,c_Groups_Ozero__class_Ozero(X17),X16)
| ~ c_Orderings_Oord__class_Oless__eq(X17,X16,c_Groups_Oone__class_Oone(X17))
| c_Orderings_Oord__class_Oless__eq(X17,c_Groups_Oone__class_Oone(X17),c_Rings_Oinverse__class_Oinverse(X17,X16))
| ~ class_Fields_Olinordered__field__inverse__zero(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1695])])]) ).
fof(c_0_2952,plain,
! [X9,X10] :
( ~ class_Fields_Olinordered__field(X10)
| ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
| ~ c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Oone__class_Oone(X10))
| c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Rings_Oinverse__class_Oinverse(X10,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1696])]) ).
fof(c_0_2953,plain,
! [X16,X17] :
( ( c_Orderings_Oord__class_Oless(X17,c_Groups_Ozero__class_Ozero(X17),X16)
| ~ c_Orderings_Oord__class_Oless(X17,c_Groups_Oone__class_Oone(X17),c_Rings_Oinverse__class_Oinverse(X17,X16))
| ~ class_Fields_Olinordered__field__inverse__zero(X17) )
& ( c_Orderings_Oord__class_Oless(X17,X16,c_Groups_Oone__class_Oone(X17))
| ~ c_Orderings_Oord__class_Oless(X17,c_Groups_Oone__class_Oone(X17),c_Rings_Oinverse__class_Oinverse(X17,X16))
| ~ class_Fields_Olinordered__field__inverse__zero(X17) )
& ( ~ c_Orderings_Oord__class_Oless(X17,c_Groups_Ozero__class_Ozero(X17),X16)
| ~ c_Orderings_Oord__class_Oless(X17,X16,c_Groups_Oone__class_Oone(X17))
| c_Orderings_Oord__class_Oless(X17,c_Groups_Oone__class_Oone(X17),c_Rings_Oinverse__class_Oinverse(X17,X16))
| ~ class_Fields_Olinordered__field__inverse__zero(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1697])])]) ).
fof(c_0_2954,plain,
! [X36,X37,X38] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X38),X37),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X38),X36),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X37 = X36
| X37 = c_Groups_Ouminus__class_Ouminus(X38,X36)
| ~ class_Rings_Oidom(X38) )
& ( X37 != X36
| hAPP(hAPP(c_Power_Opower__class_Opower(X38),X37),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X38),X36),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X38) )
& ( X37 != c_Groups_Ouminus__class_Ouminus(X38,X36)
| hAPP(hAPP(c_Power_Opower__class_Opower(X38),X37),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X38),X36),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1698])])]) ).
fof(c_0_2955,plain,
! [X9,X10,X11] :
( ~ class_Rings_Olinordered__semidom(X11)
| ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Oone__class_Oone(X11),X10)
| c_Orderings_Oord__class_Oless(X11,c_Groups_Oone__class_Oone(X11),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),c_Nat_OSuc(X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1699])]) ).
fof(c_0_2956,plain,
! [X36,X37,X38] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X38),X37,X36)
| X37 = X36
| c_Polynomial_Opos__poly(X38,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X38),X36,X37))
| ~ class_Rings_Olinordered__idom(X38) )
& ( X37 != X36
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X38),X37,X36)
| ~ class_Rings_Olinordered__idom(X38) )
& ( ~ c_Polynomial_Opos__poly(X38,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X38),X36,X37))
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X38),X37,X36)
| ~ class_Rings_Olinordered__idom(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1700])])]) ).
fof(c_0_2957,plain,
! [X62,X63] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk7_2(X62,X63))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X63) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk7_2(X62,X63)),X63) = X62
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X63) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1701])])])]) ).
fof(c_0_2958,plain,
! [X40,X41,X42,X43] :
( ~ class_Fields_Ofield(X43)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X43),X42,X41)
| X40 = c_Groups_Ozero__class_Ozero(X43)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X43),c_Polynomial_Osmult(X43,X40,X42),X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1702])]) ).
fof(c_0_2959,plain,
! [X12,X13] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1703])]) ).
fof(c_0_2960,plain,
! [X25,X26] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1704])]) ).
fof(c_0_2961,plain,
! [X12,X13] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1705])]) ).
fof(c_0_2962,plain,
! [X12,X13] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1706])]) ).
fof(c_0_2963,plain,
! [X64,X65,X66] :
( ( X64 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| c_Polynomial_Opos__poly(X66,X64)
| ~ c_Polynomial_Opos__poly(X66,c_Polynomial_OpCons(X66,X65,X64))
| ~ class_Rings_Olinordered__idom(X66) )
& ( c_Orderings_Oord__class_Oless(X66,c_Groups_Ozero__class_Ozero(X66),X65)
| c_Polynomial_Opos__poly(X66,X64)
| ~ c_Polynomial_Opos__poly(X66,c_Polynomial_OpCons(X66,X65,X64))
| ~ class_Rings_Olinordered__idom(X66) )
& ( ~ c_Polynomial_Opos__poly(X66,X64)
| c_Polynomial_Opos__poly(X66,c_Polynomial_OpCons(X66,X65,X64))
| ~ class_Rings_Olinordered__idom(X66) )
& ( X64 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| ~ c_Orderings_Oord__class_Oless(X66,c_Groups_Ozero__class_Ozero(X66),X65)
| c_Polynomial_Opos__poly(X66,c_Polynomial_OpCons(X66,X65,X64))
| ~ class_Rings_Olinordered__idom(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1707])])]) ).
fof(c_0_2964,plain,
! [X64] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X64),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X64))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X64),esk20_1(X64)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1708])])]) ).
fof(c_0_2965,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__1(X43)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X43),X42,X41)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X43),X42,c_Polynomial_Osmult(X43,X40,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1709])]) ).
fof(c_0_2966,plain,
! [X37,X38,X39,X40] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X40),X39),X38) != hAPP(hAPP(c_Power_Opower__class_Opower(X40),X39),X37)
| X38 = X37
| ~ c_Orderings_Oord__class_Oless(X40,c_Groups_Oone__class_Oone(X40),X39)
| ~ class_Rings_Olinordered__semidom(X40) )
& ( X38 != X37
| hAPP(hAPP(c_Power_Opower__class_Opower(X40),X39),X38) = hAPP(hAPP(c_Power_Opower__class_Opower(X40),X39),X37)
| ~ c_Orderings_Oord__class_Oless(X40,c_Groups_Oone__class_Oone(X40),X39)
| ~ class_Rings_Olinordered__semidom(X40) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1710])])]) ).
fof(c_0_2967,plain,
! [X19,X20] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19))),
inference(variable_rename,[status(thm)],[c_0_1711]) ).
fof(c_0_2968,plain,
! [X19,X20] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20))),
inference(variable_rename,[status(thm)],[c_0_1712]) ).
fof(c_0_2969,plain,
! [X9,X10,X11] :
( ~ class_Rings_Olinordered__semidom(X11)
| ~ c_Orderings_Oord__class_Oless__eq(X11,c_Groups_Oone__class_Oone(X11),X10)
| c_Orderings_Oord__class_Oless__eq(X11,c_Groups_Oone__class_Oone(X11),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1713])]) ).
fof(c_0_2970,plain,
! [X9,X10,X11] :
( ~ class_Rings_Olinordered__semidom(X11)
| ~ c_Orderings_Oord__class_Oless__eq(X11,c_Groups_Ozero__class_Ozero(X11),X10)
| c_Orderings_Oord__class_Oless__eq(X11,c_Groups_Ozero__class_Ozero(X11),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1714])]) ).
fof(c_0_2971,plain,
! [X9,X10,X11] :
( ~ class_Rings_Olinordered__semidom(X11)
| ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Ozero__class_Ozero(X11),X10)
| c_Orderings_Oord__class_Oless(X11,c_Groups_Ozero__class_Ozero(X11),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1715])]) ).
fof(c_0_2972,plain,
! [X16,X17] :
( ( ~ c_Orderings_Oord__class_Oless(X17,c_Rings_Oinverse__class_Oinverse(X17,X16),c_Groups_Oone__class_Oone(X17))
| c_Orderings_Oord__class_Oless__eq(X17,X16,c_Groups_Ozero__class_Ozero(X17))
| c_Orderings_Oord__class_Oless(X17,c_Groups_Oone__class_Oone(X17),X16)
| ~ class_Fields_Olinordered__field__inverse__zero(X17) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X17,X16,c_Groups_Ozero__class_Ozero(X17))
| c_Orderings_Oord__class_Oless(X17,c_Rings_Oinverse__class_Oinverse(X17,X16),c_Groups_Oone__class_Oone(X17))
| ~ class_Fields_Olinordered__field__inverse__zero(X17) )
& ( ~ c_Orderings_Oord__class_Oless(X17,c_Groups_Oone__class_Oone(X17),X16)
| c_Orderings_Oord__class_Oless(X17,c_Rings_Oinverse__class_Oinverse(X17,X16),c_Groups_Oone__class_Oone(X17))
| ~ class_Fields_Olinordered__field__inverse__zero(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1716])])]) ).
fof(c_0_2973,plain,
! [X16,X17] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X17,c_Rings_Oinverse__class_Oinverse(X17,X16),c_Groups_Oone__class_Oone(X17))
| c_Orderings_Oord__class_Oless__eq(X17,X16,c_Groups_Ozero__class_Ozero(X17))
| c_Orderings_Oord__class_Oless__eq(X17,c_Groups_Oone__class_Oone(X17),X16)
| ~ class_Fields_Olinordered__field__inverse__zero(X17) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X17,X16,c_Groups_Ozero__class_Ozero(X17))
| c_Orderings_Oord__class_Oless__eq(X17,c_Rings_Oinverse__class_Oinverse(X17,X16),c_Groups_Oone__class_Oone(X17))
| ~ class_Fields_Olinordered__field__inverse__zero(X17) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X17,c_Groups_Oone__class_Oone(X17),X16)
| c_Orderings_Oord__class_Oless__eq(X17,c_Rings_Oinverse__class_Oinverse(X17,X16),c_Groups_Oone__class_Oone(X17))
| ~ class_Fields_Olinordered__field__inverse__zero(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1717])])]) ).
fof(c_0_2974,plain,
! [X25,X26,X27] :
( ~ class_Rings_Odivision__ring(X27)
| X26 = c_Groups_Ozero__class_Ozero(X27)
| X25 = c_Groups_Ozero__class_Ozero(X27)
| c_Rings_Oinverse__class_Oinverse(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Rings_Oinverse__class_Oinverse(X27,X25)),c_Rings_Oinverse__class_Oinverse(X27,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1718])]) ).
fof(c_0_2975,plain,
! [X9,X10] :
( ~ class_Rings_Olinordered__ring(X10)
| ~ c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X9),c_Groups_Ozero__class_Ozero(X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1719])]) ).
fof(c_0_2976,plain,
! [X24] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24),X24) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[c_0_1720]) ).
fof(c_0_2977,plain,
! [X12,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X13,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1721])]) ).
fof(c_0_2978,plain,
! [X19,X20] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20),X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1722])]) ).
fof(c_0_2979,plain,
! [X19,X20] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Nat_OSuc(X19)),X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1723])]) ).
fof(c_0_2980,plain,
! [X61,X62,X63,X64] : hAPP(hAPP(c_Power_Opower_Opower(X64,X63,X62),X61),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X63,
inference(variable_rename,[status(thm)],[c_0_1724]) ).
fof(c_0_2981,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1725])]) ).
fof(c_0_2982,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X19,X18)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X18,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1726])]) ).
fof(c_0_2983,plain,
! [X24] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1727])]) ).
fof(c_0_2984,plain,
! [X25,X26,X27] :
( ~ class_Fields_Ofield__inverse__zero(X27)
| c_Rings_Oinverse__class_Oinverse(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Rings_Oinverse__class_Oinverse(X27,X26)),c_Rings_Oinverse__class_Oinverse(X27,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1728])]) ).
fof(c_0_2985,plain,
! [X10,X11,X12] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
| c_Rings_Odvd__class_Odvd(X12,X10,hAPP(hAPP(c_Power_Opower__class_Opower(X12),X10),X11))
| ~ class_Rings_Ocomm__semiring__1(X12) )
& ( X10 != c_Groups_Oone__class_Oone(X12)
| c_Rings_Odvd__class_Odvd(X12,X10,hAPP(hAPP(c_Power_Opower__class_Opower(X12),X10),X11))
| ~ class_Rings_Ocomm__semiring__1(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1729])])]) ).
fof(c_0_2986,plain,
! [X40,X41,X42] :
( ~ class_Groups_Oab__group__add(X42)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X42),c_Polynomial_OpCons(X42,X41,X40)) = c_Polynomial_OpCons(X42,c_Groups_Ouminus__class_Ouminus(X42,X41),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X42),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1730])]) ).
fof(c_0_2987,plain,
! [X78,X79,X80] :
( ~ class_Groups_Oab__group__add(X80)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X80),c_Polynomial_OpCons(X80,X79,X78)) = c_Polynomial_OpCons(X80,c_Groups_Ouminus__class_Ouminus(X80,X79),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X80),X78)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1731])]) ).
fof(c_0_2988,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X18),X19) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1732])]) ).
fof(c_0_2989,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring__1(X31)
| ~ c_Rings_Odvd__class_Odvd(X31,X30,X29)
| c_Rings_Odvd__class_Odvd(X31,X30,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X29),X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1733])]) ).
fof(c_0_2990,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring__1(X31)
| ~ c_Rings_Odvd__class_Odvd(X31,X30,X29)
| c_Rings_Odvd__class_Odvd(X31,X30,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X28),X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1734])]) ).
fof(c_0_2991,plain,
! [X25,X26,X27] :
( ~ class_RealVector_Oreal__normed__vector(X27)
| c_RealVector_Onorm__class_Onorm(X27,c_Groups_Ominus__class_Ominus(X27,X26,X25)) = c_RealVector_Onorm__class_Onorm(X27,c_Groups_Ominus__class_Ominus(X27,X25,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1735])]) ).
fof(c_0_2992,plain,
! [X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__div__algebra(X14)
| c_RealVector_Onorm__class_Onorm(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X14,X13)),c_RealVector_Onorm__class_Onorm(X14,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1736])]) ).
fof(c_0_2993,plain,
! [X24,X25] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X24)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,c_Groups_Oone__class_Oone(tc_Int_Oint)),X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1737])]) ).
fof(c_0_2994,plain,
! [X50,X51] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),X51),
inference(variable_rename,[status(thm)],[c_0_1738]) ).
fof(c_0_2995,plain,
! [X50,X51] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50),X50),
inference(variable_rename,[status(thm)],[c_0_1739]) ).
fof(c_0_2996,plain,
! [X72,X73,X75,X76,X77] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X73,X72)
| X72 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X73,esk12_2(X72,X73))) )
& ( X75 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X76,X77))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X76,X75) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1740])])])])]) ).
fof(c_0_2997,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X19)) = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1741])]) ).
fof(c_0_2998,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X19),X19) = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1742])]) ).
fof(c_0_2999,plain,
! [X19,X20] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = X20 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1743])]) ).
fof(c_0_3000,plain,
! [X78,X79,X80,X81,X82] :
( ~ class_Orderings_Oord(X82)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X81,X82),X80,X79)
| c_Orderings_Oord__class_Oless__eq(X82,hAPP(X80,X78),hAPP(X79,X78)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1744])]) ).
fof(c_0_3001,plain,
! [X78,X79,X80,X81,X82] :
( ~ class_Orderings_Oord(X82)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X81,X82),X80,X79)
| c_Orderings_Oord__class_Oless__eq(X82,hAPP(X80,X78),hAPP(X79,X78)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1745])]) ).
fof(c_0_3002,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1746])]) ).
fof(c_0_3003,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1747])]) ).
fof(c_0_3004,plain,
! [X24,X25,X26] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1748])]) ).
fof(c_0_3005,plain,
! [X24,X25,X26] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1749])]) ).
fof(c_0_3006,plain,
! [X24,X25,X26] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1750])]) ).
fof(c_0_3007,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X50),X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1751])]) ).
fof(c_0_3008,plain,
! [X24,X25,X26] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1752])]) ).
fof(c_0_3009,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1753])]) ).
fof(c_0_3010,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1754])]) ).
fof(c_0_3011,plain,
! [X16,X17] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X16))
| X16 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X17 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X17)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1755])])])]) ).
fof(c_0_3012,plain,
! [X51,X52,X53] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51)
| X52 = X51
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53) )
& ( X52 != X51
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1756])])]) ).
fof(c_0_3013,plain,
! [X9,X10,X11] :
( ~ class_Groups_Ozero(X11)
| c_Polynomial_Omonom(X11,X10,c_Nat_OSuc(X9)) = c_Polynomial_OpCons(X11,c_Groups_Ozero__class_Ozero(X11),c_Polynomial_Omonom(X11,X10,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1757])]) ).
fof(c_0_3014,plain,
! [X10,X11] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X11),X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1758])]) ).
fof(c_0_3015,plain,
! [X24,X25,X26,X27] :
( ~ class_Orderings_Opreorder(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X25,X24)
| c_Orderings_Oord__class_Oless(X27,X26,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1759])]) ).
fof(c_0_3016,plain,
! [X24,X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X24,X26)
| c_Orderings_Oord__class_Oless(X27,X24,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1760])]) ).
fof(c_0_3017,plain,
! [X24,X25,X26,X27] :
( ~ class_Orderings_Opreorder(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless(X27,X25,X24)
| c_Orderings_Oord__class_Oless(X27,X26,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1761])]) ).
fof(c_0_3018,plain,
! [X24,X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless(X27,X24,X26)
| c_Orderings_Oord__class_Oless(X27,X24,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1762])]) ).
fof(c_0_3019,plain,
! [X24,X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless(X27,X24,X26)
| c_Orderings_Oord__class_Oless(X27,X24,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1763])]) ).
fof(c_0_3020,plain,
! [X24,X25,X26,X27] :
( ~ class_Orderings_Opreorder(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless(X27,X25,X24)
| c_Orderings_Oord__class_Oless(X27,X26,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1764])]) ).
fof(c_0_3021,plain,
! [X24,X25,X26,X27] :
( ~ class_Orderings_Opreorder(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X25,X24)
| c_Orderings_Oord__class_Oless__eq(X27,X26,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1765])]) ).
fof(c_0_3022,plain,
! [X24,X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X24,X26)
| c_Orderings_Oord__class_Oless__eq(X27,X24,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1766])]) ).
fof(c_0_3023,plain,
! [X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring__1(X31)
| ~ c_Rings_Odvd__class_Odvd(X31,X30,X29)
| ~ c_Rings_Odvd__class_Odvd(X31,X29,X28)
| c_Rings_Odvd__class_Odvd(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1767])]) ).
fof(c_0_3024,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oab__group__add(X27)
| c_Groups_Ominus__class_Ominus(X27,c_Groups_Ouminus__class_Ouminus(X27,X26),c_Groups_Ouminus__class_Ouminus(X27,X25)) = c_Groups_Ouminus__class_Ouminus(X27,c_Groups_Ominus__class_Ominus(X27,X26,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1768])]) ).
fof(c_0_3025,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oab__group__add(X27)
| c_Groups_Ouminus__class_Ouminus(X27,c_Groups_Oplus__class_Oplus(X27,X26,X25)) = c_Groups_Oplus__class_Oplus(X27,c_Groups_Ouminus__class_Ouminus(X27,X26),c_Groups_Ouminus__class_Ouminus(X27,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1769])]) ).
fof(c_0_3026,plain,
! [X25,X26,X27] :
( ~ class_Groups_Ogroup__add(X27)
| c_Groups_Ouminus__class_Ouminus(X27,c_Groups_Oplus__class_Oplus(X27,X26,X25)) = c_Groups_Oplus__class_Oplus(X27,c_Groups_Ouminus__class_Ouminus(X27,X25),c_Groups_Ouminus__class_Ouminus(X27,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1770])]) ).
fof(c_0_3027,plain,
! [X9,X10,X11] :
( ~ class_Rings_Odivision__ring(X11)
| X10 = c_Groups_Ozero__class_Ozero(X11)
| c_Rings_Oinverse__class_Oinverse(X11,hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)) = hAPP(hAPP(c_Power_Opower__class_Opower(X11),c_Rings_Oinverse__class_Oinverse(X11,X10)),X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1771])]) ).
fof(c_0_3028,plain,
! [X27,X28,X29] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),c_Groups_Ouminus__class_Ouminus(X29,X27))
| c_Orderings_Oord__class_Oless__eq(X29,X27,X28)
| ~ class_Groups_Oordered__ab__group__add(X29) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X29,X27,X28)
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),c_Groups_Ouminus__class_Ouminus(X29,X27))
| ~ class_Groups_Oordered__ab__group__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1772])])]) ).
fof(c_0_3029,plain,
! [X27,X28,X29] :
( ( ~ c_Orderings_Oord__class_Oless(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),c_Groups_Ouminus__class_Ouminus(X29,X27))
| c_Orderings_Oord__class_Oless(X29,X27,X28)
| ~ class_Groups_Oordered__ab__group__add(X29) )
& ( ~ c_Orderings_Oord__class_Oless(X29,X27,X28)
| c_Orderings_Oord__class_Oless(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),c_Groups_Ouminus__class_Ouminus(X29,X27))
| ~ class_Groups_Oordered__ab__group__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1773])])]) ).
fof(c_0_3030,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X19)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1774])]) ).
fof(c_0_3031,plain,
! [X25,X26,X27] :
( ~ class_Rings_Oring(X27)
| c_Groups_Ouminus__class_Ouminus(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Ouminus__class_Ouminus(X27,X26)),X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1775])]) ).
fof(c_0_3032,plain,
! [X25,X26,X27] :
( ~ class_RealVector_Oreal__normed__algebra(X27)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Ouminus__class_Ouminus(X27,X26)),X25) = c_Groups_Ouminus__class_Ouminus(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1776])]) ).
fof(c_0_3033,plain,
! [X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__algebra(X14)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),c_Groups_Ouminus__class_Ouminus(X14,X13)),X12) = c_Groups_Ouminus__class_Ouminus(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1777])]) ).
fof(c_0_3034,plain,
! [X9,X10,X11] :
( ~ class_Rings_Odivision__ring__inverse__zero(X11)
| c_Rings_Oinverse__class_Oinverse(X11,hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)) = hAPP(hAPP(c_Power_Opower__class_Opower(X11),c_Rings_Oinverse__class_Oinverse(X11,X10)),X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1778])]) ).
fof(c_0_3035,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X51)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X51,X50)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X52),X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1779])]) ).
fof(c_0_3036,plain,
! [X40,X41,X42] :
( ~ class_Rings_Ocomm__ring(X42)
| c_Polynomial_Osmult(X42,X41,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X42),X40)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X42),c_Polynomial_Osmult(X42,X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1780])]) ).
fof(c_0_3037,plain,
! [X49,X50] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X50,X49)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X49)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1781])]) ).
fof(c_0_3038,plain,
! [X24,X25] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,X24)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1782])]) ).
fof(c_0_3039,plain,
! [X28,X29,X30] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,X28)
| X29 != X28
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,X29)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X29,X30) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X28,X30)
| X29 != X28
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,X29)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X29,X30) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1783])])]) ).
fof(c_0_3040,plain,
! [X28,X29,X30] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,X28)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X29,X28)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X28,X29)
| X30 != X29 )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X28,X30)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X29,X28)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X28,X29)
| X30 != X29 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1784])])]) ).
fof(c_0_3041,plain,
! [X58,X59,X60] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X59,X60) != X58
| X59 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X58,X60)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,X59) )
& ( X59 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X58,X60)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X59,X60) = X58
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,X59) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1785])])]) ).
fof(c_0_3042,plain,
! [X7] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X7 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1786])]) ).
fof(c_0_3043,plain,
! [X18,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Nat_OSuc(X18)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X18),
inference(variable_rename,[status(thm)],[c_0_1787]) ).
fof(c_0_3044,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
c_0_1788 ).
fof(c_0_3045,plain,
! [X25,X26,X27] :
( ~ class_Groups_Ogroup__add(X27)
| c_Groups_Oplus__class_Oplus(X27,X26,c_Groups_Oplus__class_Oplus(X27,c_Groups_Ouminus__class_Ouminus(X27,X26),X25)) = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1789])]) ).
fof(c_0_3046,plain,
! [X10,X11,X12] :
( ~ class_RealVector_Oreal__normed__div__algebra(X12)
| c_RealVector_Onorm__class_Onorm(X12,hAPP(hAPP(c_Power_Opower__class_Opower(X12),X11),X10)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X12,X11)),X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1790])]) ).
fof(c_0_3047,plain,
! [X24,X25,X26] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1791])]) ).
fof(c_0_3048,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X51,X50)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1792])]) ).
fof(c_0_3049,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X52,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X51,X50)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X52,X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1793])]) ).
fof(c_0_3050,plain,
! [X50,X51,X52] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X51)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X50)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1794])]) ).
fof(c_0_3051,plain,
! [X9,X10,X11] :
( ~ class_Power_Opower(X11)
| hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),c_Nat_OSuc(X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1795])]) ).
fof(c_0_3052,plain,
! [X39,X40,X41] :
( ~ class_Rings_Ocomm__semiring__1(X41)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X41),X40),hAPP(hAPP(c_Power_Opower__class_Opower(X41),X40),X39)) = hAPP(hAPP(c_Power_Opower__class_Opower(X41),X40),c_Nat_OSuc(X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1796])]) ).
fof(c_0_3053,plain,
! [X39,X40,X41] :
( ~ class_Rings_Ocomm__semiring__1(X41)
| hAPP(hAPP(c_Power_Opower__class_Opower(X41),X40),c_Nat_OSuc(X39)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X41),X40),hAPP(hAPP(c_Power_Opower__class_Opower(X41),X40),X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1797])]) ).
fof(c_0_3054,plain,
! [X40,X41,X42] :
( ~ class_Rings_Olinordered__idom(X42)
| ~ c_Polynomial_Opos__poly(X42,X41)
| ~ c_Polynomial_Opos__poly(X42,X40)
| c_Polynomial_Opos__poly(X42,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X42)),X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1798])]) ).
fof(c_0_3055,plain,
! [X40,X41,X42] :
( ~ class_Rings_Ocomm__ring(X42)
| hAPP(c_Polynomial_Opoly(X42,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X42),X41)),X40) = c_Groups_Ouminus__class_Ouminus(X42,hAPP(c_Polynomial_Opoly(X42,X41),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1799])]) ).
fof(c_0_3056,plain,
! [X27,X28,X29] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),X27)
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X27),X28)
| ~ class_Groups_Oordered__ab__group__add(X29) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X27),X28)
| c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),X27)
| ~ class_Groups_Oordered__ab__group__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1800])])]) ).
fof(c_0_3057,plain,
! [X27,X28,X29] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X29,X28,c_Groups_Ouminus__class_Ouminus(X29,X27))
| c_Orderings_Oord__class_Oless__eq(X29,X27,c_Groups_Ouminus__class_Ouminus(X29,X28))
| ~ class_Groups_Oordered__ab__group__add(X29) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X29,X27,c_Groups_Ouminus__class_Ouminus(X29,X28))
| c_Orderings_Oord__class_Oless__eq(X29,X28,c_Groups_Ouminus__class_Ouminus(X29,X27))
| ~ class_Groups_Oordered__ab__group__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1801])])]) ).
fof(c_0_3058,plain,
! [X24,X25] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X25),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X24)),
inference(variable_rename,[status(thm)],[c_0_1802]) ).
fof(c_0_3059,plain,
! [X27,X28,X29] :
( ( ~ c_Orderings_Oord__class_Oless(X29,X28,c_Groups_Ouminus__class_Ouminus(X29,X27))
| c_Orderings_Oord__class_Oless(X29,X27,c_Groups_Ouminus__class_Ouminus(X29,X28))
| ~ class_Groups_Oordered__ab__group__add(X29) )
& ( ~ c_Orderings_Oord__class_Oless(X29,X27,c_Groups_Ouminus__class_Ouminus(X29,X28))
| c_Orderings_Oord__class_Oless(X29,X28,c_Groups_Ouminus__class_Ouminus(X29,X27))
| ~ class_Groups_Oordered__ab__group__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1803])])]) ).
fof(c_0_3060,plain,
! [X27,X28,X29] :
( ( ~ c_Orderings_Oord__class_Oless(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),X27)
| c_Orderings_Oord__class_Oless(X29,c_Groups_Ouminus__class_Ouminus(X29,X27),X28)
| ~ class_Groups_Oordered__ab__group__add(X29) )
& ( ~ c_Orderings_Oord__class_Oless(X29,c_Groups_Ouminus__class_Ouminus(X29,X27),X28)
| c_Orderings_Oord__class_Oless(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),X27)
| ~ class_Groups_Oordered__ab__group__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1804])])]) ).
fof(c_0_3061,plain,
! [X9,X10,X11] :
( ~ class_Groups_Oab__group__add(X11)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X11),c_Polynomial_Omonom(X11,X10,X9)) = c_Polynomial_Omonom(X11,c_Groups_Ouminus__class_Ouminus(X11,X10),X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1805])]) ).
fof(c_0_3062,plain,
! [X40,X41,X42] :
( ~ class_Rings_Ocomm__ring(X42)
| c_Polynomial_Osmult(X42,c_Groups_Ouminus__class_Ouminus(X42,X41),X40) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X42),c_Polynomial_Osmult(X42,X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1806])]) ).
fof(c_0_3063,plain,
! [X18,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18)) = X19 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1807])]) ).
fof(c_0_3064,plain,
! [X9,X10] :
( ~ class_Fields_Olinordered__field(X10)
| ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Oinverse(X10,X9))
| X9 = c_Groups_Ozero__class_Ozero(X10)
| c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1808])]) ).
fof(c_0_3065,plain,
! [X9,X10] :
( ~ class_Fields_Olinordered__field(X10)
| ~ c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),c_Groups_Ozero__class_Ozero(X10))
| X9 = c_Groups_Ozero__class_Ozero(X10)
| c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1809])]) ).
fof(c_0_3066,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Rings_Oinverse__class_Oinverse(X28,X27),c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| ~ class_Fields_Olinordered__field__inverse__zero(X28) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless__eq(X28,c_Rings_Oinverse__class_Oinverse(X28,X27),c_Groups_Ozero__class_Ozero(X28))
| ~ class_Fields_Olinordered__field__inverse__zero(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1810])])]) ).
fof(c_0_3067,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Rings_Oinverse__class_Oinverse(X28,X27))
| c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ class_Fields_Olinordered__field__inverse__zero(X28) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Rings_Oinverse__class_Oinverse(X28,X27))
| ~ class_Fields_Olinordered__field__inverse__zero(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1811])])]) ).
fof(c_0_3068,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Ouminus__class_Ouminus(X28,X27))
| c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| ~ class_Groups_Oordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Ouminus__class_Ouminus(X28,X27))
| ~ class_Groups_Oordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1812])])]) ).
fof(c_0_3069,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ouminus__class_Ouminus(X28,X27),c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ class_Groups_Oordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ouminus__class_Ouminus(X28,X27),c_Groups_Ozero__class_Ozero(X28))
| ~ class_Groups_Oordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1813])])]) ).
fof(c_0_3070,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Ouminus__class_Ouminus(X28,X27))
| c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| ~ class_Groups_Oordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Ouminus__class_Ouminus(X28,X27))
| ~ class_Groups_Oordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1814])])]) ).
fof(c_0_3071,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Ouminus__class_Ouminus(X28,X27),c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ class_Groups_Oordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| c_Orderings_Oord__class_Oless(X28,c_Groups_Ouminus__class_Ouminus(X28,X27),c_Groups_Ozero__class_Ozero(X28))
| ~ class_Groups_Oordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1815])])]) ).
fof(c_0_3072,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),c_Rings_Oinverse__class_Oinverse(X28,X27))
| c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ class_Fields_Olinordered__field__inverse__zero(X28) )
& ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),c_Rings_Oinverse__class_Oinverse(X28,X27))
| ~ class_Fields_Olinordered__field__inverse__zero(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1816])])]) ).
fof(c_0_3073,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(X28,c_Rings_Oinverse__class_Oinverse(X28,X27),c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| ~ class_Fields_Olinordered__field__inverse__zero(X28) )
& ( ~ c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless(X28,c_Rings_Oinverse__class_Oinverse(X28,X27),c_Groups_Ozero__class_Ozero(X28))
| ~ class_Fields_Olinordered__field__inverse__zero(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1817])])]) ).
fof(c_0_3074,plain,
! [X7] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X7 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1818])]) ).
fof(c_0_3075,plain,
! [X7] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
| X7 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1819])]) ).
fof(c_0_3076,plain,
! [X36,X37,X38] :
( ( c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| ~ c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Opreorder(X38) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X38,X36,X37)
| ~ c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Opreorder(X38) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| c_Orderings_Oord__class_Oless__eq(X38,X36,X37)
| c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Opreorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1820])])]) ).
fof(c_0_3077,plain,
! [X25,X26,X27] :
( ~ class_Rings_Oring(X27)
| c_Groups_Ouminus__class_Ouminus(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),c_Groups_Ouminus__class_Ouminus(X27,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1821])]) ).
fof(c_0_3078,plain,
! [X25,X26,X27] :
( ~ class_RealVector_Oreal__normed__algebra(X27)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),c_Groups_Ouminus__class_Ouminus(X27,X25)) = c_Groups_Ouminus__class_Ouminus(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1822])]) ).
fof(c_0_3079,plain,
! [X32,X33,X34] :
( ~ class_RealVector_Oreal__normed__algebra(X34)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),X33),c_Groups_Ouminus__class_Ouminus(X34,X32)) = c_Groups_Ouminus__class_Ouminus(X34,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),X33),X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1823])]) ).
fof(c_0_3080,plain,
! [X18,X19] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X19)),X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X18)),
inference(variable_rename,[status(thm)],[c_0_1824]) ).
fof(c_0_3081,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oordered__ab__group__add(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,X25)
| c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ouminus__class_Ouminus(X27,X25),c_Groups_Ouminus__class_Ouminus(X27,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1825])]) ).
fof(c_0_3082,plain,
! [X9] :
( ~ class_Rings_Olinordered__semidom(X9)
| c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),c_Groups_Oplus__class_Oplus(X9,c_Groups_Oone__class_Oone(X9),c_Groups_Oone__class_Oone(X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1826])]) ).
fof(c_0_3083,plain,
! [X25,X26,X27] :
( ~ class_Groups_Ogroup__add(X27)
| c_Groups_Oplus__class_Oplus(X27,c_Groups_Ouminus__class_Ouminus(X27,X26),c_Groups_Oplus__class_Oplus(X27,X26,X25)) = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1827])]) ).
fof(c_0_3084,plain,
! [X18,X19] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),c_Nat_OSuc(X18)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X18)),
inference(variable_rename,[status(thm)],[c_0_1828]) ).
fof(c_0_3085,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ouminus__class_Ouminus(X28,X27))
| c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ouminus__class_Ouminus(X28,X27))
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1829])])]) ).
fof(c_0_3086,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ouminus__class_Ouminus(X28,X27),X27)
| c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ouminus__class_Ouminus(X28,X27),X27)
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1830])])]) ).
fof(c_0_3087,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Ouminus__class_Ouminus(X28,X27),X27)
| c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Ozero__class_Ozero(X28),X27)
| c_Orderings_Oord__class_Oless(X28,c_Groups_Ouminus__class_Ouminus(X28,X27),X27)
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1831])])]) ).
fof(c_0_3088,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ouminus__class_Ouminus(X28,X27))
| c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| ~ class_Rings_Olinordered__idom(X28) )
& ( ~ c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ozero__class_Ozero(X28))
| c_Orderings_Oord__class_Oless(X28,X27,c_Groups_Ouminus__class_Ouminus(X28,X27))
| ~ class_Rings_Olinordered__idom(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1832])])]) ).
fof(c_0_3089,plain,
! [X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X25)),X24) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X24)),
inference(variable_rename,[status(thm)],[c_0_1833]) ).
fof(c_0_3090,plain,
! [X12,X13] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1834])]) ).
fof(c_0_3091,plain,
! [X36,X37,X38,X39] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,X36)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,X36)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X37) )
& ( X37 != X36
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,X36)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X37) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X39,X38)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X39,X38)
| X39 = X38 )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,X39)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X39,X38)
| X39 = X38 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1835])])])])]) ).
fof(c_0_3092,plain,
! [X36,X37,X38,X39] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,X36)
| X37 = X36
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,X36) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X37)
| X37 = X36
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,X36) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X39,X38)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,X39)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X39,X38) )
& ( X39 != X38
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X39,X38) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1836])])])])]) ).
fof(c_0_3093,plain,
! [X40,X41,X42,X43] :
( ~ class_Rings_Ocomm__semiring__0(X43)
| c_Polynomial_Osmult(X43,X42,X41) != c_Polynomial_OpCons(X43,X40,X41)
| X41 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1837])]) ).
fof(c_0_3094,plain,
! [X9,X10] :
( ~ class_Fields_Olinordered__field(X10)
| ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
| c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Oinverse(X10,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1838])]) ).
fof(c_0_3095,plain,
! [X9,X10] :
( ~ class_Fields_Olinordered__field(X10)
| ~ c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
| c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),c_Groups_Ozero__class_Ozero(X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1839])]) ).
fof(c_0_3096,plain,
! [X25,X26,X27] :
( ~ class_Rings_Oring(X27)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Ouminus__class_Ouminus(X27,X26)),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),c_Groups_Ouminus__class_Ouminus(X27,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1840])]) ).
fof(c_0_3097,plain,
! [X25,X26,X27] :
( ~ class_Rings_Oring(X27)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Ouminus__class_Ouminus(X27,X26)),c_Groups_Ouminus__class_Ouminus(X27,X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1841])]) ).
fof(c_0_3098,plain,
! [X36,X37,X38] :
( ( ~ c_Rings_Odvd__class_Odvd(X38,c_Groups_Ouminus__class_Ouminus(X38,X37),X36)
| c_Rings_Odvd__class_Odvd(X38,X37,X36)
| ~ class_Rings_Ocomm__ring__1(X38) )
& ( ~ c_Rings_Odvd__class_Odvd(X38,X37,X36)
| c_Rings_Odvd__class_Odvd(X38,c_Groups_Ouminus__class_Ouminus(X38,X37),X36)
| ~ class_Rings_Ocomm__ring__1(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1842])])]) ).
fof(c_0_3099,plain,
! [X36,X37,X38] :
( ( ~ c_Rings_Odvd__class_Odvd(X38,X37,c_Groups_Ouminus__class_Ouminus(X38,X36))
| c_Rings_Odvd__class_Odvd(X38,X37,X36)
| ~ class_Rings_Ocomm__ring__1(X38) )
& ( ~ c_Rings_Odvd__class_Odvd(X38,X37,X36)
| c_Rings_Odvd__class_Odvd(X38,X37,c_Groups_Ouminus__class_Ouminus(X38,X36))
| ~ class_Rings_Ocomm__ring__1(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1843])])]) ).
fof(c_0_3100,plain,
! [X27,X28,X29] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X28) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X27),X27)
| X28 = X27
| X28 = c_Groups_Ouminus__class_Ouminus(X29,X27)
| ~ class_Rings_Oidom(X29) )
& ( X28 != X27
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X27),X27)
| ~ class_Rings_Oidom(X29) )
& ( X28 != c_Groups_Ouminus__class_Ouminus(X29,X27)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X27),X27)
| ~ class_Rings_Oidom(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1844])])]) ).
fof(c_0_3101,plain,
! [X40,X41,X42] :
( ~ class_Rings_Olinordered__idom(X42)
| ~ c_Polynomial_Opos__poly(X42,X41)
| ~ c_Polynomial_Opos__poly(X42,X40)
| c_Polynomial_Opos__poly(X42,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X42),X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1845])]) ).
fof(c_0_3102,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X53)),X52) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X53)),X51)
| X52 = X51 )
& ( X55 != X54
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X56)),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X56)),X54) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1846])])])]) ).
fof(c_0_3103,plain,
! [X46,X47,X48,X49,X50] :
( ( X49 != X48
| X47 = X46
| c_Groups_Ominus__class_Ominus(X50,X49,X48) != c_Groups_Ominus__class_Ominus(X50,X47,X46)
| ~ class_Groups_Oab__group__add(X50) )
& ( X47 != X46
| X49 = X48
| c_Groups_Ominus__class_Ominus(X50,X49,X48) != c_Groups_Ominus__class_Ominus(X50,X47,X46)
| ~ class_Groups_Oab__group__add(X50) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1847])])]) ).
fof(c_0_3104,plain,
! [X36,X37,X38] :
( ( c_Orderings_Oord__class_Oless(X38,X37,X36)
| X37 = X36
| ~ c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| ~ class_Orderings_Olinorder(X38) )
& ( X37 != X36
| ~ c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| ~ class_Orderings_Olinorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1848])])]) ).
fof(c_0_3105,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oab__group__add(X27)
| c_Groups_Ouminus__class_Ouminus(X27,c_Groups_Ominus__class_Ominus(X27,X26,X25)) = c_Groups_Ominus__class_Ominus(X27,X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1849])]) ).
fof(c_0_3106,plain,
! [X36,X37,X38] :
( ( c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| X37 != X36
| ~ class_Orderings_Oorder(X38) )
& ( c_Orderings_Oord__class_Oless__eq(X38,X36,X37)
| X37 != X36
| ~ class_Orderings_Oorder(X38) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| ~ c_Orderings_Oord__class_Oless__eq(X38,X36,X37)
| X37 = X36
| ~ class_Orderings_Oorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1850])])]) ).
fof(c_0_3107,plain,
! [X36,X37,X38] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X38,X36,X37)
| X36 = X37
| ~ c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| ~ class_Orderings_Oorder(X38) )
& ( X36 != X37
| c_Orderings_Oord__class_Oless__eq(X38,X36,X37)
| ~ c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| ~ class_Orderings_Oorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1851])])]) ).
fof(c_0_3108,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ c_Orderings_Oord__class_Oless__eq(X14,X13,X12)
| ~ c_Orderings_Oord__class_Oless__eq(X14,X12,X13)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1852])]) ).
fof(c_0_3109,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ c_Orderings_Oord__class_Oless__eq(X14,X13,X12)
| ~ c_Orderings_Oord__class_Oless__eq(X14,X12,X13)
| X12 = X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1853])]) ).
fof(c_0_3110,plain,
! [X9,X10] :
( ~ class_Rings_Olinordered__semidom(X10)
| c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oone__class_Oone(X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1854])]) ).
fof(c_0_3111,plain,
! [X27,X28,X29,X30] :
( ( c_Polynomial_Omonom(X30,X29,X28) != c_Polynomial_Omonom(X30,X27,X28)
| X29 = X27
| ~ class_Groups_Ozero(X30) )
& ( X29 != X27
| c_Polynomial_Omonom(X30,X29,X28) = c_Polynomial_Omonom(X30,X27,X28)
| ~ class_Groups_Ozero(X30) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1855])])]) ).
fof(c_0_3112,plain,
! [X81,X82,X83,X84,X85] :
( ( X84 = X82
| c_Polynomial_OpCons(X85,X84,X83) != c_Polynomial_OpCons(X85,X82,X81)
| ~ class_Groups_Ozero(X85) )
& ( X83 = X81
| c_Polynomial_OpCons(X85,X84,X83) != c_Polynomial_OpCons(X85,X82,X81)
| ~ class_Groups_Ozero(X85) )
& ( X84 != X82
| X83 != X81
| c_Polynomial_OpCons(X85,X84,X83) = c_Polynomial_OpCons(X85,X82,X81)
| ~ class_Groups_Ozero(X85) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1856])])]) ).
fof(c_0_3113,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Ocancel__semigroup__add(X31)
| c_Groups_Oplus__class_Oplus(X31,X30,X29) != c_Groups_Oplus__class_Oplus(X31,X28,X29)
| X30 = X28 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1857])]) ).
fof(c_0_3114,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X31)
| c_Groups_Oplus__class_Oplus(X31,X30,X29) != c_Groups_Oplus__class_Oplus(X31,X30,X28)
| X29 = X28 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1858])]) ).
fof(c_0_3115,plain,
! [X28,X29,X30,X31] :
( ~ class_Groups_Ocancel__semigroup__add(X31)
| c_Groups_Oplus__class_Oplus(X31,X30,X29) != c_Groups_Oplus__class_Oplus(X31,X30,X28)
| X29 = X28 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1859])]) ).
fof(c_0_3116,plain,
! [X34,X35,X36,X37] :
( ( c_Groups_Oplus__class_Oplus(X37,X36,X35) != c_Groups_Oplus__class_Oplus(X37,X34,X35)
| X36 = X34
| ~ class_Groups_Ocancel__semigroup__add(X37) )
& ( X36 != X34
| c_Groups_Oplus__class_Oplus(X37,X36,X35) = c_Groups_Oplus__class_Oplus(X37,X34,X35)
| ~ class_Groups_Ocancel__semigroup__add(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1860])])]) ).
fof(c_0_3117,plain,
! [X34,X35,X36,X37] :
( ( c_Groups_Oplus__class_Oplus(X37,X36,X35) != c_Groups_Oplus__class_Oplus(X37,X36,X34)
| X35 = X34
| ~ class_Groups_Ocancel__semigroup__add(X37) )
& ( X35 != X34
| c_Groups_Oplus__class_Oplus(X37,X36,X35) = c_Groups_Oplus__class_Oplus(X37,X36,X34)
| ~ class_Groups_Ocancel__semigroup__add(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1861])])]) ).
fof(c_0_3118,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
c_0_1862 ).
fof(c_0_3119,plain,
! [X36,X37,X38] :
( ( c_Orderings_Oord__class_Oless(X38,X37,X36)
| c_Orderings_Oord__class_Oless__eq(X38,X36,X37)
| ~ class_Orderings_Olinorder(X38) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X38,X36,X37)
| ~ c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Olinorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1863])])]) ).
fof(c_0_3120,plain,
! [X36,X37,X38] :
( ( c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| c_Orderings_Oord__class_Oless(X38,X36,X37)
| ~ class_Orderings_Olinorder(X38) )
& ( ~ c_Orderings_Oord__class_Oless(X38,X36,X37)
| ~ c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| ~ class_Orderings_Olinorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1864])])]) ).
fof(c_0_3121,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| ~ c_Orderings_Oord__class_Oless__eq(X14,X13,X12)
| ~ c_Orderings_Oord__class_Oless(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1865])]) ).
fof(c_0_3122,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_Orderings_Oord__class_Oless(X14,X13,X12)
| ~ c_Orderings_Oord__class_Oless(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1866])]) ).
fof(c_0_3123,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless(X27,X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1867])]) ).
fof(c_0_3124,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Opreorder(X27)
| ~ c_Orderings_Oord__class_Oless(X27,X26,X25)
| ~ c_Orderings_Oord__class_Oless(X27,X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1868])]) ).
fof(c_0_3125,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_Orderings_Oord__class_Oless(X14,X13,X12)
| ~ c_Orderings_Oord__class_Oless(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1869])]) ).
fof(c_0_3126,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_Orderings_Oord__class_Oless(X14,X13,X12)
| ~ c_Orderings_Oord__class_Oless(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1870])]) ).
fof(c_0_3127,plain,
! [X36,X37,X38] :
( ( c_Orderings_Oord__class_Oless(X38,X37,X36)
| c_Orderings_Oord__class_Oless(X38,X36,X37)
| X37 = X36
| ~ class_Orderings_Olinorder(X38) )
& ( ~ c_Orderings_Oord__class_Oless(X38,X36,X37)
| ~ c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Olinorder(X38) )
& ( X37 != X36
| ~ c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Olinorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1871])])]) ).
fof(c_0_3128,plain,
! [X37,X38] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,c_Nat_OSuc(X38))
| X37 = X38
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37) )
& ( X37 != X38
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,c_Nat_OSuc(X38))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1872])])]) ).
fof(c_0_3129,plain,
! [X64,X65,X66] :
( ( hAPP(c_Polynomial_Opoly(X66,X65),X64) != c_Groups_Ozero__class_Ozero(X66)
| X65 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| c_Polynomial_Oorder(X66,X64,X65) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X66) )
& ( X65 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| hAPP(c_Polynomial_Opoly(X66,X65),X64) = c_Groups_Ozero__class_Ozero(X66)
| ~ class_Rings_Oidom(X66) )
& ( c_Polynomial_Oorder(X66,X64,X65) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X66,X65),X64) = c_Groups_Ozero__class_Ozero(X66)
| ~ class_Rings_Oidom(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1873])])]) ).
fof(c_0_3130,plain,
! [X37,X38,X39,X40] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,c_Nat_OSuc(X38)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,c_Nat_OSuc(X40))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X39) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1874])])])]) ).
fof(c_0_3131,plain,
! [X37,X38,X39,X40] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X37),X38) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X39),X40)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X39) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1875])])])]) ).
fof(c_0_3132,plain,
! [X18,X19] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1876])]) ).
fof(c_0_3133,plain,
! [X73,X74,X76,X77,X78] :
( ( X74 = c_Nat_OSuc(esk10_2(X73,X74))
| X74 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X74,c_Nat_OSuc(X73)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk10_2(X73,X74),X73)
| X74 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X74,c_Nat_OSuc(X73)) )
& ( X77 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X77,c_Nat_OSuc(X76)) )
& ( X77 != c_Nat_OSuc(X78)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X78,X76)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X77,c_Nat_OSuc(X76)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1877])])])])])]) ).
fof(c_0_3134,plain,
! [X84,X85,X86,X87] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X85,X84)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X85),X84) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X87),X86)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X87,X86) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1878])])])]) ).
fof(c_0_3135,plain,
! [X84,X85,X86,X87] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X85,X84)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X85,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X84)) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X87,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X86))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X87,X86) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1879])])])]) ).
fof(c_0_3136,plain,
! [X25,X26] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X26,X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X26)),c_Complex_Oexpi(X25)),
inference(variable_rename,[status(thm)],[c_0_1880]) ).
fof(c_0_3137,plain,
! [X25,X26,X27] :
( ~ class_Divides_Osemiring__div(X27)
| X26 = c_Groups_Ozero__class_Ozero(X27)
| c_Divides_Odiv__class_Odiv(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25),X26) = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1881])]) ).
fof(c_0_3138,plain,
! [X25,X26,X27] :
( ~ class_Divides_Osemiring__div(X27)
| X26 = c_Groups_Ozero__class_Ozero(X27)
| c_Divides_Odiv__class_Odiv(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X25),X26),X26) = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1882])]) ).
fof(c_0_3139,plain,
! [X9,X10] :
( ~ class_Rings_Olinordered__ring(X10)
| c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1883])]) ).
fof(c_0_3140,plain,
! [X12,X13] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1884])]) ).
fof(c_0_3141,plain,
! [X18,X19] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X18)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X19)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1885])]) ).
fof(c_0_3142,plain,
! [X25,X26] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
| X26 = X25
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26)
| X26 = X25
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1886])])]) ).
fof(c_0_3143,plain,
! [X12,X13] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12)
| X13 = X12
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| X13 = X12
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1887])])]) ).
fof(c_0_3144,plain,
! [X36,X37] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X37)
| X36 = X37
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,X36) )
& ( X36 != X37
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X37)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,X36) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1888])])]) ).
fof(c_0_3145,plain,
! [X25,X26] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
| X26 = X25 )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
| X26 = X25 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1889])])]) ).
fof(c_0_3146,plain,
! [X36,X37,X38,X39] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,X36)
| X37 != X36 )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X37)
| X37 != X36 )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X39,X38)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,X39)
| X39 = X38 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1890])])])])]) ).
fof(c_0_3147,plain,
! [X24,X25] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X24)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X25)
| X25 = X24 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1891])]) ).
fof(c_0_3148,plain,
! [X24,X25] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X24)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X25)
| X25 = X24 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1892])]) ).
fof(c_0_3149,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1893])]) ).
fof(c_0_3150,plain,
! [X25,X26,X27] :
( ~ class_Groups_Ogroup__add(X27)
| c_Groups_Oplus__class_Oplus(X27,c_Groups_Ominus__class_Ominus(X27,X26,X25),X25) = X26 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1894])]) ).
fof(c_0_3151,plain,
! [X25,X26,X27] :
( ~ class_Groups_Ogroup__add(X27)
| c_Groups_Ominus__class_Ominus(X27,c_Groups_Oplus__class_Oplus(X27,X26,X25),X25) = X26 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1895])]) ).
fof(c_0_3152,plain,
! [X37,X38] :
( ( X38 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X37) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38) )
& ( X37 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X37) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38) )
& ( X38 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X37 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X37) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1896])])]) ).
fof(c_0_3153,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X52) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51)
| X52 = X51 )
& ( X55 != X54
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X55) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X54) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1897])])])]) ).
fof(c_0_3154,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X52) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X52)
| X53 = X51 )
& ( X56 != X54
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X55) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,X55) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1898])])])]) ).
fof(c_0_3155,plain,
! [X78] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk32_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk32_0),X78) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X78)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1899])])])]) ).
fof(c_0_3156,plain,
! [X78] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk14_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk14_0),X78) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X78)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1900])])]) ).
fof(c_0_3157,plain,
! [X4] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X4) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X4)),
inference(variable_rename,[status(thm)],[c_0_1901]) ).
fof(c_0_3158,plain,
! [X18,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Nat_OSuc(X18)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18)),
inference(variable_rename,[status(thm)],[c_0_1902]) ).
fof(c_0_3159,plain,
! [X18,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X19),X18) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18)),
inference(variable_rename,[status(thm)],[c_0_1903]) ).
fof(c_0_3160,plain,
! [X25,X26,X27] :
( ~ class_Rings_Ocomm__semiring__1(X27)
| c_Rings_Odvd__class_Odvd(X27,X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1904])]) ).
fof(c_0_3161,plain,
! [X25,X26,X27] :
( ~ class_Rings_Ocomm__semiring__1(X27)
| c_Rings_Odvd__class_Odvd(X27,X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X25),X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1905])]) ).
fof(c_0_3162,plain,
! [X82,X83,X85,X86,X87] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83,X82)
| X82 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X83,esk23_2(X82,X83)) )
& ( X85 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X86,X87)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X86,X85) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1906])])])])]) ).
fof(c_0_3163,plain,
! [X72,X73,X75,X76,X77] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72)
| X72 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X73,esk9_2(X72,X73)) )
& ( X75 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X76,X77)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X76,X75) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1907])])])])]) ).
fof(c_0_3164,plain,
! [X18,X19] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18),c_Nat_OSuc(X19)),
inference(variable_rename,[status(thm)],[c_0_1908]) ).
fof(c_0_3165,plain,
! [X18,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_1909]) ).
fof(c_0_3166,plain,
! [X18,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18),X18) = X19,
inference(variable_rename,[status(thm)],[c_0_1910]) ).
fof(c_0_3167,plain,
! [X18,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18),X19) = X18,
inference(variable_rename,[status(thm)],[c_0_1911]) ).
fof(c_0_3168,plain,
! [X18,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18),X19),
inference(variable_rename,[status(thm)],[c_0_1912]) ).
fof(c_0_3169,plain,
! [X18,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X19)),
inference(variable_rename,[status(thm)],[c_0_1913]) ).
fof(c_0_3170,plain,
! [X18,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18)),
inference(variable_rename,[status(thm)],[c_0_1914]) ).
fof(c_0_3171,plain,
! [X37,X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X38),c_Nat_OSuc(X37))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X39)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X40),c_Nat_OSuc(X39)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1915])])])]) ).
fof(c_0_3172,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X18))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1916])]) ).
fof(c_0_3173,plain,
! [X37,X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X38),c_Nat_OSuc(X37))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X39)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X40),c_Nat_OSuc(X39)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1917])])])]) ).
fof(c_0_3174,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Nat_OSuc(X18))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| X19 = c_Nat_OSuc(X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1918])]) ).
fof(c_0_3175,plain,
! [X37,X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,c_Nat_OSuc(X37))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37)
| X38 = c_Nat_OSuc(X37) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X39)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,c_Nat_OSuc(X39)) )
& ( X40 != c_Nat_OSuc(X39)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,c_Nat_OSuc(X39)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1919])])])])]) ).
fof(c_0_3176,plain,
! [X28,X29,X30,X31] :
( ~ class_Orderings_Oorder(X31)
| ~ c_Orderings_Oord__class_Oless(X31,X30,X29)
| X30 != X28
| c_Orderings_Oord__class_Oless(X31,X28,X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1920])]) ).
fof(c_0_3177,plain,
! [X28,X29,X30,X31] :
( ~ class_Orderings_Oord(X31)
| ~ c_Orderings_Oord__class_Oless(X31,X30,X29)
| X29 != X28
| c_Orderings_Oord__class_Oless(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1921])]) ).
fof(c_0_3178,plain,
! [X28,X29,X30,X31] :
( ~ class_Orderings_Oorder(X31)
| X30 != X29
| ~ c_Orderings_Oord__class_Oless(X31,X28,X29)
| c_Orderings_Oord__class_Oless(X31,X28,X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1922])]) ).
fof(c_0_3179,plain,
! [X28,X29,X30,X31] :
( ~ class_Orderings_Oord(X31)
| X30 != X29
| ~ c_Orderings_Oord__class_Oless(X31,X29,X28)
| c_Orderings_Oord__class_Oless(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1923])]) ).
fof(c_0_3180,plain,
! [X36,X37,X38] :
( ( c_Orderings_Oord__class_Oless(X38,X36,X37)
| X36 = X37
| c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Olinorder(X38) )
& ( X36 != X37
| ~ c_Orderings_Oord__class_Oless(X38,X36,X37)
| c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Olinorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1924])])]) ).
fof(c_0_3181,plain,
! [X28,X29,X30,X31] :
( ~ class_Orderings_Oord(X31)
| X30 != X29
| ~ c_Orderings_Oord__class_Oless__eq(X31,X29,X28)
| c_Orderings_Oord__class_Oless__eq(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1925])]) ).
fof(c_0_3182,plain,
! [X28,X29,X30,X31] :
( ~ class_Orderings_Oorder(X31)
| X30 != X29
| ~ c_Orderings_Oord__class_Oless__eq(X31,X28,X29)
| c_Orderings_Oord__class_Oless__eq(X31,X28,X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1926])]) ).
fof(c_0_3183,plain,
! [X28,X29,X30,X31] :
( ~ class_Orderings_Oord(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X30,X29)
| X29 != X28
| c_Orderings_Oord__class_Oless__eq(X31,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1927])]) ).
fof(c_0_3184,plain,
! [X28,X29,X30,X31] :
( ~ class_Orderings_Oorder(X31)
| ~ c_Orderings_Oord__class_Oless__eq(X31,X30,X29)
| X30 != X28
| c_Orderings_Oord__class_Oless__eq(X31,X28,X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1928])]) ).
fof(c_0_3185,plain,
! [X6] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_1(X6))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_1(X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_1(X6),X6)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1929])])])]) ).
fof(c_0_3186,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X52)
| X53 = X51
| X52 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X56 != X54
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X54),X55) )
& ( X55 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X54),X55) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1930])])])])]) ).
fof(c_0_3187,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51)
| X52 = X51
| X53 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X55 != X54
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X54) )
& ( X56 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X54) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1931])])])])]) ).
fof(c_0_3188,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X52) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X51)
| X53 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X52 = X51 )
& ( X56 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X54) )
& ( X55 != X54
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X54) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1932])])])])]) ).
fof(c_0_3189,plain,
! [X34,X35,X36] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X35),X36) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X34),X36)
| X35 = X34
| X36 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X35 != X34
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X35),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X34),X36)
| X36 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1933])])]) ).
fof(c_0_3190,plain,
! [X34,X35,X36] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X35) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X34)
| X35 = X34
| X36 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X35 != X34
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X34)
| X36 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1934])])]) ).
fof(c_0_3191,plain,
! [X12,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,X12)
| c_Nat__Transfer_Otsub(X12,X13) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1935])]) ).
fof(c_0_3192,plain,
! [X12,X13,X14,X15] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,X12)
| c_Nat__Transfer_Otsub(X12,X13) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X12,X13) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X14)
| c_Nat__Transfer_Otsub(X14,X15) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1936])])])]) ).
fof(c_0_3193,plain,
! [X36,X37,X38] :
( ( c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| ~ c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Oorder(X38) )
& ( X37 != X36
| ~ c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Oorder(X38) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| X37 = X36
| c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Oorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1937])])]) ).
fof(c_0_3194,plain,
! [X36,X37,X38] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| c_Orderings_Oord__class_Oless(X38,X37,X36)
| X37 = X36
| ~ class_Orderings_Oorder(X38) )
& ( ~ c_Orderings_Oord__class_Oless(X38,X37,X36)
| c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| ~ class_Orderings_Oorder(X38) )
& ( X37 != X36
| c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| ~ class_Orderings_Oorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1938])])]) ).
fof(c_0_3195,plain,
! [X36,X37,X38] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| X37 = X36
| c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Olinorder(X38) )
& ( X37 != X36
| c_Orderings_Oord__class_Oless__eq(X38,X37,X36)
| c_Orderings_Oord__class_Oless(X38,X37,X36)
| ~ class_Orderings_Olinorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1939])])]) ).
fof(c_0_3196,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| X26 = X25
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,X25)
| c_Orderings_Oord__class_Oless(X27,X26,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1940])]) ).
fof(c_0_3197,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| X26 = X25
| ~ c_Orderings_Oord__class_Oless__eq(X27,X25,X26)
| c_Orderings_Oord__class_Oless(X27,X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1941])]) ).
fof(c_0_3198,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ c_Orderings_Oord__class_Oless__eq(X14,X13,X12)
| c_Orderings_Oord__class_Oless(X14,X13,X12)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1942])]) ).
fof(c_0_3199,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,X25)
| X26 = X25
| c_Orderings_Oord__class_Oless(X27,X26,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1943])]) ).
fof(c_0_3200,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| ~ c_Orderings_Oord__class_Oless__eq(X27,X26,X25)
| X25 = X26
| c_Orderings_Oord__class_Oless(X27,X26,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1944])]) ).
fof(c_0_3201,plain,
! [X10,X11] :
( ~ class_Rings_Ocomm__ring__1(X11)
| c_Groups_Ouminus__class_Ouminus(X11,X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),c_Groups_Ouminus__class_Ouminus(X11,c_Groups_Oone__class_Oone(X11))),X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1945])]) ).
fof(c_0_3202,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1946])]) ).
fof(c_0_3203,plain,
! [X37,X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,c_Nat_OSuc(X37))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37)
| X38 = X37 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X39)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,c_Nat_OSuc(X39)) )
& ( X40 != X39
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,c_Nat_OSuc(X39)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1947])])])])]) ).
fof(c_0_3204,plain,
! [X37,X38] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,c_Nat_OSuc(X37))
| X38 = X37
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37) )
& ( X38 != X37
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,c_Nat_OSuc(X37))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1948])])]) ).
fof(c_0_3205,plain,
! [X18,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X18))
| X18 = X19 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1949])]) ).
fof(c_0_3206,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X18))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1950])]) ).
fof(c_0_3207,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| c_Nat_OSuc(X19) = X18
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1951])]) ).
fof(c_0_3208,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_Orderings_Oord__class_Oless(X14,X13,X12)
| c_Orderings_Oord__class_Oless__eq(X14,X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1952])]) ).
fof(c_0_3209,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1953])]) ).
fof(c_0_3210,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X18)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1954])]) ).
fof(c_0_3211,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1955])]) ).
fof(c_0_3212,plain,
! [X37,X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X38),X37)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X39)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X40),X39) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1956])])])]) ).
fof(c_0_3213,plain,
! [X37,X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,c_Nat_OSuc(X37))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X39)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,c_Nat_OSuc(X39)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1957])])])]) ).
fof(c_0_3214,plain,
! [X37,X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X38),X37) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X40),X39)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X39) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1958])])])]) ).
fof(c_0_3215,plain,
! [X49,X50,X51,X52] :
( ~ class_Rings_Odvd(X52)
| X51 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),X50),X49)
| c_Rings_Odvd__class_Odvd(X52,X50,X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1959])]) ).
fof(c_0_3216,plain,
! [X38,X39] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X38)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X39) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1960])])])]) ).
fof(c_0_3217,plain,
! [X16,X17] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X17,X16))
| X16 != c_Groups_Ozero__class_Ozero(X17)
| ~ class_RealVector_Oreal__normed__vector(X17) )
& ( X16 = c_Groups_Ozero__class_Ozero(X17)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X17,X16))
| ~ class_RealVector_Oreal__normed__vector(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1961])])]) ).
fof(c_0_3218,plain,
! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X10)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X10)),
inference(variable_rename,[status(thm)],[c_0_1962]) ).
fof(c_0_3219,plain,
! [X10] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X10 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1963])]) ).
fof(c_0_3220,plain,
! [X18] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X18)),
inference(variable_rename,[status(thm)],[c_0_1964]) ).
fof(c_0_3221,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1965])]) ).
fof(c_0_3222,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Nat_OSuc(X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1966])]) ).
fof(c_0_3223,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1967])]) ).
fof(c_0_3224,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1968])]) ).
fof(c_0_3225,plain,
! [X25,X26,X27] :
( ~ class_Groups_Ogroup__add(X27)
| c_Groups_Ominus__class_Ominus(X27,X26,X25) = c_Groups_Oplus__class_Oplus(X27,X26,c_Groups_Ouminus__class_Ouminus(X27,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1969])]) ).
fof(c_0_3226,plain,
! [X25,X26,X27] :
( ~ class_Groups_Oab__group__add(X27)
| c_Groups_Ominus__class_Ominus(X27,X26,X25) = c_Groups_Oplus__class_Oplus(X27,X26,c_Groups_Ouminus__class_Ouminus(X27,X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1970])]) ).
fof(c_0_3227,plain,
! [X12,X13,X14] :
( ~ class_Rings_Ocomm__ring__1(X14)
| c_Groups_Ominus__class_Ominus(X14,X13,X12) = c_Groups_Oplus__class_Oplus(X14,X13,c_Groups_Ouminus__class_Ouminus(X14,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1971])]) ).
fof(c_0_3228,plain,
! [X25,X26,X27] :
( ~ class_Groups_Ogroup__add(X27)
| c_Groups_Ominus__class_Ominus(X27,X26,c_Groups_Ouminus__class_Ouminus(X27,X25)) = c_Groups_Oplus__class_Oplus(X27,X26,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1972])]) ).
fof(c_0_3229,plain,
! [X16,X17] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X17,X16),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X16 = c_Groups_Ozero__class_Ozero(X17)
| ~ class_RealVector_Oreal__normed__vector(X17) )
& ( X16 != c_Groups_Ozero__class_Ozero(X17)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X17,X16),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1973])])]) ).
fof(c_0_3230,plain,
! [X12,X13] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| X12 != X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1974])]) ).
fof(c_0_3231,plain,
! [X12,X13] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| X13 != X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1975])]) ).
fof(c_0_3232,plain,
! [X12,X13] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X12,X13)
| X13 != X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1976])]) ).
fof(c_0_3233,plain,
! [X28,X29,X30] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,X29)
| X29 != X28
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1977])]) ).
fof(c_0_3234,plain,
! [X28,X29,X30] :
( X30 != X29
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X29,X28)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X30,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1978])]) ).
fof(c_0_3235,plain,
! [X37,X38,X39,X40] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X38,X37) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X39)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X39) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1979])])])]) ).
fof(c_0_3236,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1980])]) ).
fof(c_0_3237,plain,
! [X36,X37,X38,X39] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X37,X36)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X37,X36)
| X37 = X36 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X39,X38)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38) )
& ( X39 != X38
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1981])])])])]) ).
fof(c_0_3238,plain,
! [X36,X37,X38,X39] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X37,X36)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X37,X36) )
& ( X37 != X36
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X37,X36) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38)
| X39 = X38
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X39,X38) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1982])])])])]) ).
fof(c_0_3239,plain,
! [X37,X38,X39,X40] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37) )
& ( X38 != X37
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X39)
| X40 = X39
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1983])])])])]) ).
fof(c_0_3240,plain,
! [X37,X38,X39,X40] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X37)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37)
| X38 = X37 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X39)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X39) )
& ( X40 != X39
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1984])])])])]) ).
fof(c_0_3241,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| X19 = X18
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1985])]) ).
fof(c_0_3242,plain,
! [X47,X48,X49,X50] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X47)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47) )
& ( X48 != X47
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49)
| X50 = X49
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1986])])])])]) ).
fof(c_0_3243,plain,
! [X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X10)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X10),
inference(variable_rename,[status(thm)],[c_0_1987]) ).
fof(c_0_3244,plain,
! [X9,X10] :
( ~ class_Groups_Ozero(X10)
| c_Polynomial_Omonom(X10,X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X10,X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1988])]) ).
fof(c_0_3245,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1989])]) ).
fof(c_0_3246,plain,
! [X18,X19] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18) )
& ( X19 != X18
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1990])])]) ).
fof(c_0_3247,plain,
! [X12,X13] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X12)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1991])]) ).
fof(c_0_3248,plain,
! [X10,X11] :
( ~ class_RealVector_Oreal__normed__vector(X11)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X11,X10),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1992])]) ).
fof(c_0_3249,plain,
! [X39,X40] :
( ~ class_Rings_Ocomm__semiring__0(X40)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X40)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X40))),X39) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1993])]) ).
fof(c_0_3250,plain,
! [X24,X25] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X25,X24) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X24)),
inference(variable_rename,[status(thm)],[c_0_1994]) ).
fof(c_0_3251,plain,
! [X24,X25] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X24)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X25,X24),
inference(variable_rename,[status(thm)],[c_0_1995]) ).
fof(c_0_3252,plain,
! [X12,X13] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X13,X12) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12)),
inference(variable_rename,[status(thm)],[c_0_1996]) ).
fof(c_0_3253,plain,
! [X15,X16] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X16,X15) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X16,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15)),
inference(variable_rename,[status(thm)],[c_0_1997]) ).
fof(c_0_3254,plain,
! [X12,X13] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X13,X12) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X13,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X12)),
inference(variable_rename,[status(thm)],[c_0_1998]) ).
fof(c_0_3255,plain,
! [X4,X5] :
( hAPP(X5,esk1_2(X4,X5)) != hAPP(X4,esk1_2(X4,X5))
| X5 = X4 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1999])])]) ).
fof(c_0_3256,plain,
! [X64,X65,X66] :
( ( c_Polynomial_Osmult(X66,X65,X64) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| X65 = c_Groups_Ozero__class_Ozero(X66)
| X64 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| ~ class_Rings_Oidom(X66) )
& ( X65 != c_Groups_Ozero__class_Ozero(X66)
| c_Polynomial_Osmult(X66,X65,X64) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| ~ class_Rings_Oidom(X66) )
& ( X64 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| c_Polynomial_Osmult(X66,X65,X64) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| ~ class_Rings_Oidom(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2000])])]) ).
fof(c_0_3257,plain,
! [X27,X28,X29,X30] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X28,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X27)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X28 = X27 )
& ( X30 != X29
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X30,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X29)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2001])])])]) ).
fof(c_0_3258,plain,
! [X27,X28,X29] :
( ( X28 = c_Groups_Ozero__class_Ozero(X29)
| hAPP(hAPP(c_Power_Opower__class_Opower(X29),X28),X27) != c_Groups_Ozero__class_Ozero(X29)
| ~ class_Power_Opower(X29)
| ~ class_Rings_Omult__zero(X29)
| ~ class_Rings_Ono__zero__divisors(X29)
| ~ class_Rings_Ozero__neq__one(X29) )
& ( X27 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X29),X28),X27) != c_Groups_Ozero__class_Ozero(X29)
| ~ class_Power_Opower(X29)
| ~ class_Rings_Omult__zero(X29)
| ~ class_Rings_Ono__zero__divisors(X29)
| ~ class_Rings_Ozero__neq__one(X29) )
& ( X28 != c_Groups_Ozero__class_Ozero(X29)
| X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X29),X28),X27) = c_Groups_Ozero__class_Ozero(X29)
| ~ class_Power_Opower(X29)
| ~ class_Rings_Omult__zero(X29)
| ~ class_Rings_Ono__zero__divisors(X29)
| ~ class_Rings_Ozero__neq__one(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2002])])]) ).
fof(c_0_3259,plain,
! [X16,X17] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X16),X16) != c_Groups_Oone__class_Oone(X17)
| X16 = c_Groups_Oone__class_Oone(X17)
| X16 = c_Groups_Ouminus__class_Ouminus(X17,c_Groups_Oone__class_Oone(X17))
| ~ class_Rings_Oring__1__no__zero__divisors(X17) )
& ( X16 != c_Groups_Oone__class_Oone(X17)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X16),X16) = c_Groups_Oone__class_Oone(X17)
| ~ class_Rings_Oring__1__no__zero__divisors(X17) )
& ( X16 != c_Groups_Ouminus__class_Ouminus(X17,c_Groups_Oone__class_Oone(X17))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X16),X16) = c_Groups_Oone__class_Oone(X17)
| ~ class_Rings_Oring__1__no__zero__divisors(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2003])])]) ).
fof(c_0_3260,plain,
! [X9,X10] :
( ~ class_Rings_Odivision__ring(X10)
| X9 = c_Groups_Ozero__class_Ozero(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Rings_Oinverse__class_Oinverse(X10,X9)),X9) = c_Groups_Oone__class_Oone(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2004])]) ).
fof(c_0_3261,plain,
! [X9,X10] :
( ~ class_Fields_Ofield(X10)
| X9 = c_Groups_Ozero__class_Ozero(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Rings_Oinverse__class_Oinverse(X10,X9)),X9) = c_Groups_Oone__class_Oone(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2005])]) ).
fof(c_0_3262,plain,
! [X64,X65,X66] :
( ( X65 = c_Groups_Ozero__class_Ozero(X66)
| c_Polynomial_OpCons(X66,X65,X64) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| ~ class_Groups_Ozero(X66) )
& ( X64 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| c_Polynomial_OpCons(X66,X65,X64) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| ~ class_Groups_Ozero(X66) )
& ( X65 != c_Groups_Ozero__class_Ozero(X66)
| X64 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| c_Polynomial_OpCons(X66,X65,X64) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X66))
| ~ class_Groups_Ozero(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2006])])]) ).
fof(c_0_3263,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_Orderings_Oord__class_Oless(X14,X13,X12)
| X13 = X12
| c_Orderings_Oord__class_Oless(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2007])]) ).
fof(c_0_3264,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| X13 = X12
| c_Orderings_Oord__class_Oless(X14,X13,X12)
| c_Orderings_Oord__class_Oless(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2008])]) ).
fof(c_0_3265,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_Orderings_Oord__class_Oless(X14,X13,X12)
| X13 = X12
| c_Orderings_Oord__class_Oless(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2009])]) ).
fof(c_0_3266,plain,
! [X36,X37,X38] :
( ( X37 = X36
| c_Orderings_Oord__class_Oless(X38,X37,X36)
| c_Orderings_Oord__class_Oless(X38,X36,X37)
| ~ class_Orderings_Olinorder(X38) )
& ( ~ c_Orderings_Oord__class_Oless(X38,X37,X36)
| X37 != X36
| ~ class_Orderings_Olinorder(X38) )
& ( ~ c_Orderings_Oord__class_Oless(X38,X36,X37)
| X37 != X36
| ~ class_Orderings_Olinorder(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2010])])]) ).
fof(c_0_3267,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__idom(X14)
| X13 = X12
| c_Orderings_Oord__class_Oless(X14,X13,X12)
| c_Orderings_Oord__class_Oless(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2011])]) ).
fof(c_0_3268,plain,
! [X78,X79,X80,X81,X82,X83,X86,X87] :
( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X80,X79,X78)
| hAPP(X78,X81) = hAPP(X78,X82) )
& ( hAPP(X83,esk16_1(X83)) != hAPP(X83,esk17_1(X83))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X87,X86,X83) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2012])])])])]) ).
fof(c_0_3269,plain,
! [X18,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X18)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18),
inference(variable_rename,[status(thm)],[c_0_2013]) ).
fof(c_0_3270,plain,
! [X18,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X19),X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Nat_OSuc(X18)),
inference(variable_rename,[status(thm)],[c_0_2014]) ).
fof(c_0_3271,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_Orderings_Oord__class_Oless__eq(X14,X13,X12)
| c_Orderings_Oord__class_Oless(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2015])]) ).
fof(c_0_3272,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_Orderings_Oord__class_Oless(X14,X13,X12)
| c_Orderings_Oord__class_Oless__eq(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2016])]) ).
fof(c_0_3273,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_Orderings_Oord__class_Oless__eq(X14,X13,X12)
| c_Orderings_Oord__class_Oless(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2017])]) ).
fof(c_0_3274,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_Orderings_Oord__class_Oless__eq(X14,X13,X12)
| c_Orderings_Oord__class_Oless__eq(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2018])]) ).
fof(c_0_3275,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_Orderings_Oord__class_Oless__eq(X14,X13,X12)
| c_Orderings_Oord__class_Oless__eq(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2019])]) ).
fof(c_0_3276,plain,
! [X28,X29,X30] :
( ~ class_Rings_Ocomm__semiring__1(X30)
| c_Groups_Oplus__class_Oplus(X30,X29,X28) = c_Groups_Oplus__class_Oplus(X30,X28,X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2020])]) ).
fof(c_0_3277,plain,
! [X27,X28,X29] :
( ( X28 != c_Groups_Ouminus__class_Ouminus(X29,X27)
| c_Groups_Oplus__class_Oplus(X29,X28,X27) = c_Groups_Ozero__class_Ozero(X29)
| ~ class_Groups_Ogroup__add(X29) )
& ( c_Groups_Oplus__class_Oplus(X29,X28,X27) != c_Groups_Ozero__class_Ozero(X29)
| X28 = c_Groups_Ouminus__class_Ouminus(X29,X27)
| ~ class_Groups_Ogroup__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2021])])]) ).
fof(c_0_3278,plain,
! [X25,X26,X27] :
( ~ class_Groups_Ogroup__add(X27)
| c_Groups_Oplus__class_Oplus(X27,X26,X25) != c_Groups_Ozero__class_Ozero(X27)
| c_Groups_Ouminus__class_Ouminus(X27,X26) = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2022])]) ).
fof(c_0_3279,plain,
! [X36,X37,X38] :
( ( c_Groups_Oplus__class_Oplus(X38,X37,X36) != c_Groups_Ozero__class_Ozero(X38)
| X36 = c_Groups_Ouminus__class_Ouminus(X38,X37)
| ~ class_Groups_Ogroup__add(X38) )
& ( X36 != c_Groups_Ouminus__class_Ouminus(X38,X37)
| c_Groups_Oplus__class_Oplus(X38,X37,X36) = c_Groups_Ozero__class_Ozero(X38)
| ~ class_Groups_Ogroup__add(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2023])])]) ).
fof(c_0_3280,plain,
! [X27,X28,X29] :
( ( c_Polynomial_Omonom(X29,X28,X27) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X29))
| X28 = c_Groups_Ozero__class_Ozero(X29)
| ~ class_Groups_Ozero(X29) )
& ( X28 != c_Groups_Ozero__class_Ozero(X29)
| c_Polynomial_Omonom(X29,X28,X27) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X29))
| ~ class_Groups_Ozero(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2024])])]) ).
fof(c_0_3281,plain,
! [X9] :
( ~ class_Rings_Olinordered__semidom(X9)
| ~ c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Oone__class_Oone(X9),c_Groups_Ozero__class_Ozero(X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2025])]) ).
fof(c_0_3282,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
c_0_2026 ).
fof(c_0_3283,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
c_0_2027 ).
fof(c_0_3284,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
c_0_2028 ).
fof(c_0_3285,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
c_0_2029 ).
fof(c_0_3286,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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2030])]) ).
fof(c_0_3287,plain,
! [X40,X41] :
( ~ class_Rings_Ocomm__semiring__0(X41)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X41)),X40),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X41))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2031])]) ).
fof(c_0_3288,plain,
! [X25,X26,X27] :
( ~ class_Rings_Ocomm__semiring__1(X27)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X25),X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2032])]) ).
fof(c_0_3289,plain,
! [X37,X38] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X37 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X38 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2033])])])]) ).
fof(c_0_3290,plain,
! [X37,X38,X39,X40] :
( ( X38 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X38 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37) )
& ( X37 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X38 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37) )
& ( X38 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X37 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37) )
& ( X37 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X37 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37) )
& ( X40 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X39 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X39) )
& ( X40 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X39 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2034])])])])]) ).
fof(c_0_3291,plain,
! [X37,X38,X39,X40] :
( ( X38 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X38 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X37 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X38 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X38 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X37 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X37 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X37 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X40 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X39 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X39) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X40 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X39 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X39) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2035])])])])]) ).
fof(c_0_3292,plain,
! [X25,X26,X27] :
( ~ class_Rings_Odivision__ring(X27)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25) != c_Groups_Oone__class_Oone(X27)
| c_Rings_Oinverse__class_Oinverse(X27,X26) = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2036])]) ).
fof(c_0_3293,plain,
! [X12,X13] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,X12)
| X13 = X12
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_2037]) ).
fof(c_0_3294,plain,
! [X37,X38,X39,X40] :
( ( X38 = X37
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X37)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X38) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X39)
| X40 != X39 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,X40)
| X40 != X39 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2038])])])])]) ).
fof(c_0_3295,plain,
! [X12,X13] :
( X13 = X12
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X12)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2039])]) ).
fof(c_0_3296,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__1(X10)
| ~ c_Rings_Odvd__class_Odvd(X10,c_Groups_Ozero__class_Ozero(X10),X9)
| X9 = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2040])]) ).
fof(c_0_3297,plain,
! [X17,X18] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2041])])])]) ).
fof(c_0_3298,plain,
! [X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X24)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_2042]) ).
fof(c_0_3299,plain,
! [X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X24)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_2043]) ).
fof(c_0_3300,plain,
! [X18,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_2044]) ).
fof(c_0_3301,plain,
! [X27,X28,X29] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27) != c_Groups_Ozero__class_Ozero(X29)
| X28 = c_Groups_Ozero__class_Ozero(X29)
| X27 = c_Groups_Ozero__class_Ozero(X29)
| ~ class_Rings_Oring__no__zero__divisors(X29) )
& ( X28 != c_Groups_Ozero__class_Ozero(X29)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27) = c_Groups_Ozero__class_Ozero(X29)
| ~ class_Rings_Oring__no__zero__divisors(X29) )
& ( X27 != c_Groups_Ozero__class_Ozero(X29)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X27) = c_Groups_Ozero__class_Ozero(X29)
| ~ class_Rings_Oring__no__zero__divisors(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2045])])]) ).
fof(c_0_3302,plain,
! [X25,X26,X27] :
( ~ class_Rings_Ono__zero__divisors(X27)
| X26 = c_Groups_Ozero__class_Ozero(X27)
| X25 = c_Groups_Ozero__class_Ozero(X27)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25) != c_Groups_Ozero__class_Ozero(X27) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2046])]) ).
fof(c_0_3303,plain,
! [X25,X26,X27] :
( ~ class_Rings_Ono__zero__divisors(X27)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25) != c_Groups_Ozero__class_Ozero(X27)
| X26 = c_Groups_Ozero__class_Ozero(X27)
| X25 = c_Groups_Ozero__class_Ozero(X27) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2047])]) ).
fof(c_0_3304,plain,
! [X39,X40] :
( ~ class_Groups_Oab__group__add(X40)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X40),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X40)),X39) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X40),X39) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2048])]) ).
fof(c_0_3305,plain,
! [X24,X25] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,X25),
inference(variable_rename,[status(thm)],[c_0_2049]) ).
fof(c_0_3306,plain,
! [X18,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X19),
inference(variable_rename,[status(thm)],[c_0_2050]) ).
fof(c_0_3307,plain,
! [X27,X28] :
( ( c_Groups_Oplus__class_Oplus(X28,X27,X27) != c_Groups_Ozero__class_Ozero(X28)
| X27 = c_Groups_Ozero__class_Ozero(X28)
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( X27 != c_Groups_Ozero__class_Ozero(X28)
| c_Groups_Oplus__class_Oplus(X28,X27,X27) = c_Groups_Ozero__class_Ozero(X28)
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2051])])]) ).
fof(c_0_3308,plain,
! [X27,X28] :
( ( c_Groups_Ozero__class_Ozero(X28) != c_Groups_Oplus__class_Oplus(X28,X27,X27)
| X27 = c_Groups_Ozero__class_Ozero(X28)
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( X27 != c_Groups_Ozero__class_Ozero(X28)
| c_Groups_Ozero__class_Ozero(X28) = c_Groups_Oplus__class_Oplus(X28,X27,X27)
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2052])])]) ).
fof(c_0_3309,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
c_0_2053 ).
fof(c_0_3310,plain,
! [X27,X28,X29] :
( ( X28 != X27
| c_Groups_Ominus__class_Ominus(X29,X28,X27) = c_Groups_Ozero__class_Ozero(X29)
| ~ class_Groups_Oab__group__add(X29) )
& ( c_Groups_Ominus__class_Ominus(X29,X28,X27) != c_Groups_Ozero__class_Ozero(X29)
| X28 = X27
| ~ class_Groups_Oab__group__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2054])])]) ).
fof(c_0_3311,plain,
! [X27,X28,X29] :
( ( c_Groups_Ominus__class_Ominus(X29,X28,X27) != c_Groups_Ozero__class_Ozero(X29)
| X28 = X27
| ~ class_Groups_Ogroup__add(X29) )
& ( X28 != X27
| c_Groups_Ominus__class_Ominus(X29,X28,X27) = c_Groups_Ozero__class_Ozero(X29)
| ~ class_Groups_Ogroup__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2055])])]) ).
fof(c_0_3312,plain,
! [X36,X37,X38,X39] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X37,X36) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X36 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X37) )
& ( X38 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X39)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X39,X38) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2056])])])]) ).
fof(c_0_3313,plain,
! [X9,X10,X11] :
( ~ class_Rings_Oring__1__no__zero__divisors(X11)
| X10 = c_Groups_Ozero__class_Ozero(X11)
| hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),X9) != c_Groups_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2057])]) ).
fof(c_0_3314,plain,
! [X74,X76,X77] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X74)
| X74 = c_Nat_OSuc(esk11_1(X74)) )
& ( X76 != c_Nat_OSuc(X77)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X76) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2058])])])])]) ).
fof(c_0_3315,plain,
! [X27,X28,X29] :
( ( X28 != c_Groups_Oplus__class_Oplus(X29,X28,X27)
| X27 = c_Groups_Ozero__class_Ozero(X29)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X29) )
& ( X27 != c_Groups_Ozero__class_Ozero(X29)
| X28 = c_Groups_Oplus__class_Oplus(X29,X28,X27)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2059])])]) ).
fof(c_0_3316,plain,
! [X64,X65] :
( ( c_Polynomial_Opoly(X65,X64) != c_Polynomial_Opoly(X65,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X65)))
| X64 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X65))
| ~ class_Int_Oring__char__0(X65)
| ~ class_Rings_Oidom(X65) )
& ( X64 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X65))
| c_Polynomial_Opoly(X65,X64) = c_Polynomial_Opoly(X65,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X65)))
| ~ class_Int_Oring__char__0(X65)
| ~ class_Rings_Oidom(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2060])])]) ).
fof(c_0_3317,plain,
! [X10] :
( X10 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X10)),X10) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2061])]) ).
fof(c_0_3318,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ c_Orderings_Oord__class_Oless(X14,X13,X12)
| X12 != X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2062])]) ).
fof(c_0_3319,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ c_Orderings_Oord__class_Oless(X14,X13,X12)
| X13 != X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2063])]) ).
fof(c_0_3320,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ c_Orderings_Oord__class_Oless(X14,X13,X12)
| X13 != X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2064])]) ).
fof(c_0_3321,plain,
! [X9] :
( ~ class_Rings_Ocomm__semiring__1(X9)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9)) = c_Polynomial_OpCons(X9,c_Groups_Oone__class_Oone(X9),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2065])]) ).
fof(c_0_3322,plain,
! [X9] :
( ~ class_Groups_Ozero(X9)
| 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)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2066])]) ).
fof(c_0_3323,plain,
! [X37,X38,X39,X40] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X38),X37) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X37 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X38 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X39 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X40),X39) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X40 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X40),X39) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2067])])])])]) ).
fof(c_0_3324,plain,
! [X9,X10] :
( ~ class_Rings_Odivision__ring(X10)
| X9 = c_Groups_Ozero__class_Ozero(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Rings_Oinverse__class_Oinverse(X10,X9)) = c_Groups_Oone__class_Oone(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2068])]) ).
fof(c_0_3325,plain,
! [X17,X18] :
( ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
| X18 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2069])])])]) ).
fof(c_0_3326,plain,
! [X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| ~ c_Orderings_Oord__class_Oless(X11,X10,X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2070])]) ).
fof(c_0_3327,plain,
! [X7] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X7),X7),
inference(variable_rename,[status(thm)],[c_0_2071]) ).
fof(c_0_3328,plain,
! [X9,X10] :
( ~ class_RealVector_Oreal__normed__div__algebra(X10)
| ~ class_Rings_Odivision__ring__inverse__zero(X10)
| c_RealVector_Onorm__class_Onorm(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2072])]) ).
fof(c_0_3329,plain,
! [X9,X10] :
( ~ class_Rings_Odivision__ring(X10)
| X9 = c_Groups_Ozero__class_Ozero(X10)
| c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)) = c_Groups_Ouminus__class_Ouminus(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2073])]) ).
fof(c_0_3330,plain,
! [X37,X38] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X37,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X37 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X38 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X38,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2074])])])]) ).
fof(c_0_3331,plain,
! [X17,X18] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2075])])])]) ).
fof(c_0_3332,plain,
! [X37,X38,X39,X40] :
( ( X38 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X37) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X37 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X37) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X40 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X39 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X39) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2076])])])])]) ).
fof(c_0_3333,plain,
! [X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X25),
inference(variable_rename,[status(thm)],[c_0_2077]) ).
fof(c_0_3334,plain,
! [X18,X19] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X19),
inference(variable_rename,[status(thm)],[c_0_2078]) ).
fof(c_0_3335,plain,
! [X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X25),
inference(variable_rename,[status(thm)],[c_0_2079]) ).
fof(c_0_3336,plain,
! [X9,X10] :
( ~ class_Groups_Ogroup__add(X10)
| c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Ouminus__class_Ouminus(X10,X9)) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2080])]) ).
fof(c_0_3337,plain,
! [X9,X10] :
( ~ class_Groups_Ogroup__add(X10)
| c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),X9) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2081])]) ).
fof(c_0_3338,plain,
! [X9,X10] :
( ~ class_Groups_Oab__group__add(X10)
| c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),X9) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2082])]) ).
fof(c_0_3339,plain,
! [X37,X38,X39,X40] :
( ( X38 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X37 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X40 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X39 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X39) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2083])])])])]) ).
fof(c_0_3340,plain,
! [X9,X10] :
( ~ class_RealVector_Oreal__normed__div__algebra(X10)
| X9 = c_Groups_Ozero__class_Ozero(X10)
| c_RealVector_Onorm__class_Onorm(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2084])]) ).
fof(c_0_3341,plain,
! [X39,X40] :
( ~ class_Rings_Ocomm__semiring__0(X40)
| c_Polynomial_Opcompose(X40,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X40)),X39) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2085])]) ).
fof(c_0_3342,plain,
! [X28,X29] :
( ~ class_Rings_Ocomm__semiring__0(X29)
| c_Polynomial_Osynthetic__div(X29,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X29)),X28) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2086])]) ).
fof(c_0_3343,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__0(X10)
| c_Polynomial_Osmult(X10,X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2087])]) ).
fof(c_0_3344,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),esk15_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2088])])]) ).
fof(c_0_3345,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| X18 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2089])])])]) ).
fof(c_0_3346,plain,
! [X10,X11] :
( ~ class_RealVector_Oreal__normed__vector(X11)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X11,X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2090])]) ).
fof(c_0_3347,plain,
! [X9,X10] :
( ~ class_Power_Opower(X10)
| ~ class_Rings_Osemiring__0(X10)
| hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ozero__class_Ozero(X10)),c_Nat_OSuc(X9)) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2091])]) ).
fof(c_0_3348,plain,
! [X9,X10] :
( ( X9 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ozero__class_Ozero(X10)),X9) = c_Groups_Oone__class_Oone(X10)
| ~ class_Power_Opower(X10)
| ~ class_Rings_Osemiring__0(X10) )
& ( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ozero__class_Ozero(X10)),X9) = c_Groups_Ozero__class_Ozero(X10)
| ~ class_Power_Opower(X10)
| ~ class_Rings_Osemiring__0(X10) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2092])])]) ).
fof(c_0_3349,plain,
! [X18,X19] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18) != X19
| X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2093])])])]) ).
fof(c_0_3350,plain,
! [X7] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[c_0_2094]) ).
fof(c_0_3351,plain,
! [X7] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[c_0_2095]) ).
fof(c_0_3352,plain,
! [X7] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[c_0_2096]) ).
fof(c_0_3353,plain,
! [X10,X11] :
( ~ class_Rings_Ocomm__semiring__0(X11)
| hAPP(c_Polynomial_Opoly(X11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))),X10) = c_Groups_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2097])]) ).
fof(c_0_3354,plain,
! [X10,X11] :
( ~ class_Rings_Ocomm__semiring__1(X11)
| hAPP(c_Polynomial_Opoly(X11,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X11))),X10) = c_Groups_Oone__class_Oone(X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2098])]) ).
fof(c_0_3355,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
| X18 != X19 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2099])]) ).
fof(c_0_3356,plain,
! [X54,X55] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54)
| X55 != X54 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2100])]) ).
fof(c_0_3357,plain,
! [X39,X40] :
( ~ class_Groups_Ocomm__monoid__add(X40)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X40),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X40)),X39) = X39 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2101])]) ).
fof(c_0_3358,plain,
! [X40,X41] :
( ~ class_Groups_Ocomm__monoid__add(X41)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X41),X40,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X41))) = X40 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2102])]) ).
fof(c_0_3359,plain,
! [X40,X41] :
( ~ class_Groups_Oab__group__add(X41)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X41),X40,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X41))) = X40 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2103])]) ).
fof(c_0_3360,plain,
! [X9,X10] :
( ~ class_Rings_Odivision__ring__inverse__zero(X10)
| c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)) = c_Groups_Ouminus__class_Ouminus(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2104])]) ).
fof(c_0_3361,plain,
! [X37,X38,X39,X40] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X37) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X38 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X37 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X40 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X39) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X39 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X39) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2105])])])])]) ).
fof(c_0_3362,plain,
! [X7] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X7),
inference(variable_rename,[status(thm)],[c_0_2106]) ).
fof(c_0_3363,plain,
! [X7] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X7),
inference(variable_rename,[status(thm)],[c_0_2107]) ).
fof(c_0_3364,plain,
! [X9,X10] :
( ~ class_Groups_Ogroup__add(X10)
| c_Groups_Ominus__class_Ominus(X10,c_Groups_Ozero__class_Ozero(X10),X9) = c_Groups_Ouminus__class_Ouminus(X10,X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2108])]) ).
fof(c_0_3365,plain,
! [X18,X19] :
( X19 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X18)
| X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2109])]) ).
fof(c_0_3366,plain,
! [X37,X38,X39,X40] :
( ( X38 = 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),X38),X37) )
& ( X37 = 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),X38),X37) )
& ( X40 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X39 != 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),X40),X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2110])])])])]) ).
fof(c_0_3367,plain,
! [X37,X38,X39,X40] :
( ( X38 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X37) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X37 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X37) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X40 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X39 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X39) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2111])])])])]) ).
fof(c_0_3368,plain,
! [X24] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X24),X24) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[c_0_2112]) ).
fof(c_0_3369,plain,
! [X9,X10] :
( ~ class_Groups_Ozero(X10)
| c_Polynomial_Omonom(X10,c_Groups_Ozero__class_Ozero(X10),X9) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2113])]) ).
fof(c_0_3370,plain,
! [X40,X41] :
( ~ class_Rings_Ocomm__semiring__0(X41)
| c_Polynomial_Osmult(X41,c_Groups_Ozero__class_Ozero(X41),X40) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2114])]) ).
fof(c_0_3371,plain,
! [X9] :
( ~ class_Power_Opower(X9)
| c_Power_Opower__class_Opower(X9) = c_Power_Opower_Opower(X9,c_Groups_Oone__class_Oone(X9),c_Groups_Otimes__class_Otimes(X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2115])]) ).
fof(c_0_3372,plain,
! [X7] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X7) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[c_0_2116]) ).
fof(c_0_3373,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__1(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ozero__class_Ozero(X10)),X9) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2117])]) ).
fof(c_0_3374,plain,
! [X9,X10] :
( ~ class_Groups_Omonoid__mult(X10)
| hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Oone__class_Oone(X10)),X9) = c_Groups_Oone__class_Oone(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2118])]) ).
fof(c_0_3375,plain,
! [X9,X10] :
( ~ class_Rings_Omult__zero(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ozero__class_Ozero(X10)),X9) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2119])]) ).
fof(c_0_3376,plain,
! [X25,X26] :
( ~ class_RealVector_Oreal__normed__algebra(X26)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),c_Groups_Ozero__class_Ozero(X26)),X25) = c_Groups_Ozero__class_Ozero(X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2120])]) ).
fof(c_0_3377,plain,
! [X12,X13] :
( ~ class_RealVector_Oreal__normed__algebra(X13)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),c_Groups_Ozero__class_Ozero(X13)),X12) = c_Groups_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2121])]) ).
fof(c_0_3378,plain,
! [X9] :
( ~ class_Rings_Olinordered__semidom(X9)
| c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9),c_Groups_Oone__class_Oone(X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2122])]) ).
fof(c_0_3379,plain,
! [X9] :
( ~ class_Rings_Olinordered__semidom(X9)
| c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),c_Groups_Oone__class_Oone(X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2123])]) ).
fof(c_0_3380,plain,
! [X9,X10] :
( ~ class_Groups_Ocomm__monoid__mult(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oone__class_Oone(X10)),X9) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2124])]) ).
fof(c_0_3381,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__1(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oone__class_Oone(X10)),X9) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2125])]) ).
fof(c_0_3382,plain,
! [X9,X10] :
( ~ class_Groups_Omonoid__mult(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oone__class_Oone(X10)),X9) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2126])]) ).
fof(c_0_3383,plain,
! [X9,X10] :
( ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Odiv(X10,c_Groups_Ozero__class_Ozero(X10),X9) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2127])]) ).
fof(c_0_3384,plain,
! [X9,X10] :
( ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Odiv(X10,X9,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2128])]) ).
fof(c_0_3385,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__1(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2129])]) ).
fof(c_0_3386,plain,
! [X9,X10] :
( ~ class_Rings_Omult__zero(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2130])]) ).
fof(c_0_3387,plain,
! [X9,X10] :
( ~ class_RealVector_Oreal__normed__algebra(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2131])]) ).
fof(c_0_3388,plain,
! [X10,X11] :
( ~ class_RealVector_Oreal__normed__algebra(X11)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),c_Groups_Ozero__class_Ozero(X11)) = c_Groups_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2132])]) ).
fof(c_0_3389,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
c_0_2133 ).
fof(c_0_3390,plain,
! [X40,X41] :
( ~ class_Rings_Ocomm__semiring__1(X41)
| c_Polynomial_Osmult(X41,c_Groups_Oone__class_Oone(X41),X40) = X40 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2134])]) ).
fof(c_0_3391,plain,
! [X9,X10] :
( ~ class_Groups_Ogroup__add(X10)
| c_Groups_Ominus__class_Ominus(X10,X9,c_Groups_Ozero__class_Ozero(X10)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2135])]) ).
fof(c_0_3392,plain,
! [X9,X10] :
( ~ class_Groups_Ocomm__monoid__add(X10)
| c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Ozero__class_Ozero(X10)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2136])]) ).
fof(c_0_3393,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__1(X10)
| c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Ozero__class_Ozero(X10)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2137])]) ).
fof(c_0_3394,plain,
! [X9,X10] :
( ~ class_Groups_Omonoid__add(X10)
| c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Ozero__class_Ozero(X10)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2138])]) ).
fof(c_0_3395,plain,
! [X9,X10] :
( ~ class_Groups_Ocomm__monoid__add(X10)
| c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X9) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2139])]) ).
fof(c_0_3396,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__1(X10)
| c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X9) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2140])]) ).
fof(c_0_3397,plain,
! [X9,X10] :
( ~ class_Groups_Omonoid__add(X10)
| c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X9) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2141])]) ).
fof(c_0_3398,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__1(X10)
| c_Rings_Odvd__class_Odvd(X10,c_Groups_Oone__class_Oone(X10),X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2142])]) ).
fof(c_0_3399,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__1(X10)
| c_Rings_Odvd__class_Odvd(X10,X9,c_Groups_Ozero__class_Ozero(X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2143])]) ).
fof(c_0_3400,plain,
! [X9,X10] :
( ~ class_Groups_Ocomm__monoid__mult(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Groups_Oone__class_Oone(X10)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2144])]) ).
fof(c_0_3401,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__1(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Groups_Oone__class_Oone(X10)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2145])]) ).
fof(c_0_3402,plain,
! [X9,X10] :
( ~ class_Groups_Omonoid__mult(X10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Groups_Oone__class_Oone(X10)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2146])]) ).
fof(c_0_3403,plain,
! [X10,X11] :
( ~ class_Rings_Ocomm__semiring__1(X11)
| hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2147])]) ).
fof(c_0_3404,plain,
! [X9,X10] :
( ~ class_Power_Opower(X10)
| hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2148])]) ).
fof(c_0_3405,plain,
! [X9,X10] :
( ~ class_Groups_Ogroup__add(X10)
| c_Groups_Ominus__class_Ominus(X10,X9,X9) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2149])]) ).
fof(c_0_3406,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Opreorder(X14)
| X13 != X12
| c_Orderings_Oord__class_Oless__eq(X14,X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2150])]) ).
fof(c_0_3407,plain,
! [X49] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X49),
inference(variable_rename,[status(thm)],[c_0_2151]) ).
fof(c_0_3408,plain,
! [X25,X26,X27] :
( ~ class_Rings_Odivision__ring(X27)
| c_Rings_Oinverse__class_Oinverse(X27,X26) != c_Rings_Oinverse__class_Oinverse(X27,X25)
| X26 = c_Groups_Ozero__class_Ozero(X27)
| X25 = c_Groups_Ozero__class_Ozero(X27)
| X26 = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2152])]) ).
fof(c_0_3409,plain,
! [X10,X11] :
( ~ class_Rings_Ocomm__semiring__1(X11)
| hAPP(hAPP(c_Power_Opower__class_Opower(X11),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2153])]) ).
fof(c_0_3410,plain,
! [X9,X10] :
( ~ class_Groups_Omonoid__mult(X10)
| hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2154])]) ).
fof(c_0_3411,plain,
! [X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X7,
inference(variable_rename,[status(thm)],[c_0_2155]) ).
fof(c_0_3412,plain,
! [X7] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X7)),
inference(variable_rename,[status(thm)],[c_0_2156]) ).
fof(c_0_3413,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_2157 ).
fof(c_0_3414,plain,
! [X9,X10] :
( ~ class_Rings_Ocomm__semiring__1(X10)
| c_Rings_Odvd__class_Odvd(X10,X9,X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2158])]) ).
fof(c_0_3415,plain,
! [X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| c_Orderings_Oord__class_Oless__eq(X11,X10,X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2159])]) ).
fof(c_0_3416,plain,
! [X10,X11] :
( ~ class_RealVector_Oreal__normed__vector(X11)
| c_RealVector_Onorm__class_Onorm(X11,c_Groups_Ouminus__class_Ouminus(X11,X10)) = c_RealVector_Onorm__class_Onorm(X11,X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2160])]) ).
fof(c_0_3417,plain,
! [X81,X82,X83] :
( ( c_Polynomial_Opoly(X83,X82) != c_Polynomial_Opoly(X83,X81)
| X82 = X81
| ~ class_Int_Oring__char__0(X83)
| ~ class_Rings_Oidom(X83) )
& ( X82 != X81
| c_Polynomial_Opoly(X83,X82) = c_Polynomial_Opoly(X83,X81)
| ~ class_Int_Oring__char__0(X83)
| ~ class_Rings_Oidom(X83) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2161])])]) ).
fof(c_0_3418,plain,
! [X7] : c_Nat_OSuc(X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[c_0_2162]) ).
fof(c_0_3419,plain,
! [X7] : c_Nat_OSuc(X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X7),
inference(variable_rename,[status(thm)],[c_0_2163]) ).
fof(c_0_3420,plain,
! [X7] :
( X7 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2164])]) ).
fof(c_0_3421,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
c_0_2165 ).
fof(c_0_3422,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
c_0_2166 ).
fof(c_0_3423,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)),
c_0_2167 ).
fof(c_0_3424,plain,
! [X7] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Nat_OSuc(X7)),
inference(variable_rename,[status(thm)],[c_0_2168]) ).
fof(c_0_3425,plain,
! [X25] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[c_0_2169]) ).
fof(c_0_3426,plain,
! [X9] :
( ~ class_Rings_Olinordered__idom(X9)
| ~ c_Polynomial_Opos__poly(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2170])]) ).
fof(c_0_3427,plain,
! [X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2171]) ).
fof(c_0_3428,plain,
! [X24] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) = X24,
inference(variable_rename,[status(thm)],[c_0_2172]) ).
fof(c_0_3429,plain,
! [X24] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X24,
inference(variable_rename,[status(thm)],[c_0_2173]) ).
fof(c_0_3430,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
c_0_2174 ).
fof(c_0_3431,plain,
! [X18] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18,
inference(variable_rename,[status(thm)],[c_0_2175]) ).
fof(c_0_3432,plain,
! [X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7) = X7,
inference(variable_rename,[status(thm)],[c_0_2176]) ).
fof(c_0_3433,plain,
! [X18] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18,
inference(variable_rename,[status(thm)],[c_0_2177]) ).
fof(c_0_3434,plain,
! [X12,X13] :
( X13 != X12
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2178])]) ).
fof(c_0_3435,plain,
! [X18,X19] :
( X19 != X18
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2179])]) ).
fof(c_0_3436,plain,
! [X10] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X10),
inference(variable_rename,[status(thm)],[c_0_2180]) ).
fof(c_0_3437,plain,
! [X10] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[c_0_2181]) ).
fof(c_0_3438,plain,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7),
inference(variable_rename,[status(thm)],[c_0_2182]) ).
fof(c_0_3439,plain,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7),
inference(variable_rename,[status(thm)],[c_0_2183]) ).
fof(c_0_3440,plain,
! [X9] :
( ~ class_Groups_Oab__group__add(X9)
| 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)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2184])]) ).
fof(c_0_3441,plain,
! [X18] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X18) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2185]) ).
fof(c_0_3442,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_2186 ).
fof(c_0_3443,plain,
! [X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2187]) ).
fof(c_0_3444,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
c_0_2188 ).
fof(c_0_3445,plain,
! [X27,X28,X29] :
( ( c_Groups_Ouminus__class_Ouminus(X29,X28) != c_Groups_Ouminus__class_Ouminus(X29,X27)
| X28 = X27
| ~ class_Groups_Ogroup__add(X29) )
& ( X28 != X27
| c_Groups_Ouminus__class_Ouminus(X29,X28) = c_Groups_Ouminus__class_Ouminus(X29,X27)
| ~ class_Groups_Ogroup__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2189])])]) ).
fof(c_0_3446,plain,
! [X27,X28,X29] :
( ( c_Rings_Oinverse__class_Oinverse(X29,X28) != c_Rings_Oinverse__class_Oinverse(X29,X27)
| X28 = X27
| ~ class_Rings_Odivision__ring__inverse__zero(X29) )
& ( X28 != X27
| c_Rings_Oinverse__class_Oinverse(X29,X28) = c_Rings_Oinverse__class_Oinverse(X29,X27)
| ~ class_Rings_Odivision__ring__inverse__zero(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2190])])]) ).
fof(c_0_3447,plain,
! [X25,X26,X27] :
( ~ class_Rings_Odivision__ring__inverse__zero(X27)
| c_Rings_Oinverse__class_Oinverse(X27,X26) != c_Rings_Oinverse__class_Oinverse(X27,X25)
| X26 = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2191])]) ).
fof(c_0_3448,plain,
! [X9,X10] :
( ~ class_Rings_Odivision__ring(X10)
| X9 = c_Groups_Ozero__class_Ozero(X10)
| c_Rings_Oinverse__class_Oinverse(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2192])]) ).
fof(c_0_3449,plain,
! [X10] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X10),
inference(variable_rename,[status(thm)],[c_0_2193]) ).
fof(c_0_3450,plain,
! [X23] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X23),
inference(variable_rename,[status(thm)],[c_0_2194]) ).
fof(c_0_3451,plain,
! [X23] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X23),
inference(variable_rename,[status(thm)],[c_0_2195]) ).
fof(c_0_3452,plain,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X7),
inference(variable_rename,[status(thm)],[c_0_2196]) ).
fof(c_0_3453,plain,
! [X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X24) = X24,
inference(variable_rename,[status(thm)],[c_0_2197]) ).
fof(c_0_3454,plain,
! [X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X7) = X7,
inference(variable_rename,[status(thm)],[c_0_2198]) ).
fof(c_0_3455,plain,
! [X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X24) = X24,
inference(variable_rename,[status(thm)],[c_0_2199]) ).
fof(c_0_3456,plain,
! [X18] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2200]) ).
fof(c_0_3457,plain,
! [X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X24,
inference(variable_rename,[status(thm)],[c_0_2201]) ).
fof(c_0_3458,plain,
! [X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X7,
inference(variable_rename,[status(thm)],[c_0_2202]) ).
fof(c_0_3459,plain,
! [X9,X10] :
( ~ class_Groups_Ogroup__add(X10)
| c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2203])]) ).
fof(c_0_3460,plain,
! [X9,X10] :
( ~ class_Rings_Odivision__ring__inverse__zero(X10)
| c_Rings_Oinverse__class_Oinverse(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2204])]) ).
fof(c_0_3461,plain,
! [X27,X28,X29] :
( ( X28 != c_Groups_Ouminus__class_Ouminus(X29,X27)
| X27 = c_Groups_Ouminus__class_Ouminus(X29,X28)
| ~ class_Groups_Ogroup__add(X29) )
& ( X27 != c_Groups_Ouminus__class_Ouminus(X29,X28)
| X28 = c_Groups_Ouminus__class_Ouminus(X29,X27)
| ~ class_Groups_Ogroup__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2205])])]) ).
fof(c_0_3462,plain,
! [X27,X28,X29] :
( ( c_Groups_Ouminus__class_Ouminus(X29,X28) != X27
| c_Groups_Ouminus__class_Ouminus(X29,X27) = X28
| ~ class_Groups_Ogroup__add(X29) )
& ( c_Groups_Ouminus__class_Ouminus(X29,X27) != X28
| c_Groups_Ouminus__class_Ouminus(X29,X28) = X27
| ~ class_Groups_Ogroup__add(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2206])])]) ).
fof(c_0_3463,plain,
! [X64,X65] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X65,X64) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X64 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X65))
| ~ class_Groups_Ozero(X65) )
& ( X64 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X65))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X65,X64) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2207])])]) ).
fof(c_0_3464,plain,
! [X27,X28] :
( ( c_Groups_Ozero__class_Ozero(X28) != c_Groups_Ouminus__class_Ouminus(X28,X27)
| c_Groups_Ozero__class_Ozero(X28) = X27
| ~ class_Groups_Ogroup__add(X28) )
& ( c_Groups_Ozero__class_Ozero(X28) != X27
| c_Groups_Ozero__class_Ozero(X28) = c_Groups_Ouminus__class_Ouminus(X28,X27)
| ~ class_Groups_Ogroup__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2208])])]) ).
fof(c_0_3465,plain,
! [X27,X28] :
( ( c_Groups_Ouminus__class_Ouminus(X28,X27) != c_Groups_Ozero__class_Ozero(X28)
| X27 = c_Groups_Ozero__class_Ozero(X28)
| ~ class_Groups_Ogroup__add(X28) )
& ( X27 != c_Groups_Ozero__class_Ozero(X28)
| c_Groups_Ouminus__class_Ouminus(X28,X27) = c_Groups_Ozero__class_Ozero(X28)
| ~ class_Groups_Ogroup__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2209])])]) ).
fof(c_0_3466,plain,
! [X16,X17] :
( ( c_Rings_Oinverse__class_Oinverse(X17,X16) != c_Groups_Oone__class_Oone(X17)
| X16 = c_Groups_Oone__class_Oone(X17)
| ~ class_Fields_Ofield__inverse__zero(X17) )
& ( X16 != c_Groups_Oone__class_Oone(X17)
| c_Rings_Oinverse__class_Oinverse(X17,X16) = c_Groups_Oone__class_Oone(X17)
| ~ class_Fields_Ofield__inverse__zero(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2210])])]) ).
fof(c_0_3467,plain,
! [X27,X28] :
( ( c_Rings_Oinverse__class_Oinverse(X28,X27) != c_Groups_Ozero__class_Ozero(X28)
| X27 = c_Groups_Ozero__class_Ozero(X28)
| ~ class_Rings_Odivision__ring__inverse__zero(X28) )
& ( X27 != c_Groups_Ozero__class_Ozero(X28)
| c_Rings_Oinverse__class_Oinverse(X28,X27) = c_Groups_Ozero__class_Ozero(X28)
| ~ class_Rings_Odivision__ring__inverse__zero(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2211])])]) ).
fof(c_0_3468,plain,
! [X9,X10] :
( ~ class_Rings_Odivision__ring(X10)
| X9 = c_Groups_Ozero__class_Ozero(X10)
| c_Rings_Oinverse__class_Oinverse(X10,X9) != c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2212])]) ).
fof(c_0_3469,plain,
! [X9,X10] :
( ~ class_Rings_Odivision__ring(X10)
| c_Rings_Oinverse__class_Oinverse(X10,X9) != c_Groups_Ozero__class_Ozero(X10)
| X9 = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2213])]) ).
fof(c_0_3470,plain,
! [X16,X17] :
( ( c_RealVector_Onorm__class_Onorm(X17,X16) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X16 = c_Groups_Ozero__class_Ozero(X17)
| ~ class_RealVector_Oreal__normed__vector(X17) )
& ( X16 != c_Groups_Ozero__class_Ozero(X17)
| c_RealVector_Onorm__class_Onorm(X17,X16) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2214])])]) ).
fof(c_0_3471,plain,
! [X91,X92] :
( ~ class_Orderings_Oord(X92)
| class_Orderings_Oord(tc_fun(X91,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2215])]) ).
fof(c_0_3472,plain,
! [X91,X92] :
( ~ class_Orderings_Oorder(X92)
| class_Orderings_Oorder(tc_fun(X91,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2216])]) ).
fof(c_0_3473,plain,
! [X91,X92] :
( ~ class_Orderings_Opreorder(X92)
| class_Orderings_Opreorder(tc_fun(X91,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2217])]) ).
fof(c_0_3474,plain,
! [X24] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X24)) = X24,
inference(variable_rename,[status(thm)],[c_0_2218]) ).
fof(c_0_3475,plain,
! [X27,X28] :
( ( X27 != c_Groups_Ouminus__class_Ouminus(X28,X27)
| X27 = c_Groups_Ozero__class_Ozero(X28)
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( X27 != c_Groups_Ozero__class_Ozero(X28)
| X27 = c_Groups_Ouminus__class_Ouminus(X28,X27)
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2219])])]) ).
fof(c_0_3476,plain,
! [X27,X28] :
( ( c_Groups_Ouminus__class_Ouminus(X28,X27) != X27
| X27 = c_Groups_Ozero__class_Ozero(X28)
| ~ class_Groups_Olinordered__ab__group__add(X28) )
& ( X27 != c_Groups_Ozero__class_Ozero(X28)
| c_Groups_Ouminus__class_Ouminus(X28,X27) = X27
| ~ class_Groups_Olinordered__ab__group__add(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2220])])]) ).
fof(c_0_3477,plain,
! [X9] :
( ~ class_Groups_Ogroup__add(X9)
| c_Groups_Ouminus__class_Ouminus(X9,c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2221])]) ).
fof(c_0_3478,plain,
! [X9] :
( ~ class_Rings_Odivision__ring(X9)
| c_Rings_Oinverse__class_Oinverse(X9,c_Groups_Oone__class_Oone(X9)) = c_Groups_Oone__class_Oone(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2222])]) ).
fof(c_0_3479,plain,
! [X9] :
( ~ class_Fields_Ofield__inverse__zero(X9)
| c_Rings_Oinverse__class_Oinverse(X9,c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2223])]) ).
fof(c_0_3480,plain,
! [X9] :
( ~ class_Rings_Odivision__ring__inverse__zero(X9)
| c_Rings_Oinverse__class_Oinverse(X9,c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2224])]) ).
fof(c_0_3481,plain,
! [X9] :
( ~ class_RealVector_Oreal__normed__algebra__1(X9)
| c_RealVector_Onorm__class_Onorm(X9,c_Groups_Oone__class_Oone(X9)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2225])]) ).
fof(c_0_3482,plain,
! [X9] :
( ~ class_RealVector_Oreal__normed__vector(X9)
| c_RealVector_Onorm__class_Onorm(X9,c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2226])]) ).
fof(c_0_3483,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
c_0_2227 ).
fof(c_0_3484,axiom,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
c_0_2228 ).
fof(c_0_3485,plain,
! [X16,X17] :
( ( c_Groups_Oone__class_Oone(X17) != X16
| X16 = c_Groups_Oone__class_Oone(X17)
| ~ class_Groups_Oone(X17) )
& ( X16 != c_Groups_Oone__class_Oone(X17)
| c_Groups_Oone__class_Oone(X17) = X16
| ~ class_Groups_Oone(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2229])])]) ).
fof(c_0_3486,plain,
! [X16,X17] :
( ( c_Groups_Ozero__class_Ozero(X17) != X16
| X16 = c_Groups_Ozero__class_Ozero(X17)
| ~ class_Groups_Ozero(X17) )
& ( X16 != c_Groups_Ozero__class_Ozero(X17)
| c_Groups_Ozero__class_Ozero(X17) = X16
| ~ class_Groups_Ozero(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2230])])]) ).
fof(c_0_3487,plain,
! [X9] :
( ~ class_Rings_Ozero__neq__one(X9)
| c_Groups_Oone__class_Oone(X9) != c_Groups_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2231])]) ).
fof(c_0_3488,plain,
! [X9] :
( ~ class_Rings_Ozero__neq__one(X9)
| c_Groups_Ozero__class_Ozero(X9) != c_Groups_Oone__class_Oone(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2232])]) ).
fof(c_0_3489,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_2233 ).
fof(c_0_3490,axiom,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_2234 ).
fof(c_0_3491,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__1(X90)
| class_Rings_Odvd(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2235])]) ).
fof(c_0_3492,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__1(X90)
| class_Groups_Oone(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2236])]) ).
fof(c_0_3493,plain,
! [X90] :
( ~ class_Rings_Oidom(X90)
| class_Rings_Oidom(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2237])]) ).
fof(c_0_3494,plain,
! [X90] :
( ~ class_Rings_Ocomm__ring(X90)
| class_Rings_Oring(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2238])]) ).
fof(c_0_3495,plain,
! [X90] :
( ~ class_Groups_Ozero(X90)
| class_Groups_Ozero(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2239])]) ).
fof(c_0_3496,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__1(X90)
| class_Power_Opower(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2240])]) ).
fof(c_0_3497,plain,
! [X90] :
( ~ class_Rings_Ocomm__ring__1(X90)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2241])]) ).
fof(c_0_3498,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Orderings_Oord(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2242])]) ).
fof(c_0_3499,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__0(X90)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2243])]) ).
fof(c_0_3500,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2244])]) ).
fof(c_0_3501,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2245])]) ).
fof(c_0_3502,plain,
! [X90] :
( ~ class_Rings_Ocomm__ring(X90)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2246])]) ).
fof(c_0_3503,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__0(X90)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2247])]) ).
fof(c_0_3504,plain,
! [X90] :
( ~ class_Groups_Oab__group__add(X90)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2248])]) ).
fof(c_0_3505,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__0(X90)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2249])]) ).
fof(c_0_3506,plain,
! [X90] :
( ~ class_Groups_Ocomm__monoid__add(X90)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2250])]) ).
fof(c_0_3507,plain,
! [X90] :
( ~ class_Rings_Ocomm__ring__1(X90)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2251])]) ).
fof(c_0_3508,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__1(X90)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2252])]) ).
fof(c_0_3509,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2253])]) ).
fof(c_0_3510,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2254])]) ).
fof(c_0_3511,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2255])]) ).
fof(c_0_3512,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__1(X90)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2256])]) ).
fof(c_0_3513,plain,
! [X90] :
( ~ class_Groups_Oab__group__add(X90)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2257])]) ).
fof(c_0_3514,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__0(X90)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2258])]) ).
fof(c_0_3515,plain,
! [X90] :
( ~ class_Fields_Ofield(X90)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2259])]) ).
fof(c_0_3516,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__0(X90)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2260])]) ).
fof(c_0_3517,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__1(X90)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2261])]) ).
fof(c_0_3518,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2262])]) ).
fof(c_0_3519,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2263])]) ).
fof(c_0_3520,plain,
! [X90] :
( ~ class_Groups_Ocomm__monoid__add(X90)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2264])]) ).
fof(c_0_3521,plain,
! [X90] :
( ~ class_Rings_Oidom(X90)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2265])]) ).
fof(c_0_3522,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2266])]) ).
fof(c_0_3523,plain,
! [X90] :
( ~ class_Groups_Ocomm__monoid__add(X90)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2267])]) ).
fof(c_0_3524,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__1(X90)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2268])]) ).
fof(c_0_3525,plain,
! [X90] :
( ~ class_Rings_Ocomm__semiring__0(X90)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2269])]) ).
fof(c_0_3526,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2270])]) ).
fof(c_0_3527,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2271])]) ).
fof(c_0_3528,plain,
! [X90] :
( ~ class_Groups_Ocancel__comm__monoid__add(X90)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2272])]) ).
fof(c_0_3529,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2273])]) ).
fof(c_0_3530,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2274])]) ).
fof(c_0_3531,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2275])]) ).
fof(c_0_3532,plain,
! [X90] :
( ~ class_Rings_Oidom(X90)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2276])]) ).
fof(c_0_3533,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2277])]) ).
fof(c_0_3534,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2278])]) ).
fof(c_0_3535,plain,
! [X90] :
( ~ class_Rings_Oidom(X90)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2279])]) ).
fof(c_0_3536,plain,
! [X90] :
( ~ class_Groups_Ocancel__comm__monoid__add(X90)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2280])]) ).
fof(c_0_3537,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2281])]) ).
fof(c_0_3538,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2282])]) ).
fof(c_0_3539,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2283])]) ).
fof(c_0_3540,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2284])]) ).
fof(c_0_3541,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2285])]) ).
fof(c_0_3542,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2286])]) ).
fof(c_0_3543,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2287])]) ).
fof(c_0_3544,plain,
! [X90] :
( ~ class_Rings_Olinordered__idom(X90)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2288])]) ).
fof(c_0_3545,plain,
! [X90] :
( ~ class_Rings_Oidom(X90)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2289])]) ).
fof(c_0_3546,plain,
! [X90] :
( ~ class_Groups_Ocancel__comm__monoid__add(X90)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2290])]) ).
fof(c_0_3547,plain,
! [X12,X13] :
( c_Nat_OSuc(X13) != c_Nat_OSuc(X12)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2291])]) ).
fof(c_0_3548,plain,
! [X69,X70,X71,X72] :
( ( c_Nat_OSuc(X70) != c_Nat_OSuc(X69)
| X70 = X69 )
& ( X72 != X71
| c_Nat_OSuc(X72) = c_Nat_OSuc(X71) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2292])])])]) ).
fof(c_0_3549,plain,
! [X18] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X18),
inference(variable_rename,[status(thm)],[c_0_2293]) ).
fof(c_0_3550,plain,
! [X67] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X67),
inference(variable_rename,[status(thm)],[c_0_2294]) ).
fof(c_0_3551,plain,
! [X18] : c_Nat_OSuc(X18) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2295]) ).
fof(c_0_3552,plain,
! [X66] : c_Nat_OSuc(X66) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2296]) ).
fof(c_0_3553,plain,
! [X18] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X18),
inference(variable_rename,[status(thm)],[c_0_2297]) ).
fof(c_0_3554,plain,
! [X18] : c_Nat_OSuc(X18) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2298]) ).
fof(c_0_3555,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_2299 ).
fof(c_0_3556,axiom,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_2300 ).
fof(c_0_3557,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
c_0_2301 ).
fof(c_0_3558,plain,
! [X7] : c_Nat_OSuc(X7) != X7,
inference(variable_rename,[status(thm)],[c_0_2302]) ).
fof(c_0_3559,plain,
! [X7] : X7 != c_Nat_OSuc(X7),
inference(variable_rename,[status(thm)],[c_0_2303]) ).
fof(c_0_3560,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_2304 ).
fof(c_0_3561,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_2305 ).
fof(c_0_3562,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_2306 ).
fof(c_0_3563,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_2307 ).
fof(c_0_3564,axiom,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_2308 ).
fof(c_0_3565,axiom,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_2309 ).
fof(c_0_3566,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
c_0_2310 ).
fof(c_0_3567,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
c_0_2311 ).
fof(c_0_3568,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
c_0_2312 ).
fof(c_0_3569,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
c_0_2313 ).
fof(c_0_3570,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
c_0_2314 ).
fof(c_0_3571,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_2315 ).
fof(c_0_3572,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
c_0_2316 ).
fof(c_0_3573,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
c_0_2317 ).
fof(c_0_3574,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
c_0_2318 ).
fof(c_0_3575,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
c_0_2319 ).
fof(c_0_3576,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
c_0_2320 ).
fof(c_0_3577,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
c_0_2321 ).
fof(c_0_3578,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
c_0_2322 ).
fof(c_0_3579,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
c_0_2323 ).
fof(c_0_3580,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
c_0_2324 ).
fof(c_0_3581,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_2325 ).
fof(c_0_3582,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
c_0_2326 ).
fof(c_0_3583,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_2327 ).
fof(c_0_3584,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
c_0_2328 ).
fof(c_0_3585,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_2329 ).
fof(c_0_3586,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
c_0_2330 ).
fof(c_0_3587,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_2331 ).
fof(c_0_3588,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_2332 ).
fof(c_0_3589,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_2333 ).
fof(c_0_3590,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_2334 ).
fof(c_0_3591,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_2335 ).
fof(c_0_3592,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_2336 ).
fof(c_0_3593,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_2337 ).
fof(c_0_3594,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
c_0_2338 ).
fof(c_0_3595,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_2339 ).
fof(c_0_3596,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_2340 ).
fof(c_0_3597,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
c_0_2341 ).
fof(c_0_3598,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_2342 ).
fof(c_0_3599,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_2343 ).
fof(c_0_3600,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_2344 ).
fof(c_0_3601,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
c_0_2345 ).
fof(c_0_3602,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
c_0_2346 ).
fof(c_0_3603,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
c_0_2347 ).
fof(c_0_3604,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
c_0_2348 ).
fof(c_0_3605,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
c_0_2349 ).
fof(c_0_3606,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
c_0_2350 ).
fof(c_0_3607,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
c_0_2351 ).
fof(c_0_3608,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
c_0_2352 ).
fof(c_0_3609,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
c_0_2353 ).
fof(c_0_3610,axiom,
class_Power_Opower(tc_RealDef_Oreal),
c_0_2354 ).
fof(c_0_3611,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
c_0_2355 ).
fof(c_0_3612,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
c_0_2356 ).
fof(c_0_3613,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
c_0_2357 ).
fof(c_0_3614,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
c_0_2358 ).
fof(c_0_3615,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
c_0_2359 ).
fof(c_0_3616,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
c_0_2360 ).
fof(c_0_3617,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
c_0_2361 ).
fof(c_0_3618,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
c_0_2362 ).
fof(c_0_3619,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
c_0_2363 ).
fof(c_0_3620,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
c_0_2364 ).
fof(c_0_3621,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
c_0_2365 ).
fof(c_0_3622,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
c_0_2366 ).
fof(c_0_3623,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
c_0_2367 ).
fof(c_0_3624,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
c_0_2368 ).
fof(c_0_3625,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
c_0_2369 ).
fof(c_0_3626,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
c_0_2370 ).
fof(c_0_3627,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
c_0_2371 ).
fof(c_0_3628,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
c_0_2372 ).
fof(c_0_3629,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
c_0_2373 ).
fof(c_0_3630,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
c_0_2374 ).
fof(c_0_3631,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
c_0_2375 ).
fof(c_0_3632,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
c_0_2376 ).
fof(c_0_3633,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
c_0_2377 ).
fof(c_0_3634,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
c_0_2378 ).
fof(c_0_3635,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
c_0_2379 ).
fof(c_0_3636,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
c_0_2380 ).
fof(c_0_3637,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
c_0_2381 ).
fof(c_0_3638,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
c_0_2382 ).
fof(c_0_3639,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
c_0_2383 ).
fof(c_0_3640,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
c_0_2384 ).
fof(c_0_3641,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
c_0_2385 ).
fof(c_0_3642,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
c_0_2386 ).
fof(c_0_3643,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
c_0_2387 ).
fof(c_0_3644,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
c_0_2388 ).
fof(c_0_3645,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
c_0_2389 ).
fof(c_0_3646,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
c_0_2390 ).
fof(c_0_3647,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
c_0_2391 ).
fof(c_0_3648,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
c_0_2392 ).
fof(c_0_3649,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
c_0_2393 ).
fof(c_0_3650,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
c_0_2394 ).
fof(c_0_3651,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
c_0_2395 ).
fof(c_0_3652,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
c_0_2396 ).
fof(c_0_3653,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
c_0_2397 ).
fof(c_0_3654,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_2398 ).
fof(c_0_3655,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
c_0_2399 ).
fof(c_0_3656,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
c_0_2400 ).
fof(c_0_3657,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
c_0_2401 ).
fof(c_0_3658,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
c_0_2402 ).
fof(c_0_3659,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
c_0_2403 ).
fof(c_0_3660,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
c_0_2404 ).
fof(c_0_3661,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
c_0_2405 ).
fof(c_0_3662,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
c_0_2406 ).
fof(c_0_3663,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
c_0_2407 ).
fof(c_0_3664,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
c_0_2408 ).
fof(c_0_3665,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
c_0_2409 ).
fof(c_0_3666,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
c_0_2410 ).
fof(c_0_3667,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_2411 ).
fof(c_0_3668,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
c_0_2412 ).
fof(c_0_3669,axiom,
class_Orderings_Oord(tc_HOL_Obool),
c_0_2413 ).
fof(c_0_3670,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
c_0_2414 ).
fof(c_0_3671,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
c_0_2415 ).
fof(c_0_3672,axiom,
class_Rings_Odvd(tc_Nat_Onat),
c_0_2416 ).
fof(c_0_3673,axiom,
class_Groups_Oone(tc_Nat_Onat),
c_0_2417 ).
fof(c_0_3674,axiom,
class_Groups_Ozero(tc_Nat_Onat),
c_0_2418 ).
fof(c_0_3675,axiom,
class_Power_Opower(tc_Nat_Onat),
c_0_2419 ).
fof(c_0_3676,axiom,
class_Orderings_Oord(tc_Nat_Onat),
c_0_2420 ).
fof(c_0_3677,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
c_0_2421 ).
fof(c_0_3678,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
c_0_2422 ).
fof(c_0_3679,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
c_0_2423 ).
fof(c_0_3680,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
c_0_2424 ).
fof(c_0_3681,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
c_0_2425 ).
fof(c_0_3682,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
c_0_2426 ).
fof(c_0_3683,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
c_0_2427 ).
fof(c_0_3684,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
c_0_2428 ).
fof(c_0_3685,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
c_0_2429 ).
fof(c_0_3686,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
c_0_2430 ).
fof(c_0_3687,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
c_0_2431 ).
fof(c_0_3688,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
c_0_2432 ).
fof(c_0_3689,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
c_0_2433 ).
fof(c_0_3690,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
c_0_2434 ).
fof(c_0_3691,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
c_0_2435 ).
fof(c_0_3692,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
c_0_2436 ).
fof(c_0_3693,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
c_0_2437 ).
fof(c_0_3694,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
c_0_2438 ).
fof(c_0_3695,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
c_0_2439 ).
fof(c_0_3696,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
c_0_2440 ).
fof(c_0_3697,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
c_0_2441 ).
fof(c_0_3698,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
c_0_2442 ).
fof(c_0_3699,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
c_0_2443 ).
fof(c_0_3700,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
c_0_2444 ).
fof(c_0_3701,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
c_0_2445 ).
fof(c_0_3702,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
c_0_2446 ).
fof(c_0_3703,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
c_0_2447 ).
fof(c_0_3704,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
c_0_2448 ).
fof(c_0_3705,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
c_0_2449 ).
fof(c_0_3706,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
c_0_2450 ).
fof(c_0_3707,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
c_0_2451 ).
fof(c_0_3708,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
c_0_2452 ).
fof(c_0_3709,axiom,
class_Rings_Odvd(tc_Int_Oint),
c_0_2453 ).
fof(c_0_3710,axiom,
class_Groups_Oone(tc_Int_Oint),
c_0_2454 ).
fof(c_0_3711,axiom,
class_Rings_Oidom(tc_Int_Oint),
c_0_2455 ).
fof(c_0_3712,axiom,
class_Rings_Oring(tc_Int_Oint),
c_0_2456 ).
fof(c_0_3713,axiom,
class_Groups_Ozero(tc_Int_Oint),
c_0_2457 ).
fof(c_0_3714,axiom,
class_Power_Opower(tc_Int_Oint),
c_0_2458 ).
fof(c_0_3715,axiom,
class_Rings_Oring__1(tc_Int_Oint),
c_0_2459 ).
fof(c_0_3716,axiom,
class_Orderings_Oord(tc_Int_Oint),
c_0_2460 ).
fof(c_0_3717,axiom,
class_Rings_Osemiring(tc_Int_Oint),
c_0_2461 ).
fof(c_0_3718,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
c_0_2462 ).
fof(c_0_3719,axiom,
class_Orderings_Oorder(tc_Int_Oint),
c_0_2463 ).
fof(c_0_3720,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
c_0_2464 ).
fof(c_0_3721,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
c_0_2465 ).
fof(c_0_3722,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
c_0_2466 ).
fof(c_0_3723,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
c_0_2467 ).
fof(c_0_3724,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
c_0_2468 ).
fof(c_0_3725,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
c_0_2469 ).
fof(c_0_3726,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
c_0_2470 ).
fof(c_0_3727,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
c_0_2471 ).
fof(c_0_3728,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
c_0_2472 ).
fof(c_0_3729,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
c_0_2473 ).
fof(c_0_3730,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
c_0_2474 ).
fof(c_0_3731,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
c_0_2475 ).
fof(c_0_3732,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
c_0_2476 ).
fof(c_0_3733,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
c_0_2477 ).
fof(c_0_3734,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
c_0_2478 ).
fof(c_0_3735,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
c_0_2479 ).
fof(c_0_3736,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
c_0_2480 ).
fof(c_0_3737,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
c_0_2481 ).
fof(c_0_3738,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
c_0_2482 ).
fof(c_0_3739,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
c_0_2483 ).
fof(c_0_3740,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
c_0_2484 ).
fof(c_0_3741,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
c_0_2485 ).
fof(c_0_3742,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
c_0_2486 ).
fof(c_0_3743,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
c_0_2487 ).
fof(c_0_3744,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
c_0_2488 ).
fof(c_0_3745,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
c_0_2489 ).
fof(c_0_3746,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
c_0_2490 ).
fof(c_0_3747,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
c_0_2491 ).
fof(c_0_3748,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
c_0_2492 ).
fof(c_0_3749,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
c_0_2493 ).
fof(c_0_3750,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
c_0_2494 ).
fof(c_0_3751,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
c_0_2495 ).
fof(c_0_3752,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
c_0_2496 ).
fof(c_0_3753,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
c_0_2497 ).
fof(c_0_3754,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
c_0_2498 ).
fof(c_0_3755,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
c_0_2499 ).
fof(c_0_3756,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
c_0_2500 ).
fof(c_0_3757,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
c_0_2501 ).
fof(c_0_3758,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
c_0_2502 ).
fof(c_0_3759,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
c_0_2503 ).
fof(c_0_3760,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
c_0_2504 ).
fof(c_0_3761,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
c_0_2505 ).
fof(c_0_3762,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
c_0_2506 ).
fof(c_0_3763,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
c_0_2507 ).
fof(c_0_3764,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
c_0_2508 ).
fof(c_0_3765,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
c_0_2509 ).
fof(c_0_3766,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
c_0_2510 ).
fof(c_0_3767,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_2511 ).
cnf(c_0_3768,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| ~ class_Orderings_Oord(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,hAPP(X3,X5),hAPP(X3,esk31_4(X3,X5,X1,X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_2512]) ).
cnf(c_0_3769,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_2513]) ).
cnf(c_0_3770,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
inference(split_conjunct,[status(thm)],[c_0_2513]) ).
cnf(c_0_3771,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),esk25_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk26_0,esk27_0)),X1))),
inference(split_conjunct,[status(thm)],[c_0_2514]) ).
cnf(c_0_3772,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X1))),
inference(split_conjunct,[status(thm)],[c_0_2515]) ).
cnf(c_0_3773,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X2,X3))),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2516]) ).
cnf(c_0_3774,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X3,X2))),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2517]) ).
cnf(c_0_3775,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk18_0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_2518]) ).
cnf(c_0_3776,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
inference(split_conjunct,[status(thm)],[c_0_2519]) ).
cnf(c_0_3777,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
inference(split_conjunct,[status(thm)],[c_0_2520]) ).
cnf(c_0_3778,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,esk28_4(X4,X3,X2,X1)),hAPP(X4,esk28_4(X4,X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2521]) ).
cnf(c_0_3779,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
inference(split_conjunct,[status(thm)],[c_0_2522]) ).
cnf(c_0_3780,plain,
( 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)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2523]) ).
cnf(c_0_3781,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk21_0) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk22_0),
inference(split_conjunct,[status(thm)],[c_0_2524]) ).
cnf(c_0_3782,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),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)),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)],[c_0_2525]) ).
cnf(c_0_3783,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2526]) ).
cnf(c_0_3784,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2527]) ).
cnf(c_0_3785,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2528]) ).
cnf(c_0_3786,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2529]) ).
cnf(c_0_3787,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2530]) ).
cnf(c_0_3788,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2531]) ).
cnf(c_0_3789,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2532]) ).
cnf(c_0_3790,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2533]) ).
cnf(c_0_3791,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(split_conjunct,[status(thm)],[c_0_2534]) ).
cnf(c_0_3792,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Oorder(X1,X3,X2)),X2)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2517]) ).
cnf(c_0_3793,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),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)],[c_0_2535]) ).
cnf(c_0_3794,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2526]) ).
cnf(c_0_3795,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2527]) ).
cnf(c_0_3796,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2528]) ).
cnf(c_0_3797,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2529]) ).
cnf(c_0_3798,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2530]) ).
cnf(c_0_3799,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2531]) ).
cnf(c_0_3800,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2532]) ).
cnf(c_0_3801,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2533]) ).
cnf(c_0_3802,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk4_2(X2,X1)),X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_2536]) ).
cnf(c_0_3803,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2537]) ).
cnf(c_0_3804,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3)))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_3805,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_3806,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2540]) ).
cnf(c_0_3807,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)],[c_0_2541]) ).
cnf(c_0_3808,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),esk13_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2542]) ).
cnf(c_0_3809,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2543]) ).
cnf(c_0_3810,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2544]) ).
cnf(c_0_3811,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
inference(split_conjunct,[status(thm)],[c_0_2545]) ).
cnf(c_0_3812,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2546]) ).
cnf(c_0_3813,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2547]) ).
cnf(c_0_3814,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2548]) ).
cnf(c_0_3815,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk35_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2549]) ).
cnf(c_0_3816,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2550]) ).
cnf(c_0_3817,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2551]) ).
cnf(c_0_3818,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2552]) ).
cnf(c_0_3819,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4) != X5 ),
inference(split_conjunct,[status(thm)],[c_0_2553]) ).
cnf(c_0_3820,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X4 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2554]) ).
cnf(c_0_3821,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| ~ class_Rings_Oring(X1)
| X4 != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2555]) ).
cnf(c_0_3822,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4) != X6 ),
inference(split_conjunct,[status(thm)],[c_0_2556]) ).
cnf(c_0_3823,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_2557]) ).
cnf(c_0_3824,plain,
( 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)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2558]) ).
cnf(c_0_3825,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2543]) ).
cnf(c_0_3826,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2544]) ).
cnf(c_0_3827,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4) = X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2553]) ).
cnf(c_0_3828,plain,
( X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2554]) ).
cnf(c_0_3829,plain,
( X2 = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6)
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2555]) ).
cnf(c_0_3830,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5) = X6
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2556]) ).
cnf(c_0_3831,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3),X5)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2559]) ).
cnf(c_0_3832,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X5))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2548]) ).
cnf(c_0_3833,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[c_0_2560]) ).
cnf(c_0_3834,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| c_Orderings_Oord__class_Oless__eq(X1,X5,esk31_4(X3,X5,X1,X2))
| ~ class_Orderings_Oord(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2512]) ).
cnf(c_0_3835,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X3,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2561]) ).
cnf(c_0_3836,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Oplus__class_Oplus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2562]) ).
cnf(c_0_3837,plain,
( c_Orderings_Oord__class_Oless(X1,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)),X6)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2563]) ).
cnf(c_0_3838,plain,
( c_Orderings_Oord__class_Oless__eq(X1,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)),X6)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2564]) ).
cnf(c_0_3839,plain,
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),esk30_3(X3,X2,X1))))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2565]) ).
cnf(c_0_3840,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X2),X4),
inference(split_conjunct,[status(thm)],[c_0_2566]) ).
cnf(c_0_3841,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3)),X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2567]) ).
cnf(c_0_3842,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2568]) ).
cnf(c_0_3843,plain,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2569]) ).
cnf(c_0_3844,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)],[c_0_2570]) ).
cnf(c_0_3845,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,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)],[c_0_2571]) ).
cnf(c_0_3846,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,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)],[c_0_2571]) ).
cnf(c_0_3847,plain,
( ~ c_Orderings_Oord__class_Oless(X1,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))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_3848,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2573]) ).
cnf(c_0_3849,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),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)],[c_0_2574]) ).
cnf(c_0_3850,plain,
( hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_3851,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2576]) ).
cnf(c_0_3852,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2577]) ).
cnf(c_0_3853,plain,
( hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X3,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2578]) ).
cnf(c_0_3854,plain,
( X2 = X3
| X4 = X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)) != 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2579]) ).
cnf(c_0_3855,plain,
( X3 = X5
| X2 = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) != 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2580]) ).
cnf(c_0_3856,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(split_conjunct,[status(thm)],[c_0_2581]) ).
cnf(c_0_3857,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Nat_OSuc(X5)) = hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)),
inference(split_conjunct,[status(thm)],[c_0_2582]) ).
cnf(c_0_3858,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_OpCons(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),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)],[c_0_2583]) ).
cnf(c_0_3859,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),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)],[c_0_2584]) ).
cnf(c_0_3860,plain,
( c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,esk29_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2565]) ).
cnf(c_0_3861,plain,
( c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[c_0_2585]) ).
cnf(c_0_3862,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2586]) ).
cnf(c_0_3863,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2587]) ).
cnf(c_0_3864,plain,
( c_Polynomial_Opcompose(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),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)],[c_0_2588]) ).
cnf(c_0_3865,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)],[c_0_2589]) ).
cnf(c_0_3866,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)],[c_0_2590]) ).
cnf(c_0_3867,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)),
inference(split_conjunct,[status(thm)],[c_0_2591]) ).
cnf(c_0_3868,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2))),
inference(split_conjunct,[status(thm)],[c_0_2592]) ).
cnf(c_0_3869,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = 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)],[c_0_2593]) ).
cnf(c_0_3870,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,esk6_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2594]) ).
cnf(c_0_3871,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,esk5_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2595]) ).
cnf(c_0_3872,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X1,esk6_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2594]) ).
cnf(c_0_3873,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X1,esk5_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2595]) ).
cnf(c_0_3874,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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X5))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2596]) ).
cnf(c_0_3875,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))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2597]) ).
cnf(c_0_3876,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_Groups_Oplus__class_Oplus(tc_Int_Oint,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)],[c_0_2598]) ).
cnf(c_0_3877,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X5))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2599]) ).
cnf(c_0_3878,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk27_0),esk25_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
inference(split_conjunct,[status(thm)],[c_0_2514]) ).
cnf(c_0_3879,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
inference(split_conjunct,[status(thm)],[c_0_2600]) ).
cnf(c_0_3880,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)],[c_0_2601]) ).
cnf(c_0_3881,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2602]) ).
cnf(c_0_3882,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2603]) ).
cnf(c_0_3883,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2604]) ).
cnf(c_0_3884,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),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(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,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2605]) ).
cnf(c_0_3885,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),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2606]) ).
cnf(c_0_3886,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),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2607]) ).
cnf(c_0_3887,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),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_3888,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2609]) ).
cnf(c_0_3889,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2610]) ).
cnf(c_0_3890,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X5))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2611]) ).
cnf(c_0_3891,plain,
( hBOOL(hAPP(X2,esk29_3(X3,X2,X1)))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2565]) ).
cnf(c_0_3892,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,c_Polynomial_Osynthetic__div(X1,X2,X3))) = 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)],[c_0_2612]) ).
cnf(c_0_3893,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)],[c_0_2613]) ).
cnf(c_0_3894,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)],[c_0_2614]) ).
cnf(c_0_3895,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3)
| ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X3),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_3896,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(X4)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2615]) ).
cnf(c_0_3897,plain,
( c_Orderings_Oord__class_Oless__eq(X1,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2571]) ).
cnf(c_0_3898,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3)
| ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2578]) ).
cnf(c_0_3899,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2569]) ).
cnf(c_0_3900,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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)))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2569]) ).
cnf(c_0_3901,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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)))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2616]) ).
cnf(c_0_3902,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,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)],[c_0_2617]) ).
cnf(c_0_3903,plain,
( 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),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_3904,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_OpCons(X1,X2,X3)),X4) = 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)],[c_0_2619]) ).
cnf(c_0_3905,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)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_3906,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2621]) ).
cnf(c_0_3907,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(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) ),
inference(split_conjunct,[status(thm)],[c_0_2622]) ).
cnf(c_0_3908,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(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) ),
inference(split_conjunct,[status(thm)],[c_0_2623]) ).
cnf(c_0_3909,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_2624]) ).
cnf(c_0_3910,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2625]) ).
cnf(c_0_3911,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_2626]) ).
cnf(c_0_3912,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2627]) ).
cnf(c_0_3913,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2628]) ).
cnf(c_0_3914,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2629]) ).
cnf(c_0_3915,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(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)) ),
inference(split_conjunct,[status(thm)],[c_0_2630]) ).
cnf(c_0_3916,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2631]) ).
cnf(c_0_3917,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(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(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2632]) ).
cnf(c_0_3918,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(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)],[c_0_2633]) ).
cnf(c_0_3919,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)],[c_0_2634]) ).
cnf(c_0_3920,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ 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(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2635]) ).
cnf(c_0_3921,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5)) = c_Polynomial_OpCons(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2636]) ).
cnf(c_0_3922,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5)) = c_Polynomial_OpCons(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X5))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2637]) ).
cnf(c_0_3923,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)],[c_0_2638]) ).
cnf(c_0_3924,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2639]) ).
cnf(c_0_3925,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2640]) ).
cnf(c_0_3926,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2641]) ).
cnf(c_0_3927,plain,
( 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,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2642]) ).
cnf(c_0_3928,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2643]) ).
cnf(c_0_3929,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2644]) ).
cnf(c_0_3930,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_3931,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk34_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2646]) ).
cnf(c_0_3932,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk33_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2647]) ).
cnf(c_0_3933,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2648]) ).
cnf(c_0_3934,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) = 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)],[c_0_2649]) ).
cnf(c_0_3935,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) = 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)],[c_0_2650]) ).
cnf(c_0_3936,plain,
( 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),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2651]) ).
cnf(c_0_3937,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = 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)],[c_0_2652]) ).
cnf(c_0_3938,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = 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)],[c_0_2653]) ).
cnf(c_0_3939,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = 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)],[c_0_2654]) ).
cnf(c_0_3940,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = 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)],[c_0_2655]) ).
cnf(c_0_3941,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2644]) ).
cnf(c_0_3942,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2644]) ).
cnf(c_0_3943,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_3944,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_3945,plain,
( 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)) = 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)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_2579]) ).
cnf(c_0_3946,plain,
( 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)) = 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)
| X3 != X5 ),
inference(split_conjunct,[status(thm)],[c_0_2579]) ).
cnf(c_0_3947,plain,
( 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)) = 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)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_2580]) ).
cnf(c_0_3948,plain,
( 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)) = 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)
| X3 != X5 ),
inference(split_conjunct,[status(thm)],[c_0_2580]) ).
cnf(c_0_3949,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2644]) ).
cnf(c_0_3950,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_3951,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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2656]) ).
cnf(c_0_3952,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),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)],[c_0_2657]) ).
cnf(c_0_3953,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)],[c_0_2658]) ).
cnf(c_0_3954,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2659]) ).
cnf(c_0_3955,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2660]) ).
cnf(c_0_3956,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2603]) ).
cnf(c_0_3957,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2604]) ).
cnf(c_0_3958,plain,
( X4 = X6
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != c_Groups_Oplus__class_Oplus(X1,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X6))
| X2 != X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2661]) ).
cnf(c_0_3959,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2662]) ).
cnf(c_0_3960,plain,
( 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)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2663]) ).
cnf(c_0_3961,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ 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)],[c_0_2664]) ).
cnf(c_0_3962,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2665]) ).
cnf(c_0_3963,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2666]) ).
cnf(c_0_3964,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(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)],[c_0_2667]) ).
cnf(c_0_3965,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(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)],[c_0_2668]) ).
cnf(c_0_3966,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(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)],[c_0_2669]) ).
cnf(c_0_3967,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_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)],[c_0_2670]) ).
cnf(c_0_3968,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2671]) ).
cnf(c_0_3969,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2672]) ).
cnf(c_0_3970,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2673]) ).
cnf(c_0_3971,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2674]) ).
cnf(c_0_3972,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2675]) ).
cnf(c_0_3973,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2676]) ).
cnf(c_0_3974,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X2,X3)),X4) = 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)],[c_0_2677]) ).
cnf(c_0_3975,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),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2678]) ).
cnf(c_0_3976,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2679]) ).
cnf(c_0_3977,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = 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)],[c_0_2680]) ).
cnf(c_0_3978,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = 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)],[c_0_2681]) ).
cnf(c_0_3979,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X5),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2682]) ).
cnf(c_0_3980,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2683]) ).
cnf(c_0_3981,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2594]) ).
cnf(c_0_3982,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2595]) ).
cnf(c_0_3983,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2594]) ).
cnf(c_0_3984,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2595]) ).
cnf(c_0_3985,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2684]) ).
cnf(c_0_3986,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2684]) ).
cnf(c_0_3987,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3) = 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)],[c_0_2685]) ).
cnf(c_0_3988,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),X3) = 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)],[c_0_2686]) ).
cnf(c_0_3989,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = 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)],[c_0_2687]) ).
cnf(c_0_3990,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) = 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)],[c_0_2688]) ).
cnf(c_0_3991,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_2689]) ).
cnf(c_0_3992,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2690]) ).
cnf(c_0_3993,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2691]) ).
cnf(c_0_3994,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2692]) ).
cnf(c_0_3995,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2693]) ).
cnf(c_0_3996,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2694]) ).
cnf(c_0_3997,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2695]) ).
cnf(c_0_3998,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2696]) ).
cnf(c_0_3999,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2697]) ).
cnf(c_0_4000,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2698]) ).
cnf(c_0_4001,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2699]) ).
cnf(c_0_4002,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2700]) ).
cnf(c_0_4003,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2701]) ).
cnf(c_0_4004,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4005,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)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2703]) ).
cnf(c_0_4006,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk3_0),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2704]) ).
cnf(c_0_4007,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4008,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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)],[c_0_2598]) ).
cnf(c_0_4009,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2706]) ).
cnf(c_0_4010,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2707]) ).
cnf(c_0_4011,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),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)],[c_0_2708]) ).
cnf(c_0_4012,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_OpCons(X2,X4,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2709]) ).
cnf(c_0_4013,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2710]) ).
cnf(c_0_4014,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2711]) ).
cnf(c_0_4015,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2712]) ).
cnf(c_0_4016,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
inference(split_conjunct,[status(thm)],[c_0_2713]) ).
cnf(c_0_4017,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk6_3(X3,X2,X1))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[c_0_2594]) ).
cnf(c_0_4018,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk5_3(X3,X2,X1))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[c_0_2595]) ).
cnf(c_0_4019,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2714]) ).
cnf(c_0_4020,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2715]) ).
cnf(c_0_4021,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X4)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2716]) ).
cnf(c_0_4022,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X3)
| ~ class_Rings_Olinordered__semidom(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2717]) ).
cnf(c_0_4023,plain,
( 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),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)],[c_0_2718]) ).
cnf(c_0_4024,plain,
( 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),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)],[c_0_2719]) ).
cnf(c_0_4025,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk6_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2594]) ).
cnf(c_0_4026,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk5_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2595]) ).
cnf(c_0_4027,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2720]) ).
cnf(c_0_4028,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2721]) ).
cnf(c_0_4029,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_RealVector_Onorm__class_Onorm(X2,X4)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2722]) ).
cnf(c_0_4030,plain,
( c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2628]) ).
cnf(c_0_4031,plain,
( c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2629]) ).
cnf(c_0_4032,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2723]) ).
cnf(c_0_4033,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2724]) ).
cnf(c_0_4034,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2725]) ).
cnf(c_0_4035,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Oordered__comm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2726]) ).
cnf(c_0_4036,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2727]) ).
cnf(c_0_4037,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2728]) ).
cnf(c_0_4038,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),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2644]) ).
cnf(c_0_4039,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),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2644]) ).
cnf(c_0_4040,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_4041,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_4042,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))
| ~ class_Rings_Olinordered__ring__strict(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)],[c_0_2630]) ).
cnf(c_0_4043,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))
| ~ 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,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2631]) ).
cnf(c_0_4044,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),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2729]) ).
cnf(c_0_4045,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__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2730]) ).
cnf(c_0_4046,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__comm__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2731]) ).
cnf(c_0_4047,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),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2732]) ).
cnf(c_0_4048,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,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2733]) ).
cnf(c_0_4049,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2734]) ).
cnf(c_0_4050,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2735]) ).
cnf(c_0_4051,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2736]) ).
cnf(c_0_4052,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2737]) ).
cnf(c_0_4053,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2738]) ).
cnf(c_0_4054,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2633]) ).
cnf(c_0_4055,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2739]) ).
cnf(c_0_4056,plain,
( 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))
| ~ 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,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2634]) ).
cnf(c_0_4057,plain,
( 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)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2740]) ).
cnf(c_0_4058,plain,
( 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,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2741]) ).
cnf(c_0_4059,plain,
( c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2742]) ).
cnf(c_0_4060,plain,
( 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,c_Groups_Ominus__class_Ominus(X1,X2,X4),X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2743]) ).
cnf(c_0_4061,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2744]) ).
cnf(c_0_4062,plain,
( 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),X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2745]) ).
cnf(c_0_4063,plain,
( 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2746]) ).
cnf(c_0_4064,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2747]) ).
cnf(c_0_4065,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_OpCons(X1,X3,X4)) = c_Polynomial_OpCons(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2748]) ).
cnf(c_0_4066,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2749]) ).
cnf(c_0_4067,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2750]) ).
cnf(c_0_4068,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2751]) ).
cnf(c_0_4069,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2752]) ).
cnf(c_0_4070,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2753]) ).
cnf(c_0_4071,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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)],[c_0_2754]) ).
cnf(c_0_4072,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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)],[c_0_2754]) ).
cnf(c_0_4073,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) = 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)],[c_0_2755]) ).
cnf(c_0_4074,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) = 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)],[c_0_2756]) ).
cnf(c_0_4075,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = 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)],[c_0_2757]) ).
cnf(c_0_4076,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = 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)],[c_0_2758]) ).
cnf(c_0_4077,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = 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)],[c_0_2759]) ).
cnf(c_0_4078,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2760]) ).
cnf(c_0_4079,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2761]) ).
cnf(c_0_4080,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2762]) ).
cnf(c_0_4081,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2763]) ).
cnf(c_0_4082,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2764]) ).
cnf(c_0_4083,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2765]) ).
cnf(c_0_4084,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| ~ 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)],[c_0_2766]) ).
cnf(c_0_4085,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,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)],[c_0_2767]) ).
cnf(c_0_4086,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)],[c_0_2768]) ).
cnf(c_0_4087,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2617]) ).
cnf(c_0_4088,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,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2769]) ).
cnf(c_0_4089,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,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2770]) ).
cnf(c_0_4090,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,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),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2767]) ).
cnf(c_0_4091,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)) ),
inference(split_conjunct,[status(thm)],[c_0_2768]) ).
cnf(c_0_4092,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)],[c_0_2771]) ).
cnf(c_0_4093,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)],[c_0_2772]) ).
cnf(c_0_4094,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)],[c_0_2773]) ).
cnf(c_0_4095,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)],[c_0_2774]) ).
cnf(c_0_4096,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)],[c_0_2775]) ).
cnf(c_0_4097,plain,
( X4 = c_Polynomial_Osynthetic__div(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) != c_Polynomial_OpCons(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2776]) ).
cnf(c_0_4098,plain,
( c_Polynomial_Osynthetic__div(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = 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)],[c_0_2777]) ).
cnf(c_0_4099,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)],[c_0_2778]) ).
cnf(c_0_4100,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)],[c_0_2779]) ).
cnf(c_0_4101,plain,
( 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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2664]) ).
cnf(c_0_4102,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2665]) ).
cnf(c_0_4103,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2666]) ).
cnf(c_0_4104,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2669]) ).
cnf(c_0_4105,plain,
( c_Orderings_Oord__class_Oless(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))
| ~ 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,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2780]) ).
cnf(c_0_4106,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),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2767]) ).
cnf(c_0_4107,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,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2768]) ).
cnf(c_0_4108,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)],[c_0_2670]) ).
cnf(c_0_4109,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),X3),X2))
| ~ 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,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2781]) ).
cnf(c_0_4110,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)],[c_0_2782]) ).
cnf(c_0_4111,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2671]) ).
cnf(c_0_4112,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2783]) ).
cnf(c_0_4113,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2784]) ).
cnf(c_0_4114,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2785]) ).
cnf(c_0_4115,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2785]) ).
cnf(c_0_4116,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2786]) ).
cnf(c_0_4117,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2786]) ).
cnf(c_0_4118,plain,
( c_Orderings_Oord__class_Oless__eq(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),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2787]) ).
cnf(c_0_4119,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2788]) ).
cnf(c_0_4120,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2789]) ).
cnf(c_0_4121,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2790]) ).
cnf(c_0_4122,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2791]) ).
cnf(c_0_4123,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2792]) ).
cnf(c_0_4124,plain,
( X5 = hAPP(c_Polynomial_Opoly(X1,X2),X3)
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) != c_Polynomial_OpCons(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2776]) ).
cnf(c_0_4125,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Osmult(X1,X3,X4)) = 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)],[c_0_2793]) ).
cnf(c_0_4126,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4127,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4128,plain,
( hAPP(c_Polynomial_Opoly(X1,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)],[c_0_2794]) ).
cnf(c_0_4129,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2795]) ).
cnf(c_0_4130,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2795]) ).
cnf(c_0_4131,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2795]) ).
cnf(c_0_4132,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2795]) ).
cnf(c_0_4133,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2796]) ).
cnf(c_0_4134,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2796]) ).
cnf(c_0_4135,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2796]) ).
cnf(c_0_4136,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2796]) ).
cnf(c_0_4137,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),c_Nat_OSuc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X4))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2797]) ).
cnf(c_0_4138,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2798]) ).
cnf(c_0_4139,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2799]) ).
cnf(c_0_4140,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) = 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)],[c_0_2800]) ).
cnf(c_0_4141,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = 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)],[c_0_2801]) ).
cnf(c_0_4142,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) = 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)],[c_0_2802]) ).
cnf(c_0_4143,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = 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)],[c_0_2803]) ).
cnf(c_0_4144,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)],[c_0_2804]) ).
cnf(c_0_4145,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),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)],[c_0_2805]) ).
cnf(c_0_4146,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2806]) ).
cnf(c_0_4147,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2807]) ).
cnf(c_0_4148,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_2808]) ).
cnf(c_0_4149,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_2808]) ).
cnf(c_0_4150,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
inference(split_conjunct,[status(thm)],[c_0_2809]) ).
cnf(c_0_4151,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2810]) ).
cnf(c_0_4152,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2811]) ).
cnf(c_0_4153,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2812]) ).
cnf(c_0_4154,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2813]) ).
cnf(c_0_4155,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2814]) ).
cnf(c_0_4156,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2815]) ).
cnf(c_0_4157,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2816]) ).
cnf(c_0_4158,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ 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)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2817]) ).
cnf(c_0_4159,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),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,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2818]) ).
cnf(c_0_4160,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2678]) ).
cnf(c_0_4161,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2679]) ).
cnf(c_0_4162,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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_4163,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)],[c_0_2820]) ).
cnf(c_0_4164,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)],[c_0_2821]) ).
cnf(c_0_4165,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)],[c_0_2822]) ).
cnf(c_0_4166,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_2823]) ).
cnf(c_0_4167,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2824]) ).
cnf(c_0_4168,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2824]) ).
cnf(c_0_4169,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2825]) ).
cnf(c_0_4170,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2825]) ).
cnf(c_0_4171,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2826]) ).
cnf(c_0_4172,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2827]) ).
cnf(c_0_4173,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2828]) ).
cnf(c_0_4174,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2829]) ).
cnf(c_0_4175,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2830]) ).
cnf(c_0_4176,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2795]) ).
cnf(c_0_4177,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2795]) ).
cnf(c_0_4178,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2796]) ).
cnf(c_0_4179,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2796]) ).
cnf(c_0_4180,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2831]) ).
cnf(c_0_4181,plain,
( 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)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2832]) ).
cnf(c_0_4182,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),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)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2833]) ).
cnf(c_0_4183,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2834]) ).
cnf(c_0_4184,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),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,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2835]) ).
cnf(c_0_4185,plain,
( 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,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2836]) ).
cnf(c_0_4186,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2691]) ).
cnf(c_0_4187,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2692]) ).
cnf(c_0_4188,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2837]) ).
cnf(c_0_4189,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2838]) ).
cnf(c_0_4190,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2839]) ).
cnf(c_0_4191,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2840]) ).
cnf(c_0_4192,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2697]) ).
cnf(c_0_4193,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2698]) ).
cnf(c_0_4194,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2841]) ).
cnf(c_0_4195,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2842]) ).
cnf(c_0_4196,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2843]) ).
cnf(c_0_4197,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),esk24_0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(split_conjunct,[status(thm)],[c_0_2844]) ).
cnf(c_0_4198,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),esk19_0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(split_conjunct,[status(thm)],[c_0_2845]) ).
cnf(c_0_4199,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(split_conjunct,[status(thm)],[c_0_2846]) ).
cnf(c_0_4200,plain,
( X3 = esk8_2(X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X1) != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2847]) ).
cnf(c_0_4201,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
inference(split_conjunct,[status(thm)],[c_0_2848]) ).
cnf(c_0_4202,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2849]) ).
cnf(c_0_4203,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2850]) ).
cnf(c_0_4204,plain,
( 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)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2700]) ).
cnf(c_0_4205,plain,
( 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)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2701]) ).
cnf(c_0_4206,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2851]) ).
cnf(c_0_4207,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2852]) ).
cnf(c_0_4208,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2853]) ).
cnf(c_0_4209,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2854]) ).
cnf(c_0_4210,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2855]) ).
cnf(c_0_4211,plain,
( c_Rings_Odvd__class_Odvd(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__eq(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2856]) ).
cnf(c_0_4212,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,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2857]) ).
cnf(c_0_4213,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,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2858]) ).
cnf(c_0_4214,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2859]) ).
cnf(c_0_4215,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)),
inference(split_conjunct,[status(thm)],[c_0_2860]) ).
cnf(c_0_4216,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2861]) ).
cnf(c_0_4217,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2862]) ).
cnf(c_0_4218,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2863]) ).
cnf(c_0_4219,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2710]) ).
cnf(c_0_4220,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2864]) ).
cnf(c_0_4221,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2865]) ).
cnf(c_0_4222,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2866]) ).
cnf(c_0_4223,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2711]) ).
cnf(c_0_4224,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2867]) ).
cnf(c_0_4225,plain,
( X3 = X2
| hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4226,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2868]) ).
cnf(c_0_4227,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2869]) ).
cnf(c_0_4228,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2870]) ).
cnf(c_0_4229,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2871]) ).
cnf(c_0_4230,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_4231,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_4232,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2874]) ).
cnf(c_0_4233,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2875]) ).
cnf(c_0_4234,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2876]) ).
cnf(c_0_4235,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2877]) ).
cnf(c_0_4236,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2878]) ).
cnf(c_0_4237,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2879]) ).
cnf(c_0_4238,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2880]) ).
cnf(c_0_4239,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2881]) ).
cnf(c_0_4240,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2882]) ).
cnf(c_0_4241,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Nat_OSuc(X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_2883]) ).
cnf(c_0_4242,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2884]) ).
cnf(c_0_4243,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2885]) ).
cnf(c_0_4244,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2886]) ).
cnf(c_0_4245,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2887]) ).
cnf(c_0_4246,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2888]) ).
cnf(c_0_4247,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2843]) ).
cnf(c_0_4248,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_2889]) ).
cnf(c_0_4249,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2890]) ).
cnf(c_0_4250,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_2891]) ).
cnf(c_0_4251,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2892]) ).
cnf(c_0_4252,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = c_Divides_Odiv__class_Odiv(X1,X2,X4)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2893]) ).
cnf(c_0_4253,plain,
( 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)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2894]) ).
cnf(c_0_4254,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2895]) ).
cnf(c_0_4255,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2896]) ).
cnf(c_0_4256,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2897]) ).
cnf(c_0_4257,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2898]) ).
cnf(c_0_4258,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2899]) ).
cnf(c_0_4259,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2900]) ).
cnf(c_0_4260,plain,
( 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)],[c_0_2901]) ).
cnf(c_0_4261,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_Osmult(X1,X3,X4)) = 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)],[c_0_2902]) ).
cnf(c_0_4262,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2903]) ).
cnf(c_0_4263,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2904]) ).
cnf(c_0_4264,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),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2905]) ).
cnf(c_0_4265,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2906]) ).
cnf(c_0_4266,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))),
inference(split_conjunct,[status(thm)],[c_0_2907]) ).
cnf(c_0_4267,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),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)],[c_0_2908]) ).
cnf(c_0_4268,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),c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2909]) ).
cnf(c_0_4269,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2761]) ).
cnf(c_0_4270,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2762]) ).
cnf(c_0_4271,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| 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))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2766]) ).
cnf(c_0_4272,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2910]) ).
cnf(c_0_4273,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2910]) ).
cnf(c_0_4274,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2911]) ).
cnf(c_0_4275,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2911]) ).
cnf(c_0_4276,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4277,plain,
( X2 = 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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2912]) ).
cnf(c_0_4278,plain,
( X2 = 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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2913]) ).
cnf(c_0_4279,plain,
( 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_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2764]) ).
cnf(c_0_4280,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2667]) ).
cnf(c_0_4281,plain,
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2668]) ).
cnf(c_0_4282,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2914]) ).
cnf(c_0_4283,plain,
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2915]) ).
cnf(c_0_4284,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)],[c_0_2916]) ).
cnf(c_0_4285,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_2917]) ).
cnf(c_0_4286,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_2918]) ).
cnf(c_0_4287,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_2919]) ).
cnf(c_0_4288,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_2920]) ).
cnf(c_0_4289,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_2921]) ).
cnf(c_0_4290,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
inference(split_conjunct,[status(thm)],[c_0_2922]) ).
cnf(c_0_4291,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_2923]) ).
cnf(c_0_4292,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_2924]) ).
cnf(c_0_4293,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2925]) ).
cnf(c_0_4294,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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)],[c_0_2842]) ).
cnf(c_0_4295,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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)],[c_0_2842]) ).
cnf(c_0_4296,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2926]) ).
cnf(c_0_4297,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2927]) ).
cnf(c_0_4298,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2928]) ).
cnf(c_0_4299,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2929]) ).
cnf(c_0_4300,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2930]) ).
cnf(c_0_4301,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2931]) ).
cnf(c_0_4302,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2932]) ).
cnf(c_0_4303,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_2933]) ).
cnf(c_0_4304,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[c_0_2934]) ).
cnf(c_0_4305,plain,
( 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2935]) ).
cnf(c_0_4306,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2936]) ).
cnf(c_0_4307,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2937]) ).
cnf(c_0_4308,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2938]) ).
cnf(c_0_4309,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2939]) ).
cnf(c_0_4310,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2940]) ).
cnf(c_0_4311,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2940]) ).
cnf(c_0_4312,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2941]) ).
cnf(c_0_4313,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2942]) ).
cnf(c_0_4314,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2942]) ).
cnf(c_0_4315,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2943]) ).
cnf(c_0_4316,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2944]) ).
cnf(c_0_4317,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2945]) ).
cnf(c_0_4318,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2946]) ).
cnf(c_0_4319,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2947]) ).
cnf(c_0_4320,plain,
( X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_4321,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)],[c_0_2948]) ).
cnf(c_0_4322,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),X2)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2949]) ).
cnf(c_0_4323,plain,
( c_Orderings_Oord__class_Oless__eq(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)],[c_0_2667]) ).
cnf(c_0_4324,plain,
( c_Orderings_Oord__class_Oless__eq(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))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2668]) ).
cnf(c_0_4325,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_4326,plain,
( 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)
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2754]) ).
cnf(c_0_4327,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)],[c_0_2905]) ).
cnf(c_0_4328,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2905]) ).
cnf(c_0_4329,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2950]) ).
cnf(c_0_4330,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2951]) ).
cnf(c_0_4331,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2952]) ).
cnf(c_0_4332,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2953]) ).
cnf(c_0_4333,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| X2 = X3
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[c_0_2954]) ).
cnf(c_0_4334,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2889]) ).
cnf(c_0_4335,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2890]) ).
cnf(c_0_4336,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2891]) ).
cnf(c_0_4337,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2892]) ).
cnf(c_0_4338,plain,
( 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_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2894]) ).
cnf(c_0_4339,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2955]) ).
cnf(c_0_4340,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2956]) ).
cnf(c_0_4341,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_2875]) ).
cnf(c_0_4342,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk8_2(X2,X1)),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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2847]) ).
cnf(c_0_4343,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk7_2(X2,X1)),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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2957]) ).
cnf(c_0_4344,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_4345,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_4346,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2958]) ).
cnf(c_0_4347,plain,
( 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)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2700]) ).
cnf(c_0_4348,plain,
( 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)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2701]) ).
cnf(c_0_4349,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2959]) ).
cnf(c_0_4350,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2960]) ).
cnf(c_0_4351,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2931]) ).
cnf(c_0_4352,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2961]) ).
cnf(c_0_4353,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2962]) ).
cnf(c_0_4354,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2932]) ).
cnf(c_0_4355,plain,
( 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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2942]) ).
cnf(c_0_4356,plain,
( c_Polynomial_Opos__poly(X1,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2963]) ).
cnf(c_0_4357,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),esk20_1(X1)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X1),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)) ),
inference(split_conjunct,[status(thm)],[c_0_2964]) ).
cnf(c_0_4358,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2965]) ).
cnf(c_0_4359,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2878]) ).
cnf(c_0_4360,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2879]) ).
cnf(c_0_4361,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2880]) ).
cnf(c_0_4362,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2881]) ).
cnf(c_0_4363,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2882]) ).
cnf(c_0_4364,plain,
( X3 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| 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)],[c_0_2966]) ).
cnf(c_0_4365,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4366,plain,
( X3 = X2
| hBOOL(hAPP(hAPP(X1,X2),X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4367,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_2967]) ).
cnf(c_0_4368,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(split_conjunct,[status(thm)],[c_0_2968]) ).
cnf(c_0_4369,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2969]) ).
cnf(c_0_4370,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2970]) ).
cnf(c_0_4371,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2971]) ).
cnf(c_0_4372,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2972]) ).
cnf(c_0_4373,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2973]) ).
cnf(c_0_4374,plain,
( c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2974]) ).
cnf(c_0_4375,plain,
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2975]) ).
cnf(c_0_4376,plain,
( ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2947]) ).
cnf(c_0_4377,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2897]) ).
cnf(c_0_4378,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2898]) ).
cnf(c_0_4379,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,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)],[c_0_2976]) ).
cnf(c_0_4380,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2977]) ).
cnf(c_0_4381,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk8_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2847]) ).
cnf(c_0_4382,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk7_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2957]) ).
cnf(c_0_4383,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2978]) ).
cnf(c_0_4384,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,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)],[c_0_2979]) ).
cnf(c_0_4385,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)],[c_0_2980]) ).
cnf(c_0_4386,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ 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),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2981]) ).
cnf(c_0_4387,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2982]) ).
cnf(c_0_4388,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2983]) ).
cnf(c_0_4389,plain,
( c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2984]) ).
cnf(c_0_4390,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2985]) ).
cnf(c_0_4391,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3)) = c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2986]) ).
cnf(c_0_4392,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3)) = c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2987]) ).
cnf(c_0_4393,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2988]) ).
cnf(c_0_4394,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2989]) ).
cnf(c_0_4395,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2990]) ).
cnf(c_0_4396,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2991]) ).
cnf(c_0_4397,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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)],[c_0_2819]) ).
cnf(c_0_4398,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_4399,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_2808]) ).
cnf(c_0_4400,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2992]) ).
cnf(c_0_4401,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2926]) ).
cnf(c_0_4402,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,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)],[c_0_2925]) ).
cnf(c_0_4403,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2927]) ).
cnf(c_0_4404,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2993]) ).
cnf(c_0_4405,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(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)],[c_0_2928]) ).
cnf(c_0_4406,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_2994]) ).
cnf(c_0_4407,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_2995]) ).
cnf(c_0_4408,plain,
( X1 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk12_2(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2996]) ).
cnf(c_0_4409,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2933]) ).
cnf(c_0_4410,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,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)],[c_0_2934]) ).
cnf(c_0_4411,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2935]) ).
cnf(c_0_4412,plain,
( c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2963]) ).
cnf(c_0_4413,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2997]) ).
cnf(c_0_4414,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2998]) ).
cnf(c_0_4415,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2999]) ).
cnf(c_0_4416,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2937]) ).
cnf(c_0_4417,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2521]) ).
cnf(c_0_4418,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3000]) ).
cnf(c_0_4419,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3001]) ).
cnf(c_0_4420,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3002]) ).
cnf(c_0_4421,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3003]) ).
cnf(c_0_4422,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3004]) ).
cnf(c_0_4423,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3005]) ).
cnf(c_0_4424,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,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)],[c_0_3006]) ).
cnf(c_0_4425,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3007]) ).
cnf(c_0_4426,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3008]) ).
cnf(c_0_4427,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,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)],[c_0_3009]) ).
cnf(c_0_4428,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3010]) ).
cnf(c_0_4429,plain,
( 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)],[c_0_2764]) ).
cnf(c_0_4430,plain,
( c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2956]) ).
cnf(c_0_4431,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2912]) ).
cnf(c_0_4432,plain,
( 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)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2913]) ).
cnf(c_0_4433,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3011]) ).
cnf(c_0_4434,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| 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)],[c_0_3012]) ).
cnf(c_0_4435,plain,
( c_Polynomial_Omonom(X1,X2,c_Nat_OSuc(X3)) = 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)],[c_0_3013]) ).
cnf(c_0_4436,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3014]) ).
cnf(c_0_4437,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)],[c_0_2948]) ).
cnf(c_0_4438,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)],[c_0_2949]) ).
cnf(c_0_4439,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3015]) ).
cnf(c_0_4440,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3016]) ).
cnf(c_0_4441,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3017]) ).
cnf(c_0_4442,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3018]) ).
cnf(c_0_4443,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3019]) ).
cnf(c_0_4444,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3020]) ).
cnf(c_0_4445,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3021]) ).
cnf(c_0_4446,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3022]) ).
cnf(c_0_4447,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3023]) ).
cnf(c_0_4448,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3024]) ).
cnf(c_0_4449,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3025]) ).
cnf(c_0_4450,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3026]) ).
cnf(c_0_4451,plain,
( c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3027]) ).
cnf(c_0_4452,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3028]) ).
cnf(c_0_4453,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3029]) ).
cnf(c_0_4454,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ 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),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3030]) ).
cnf(c_0_4455,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3031]) ).
cnf(c_0_4456,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = 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)],[c_0_3032]) ).
cnf(c_0_4457,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = 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)],[c_0_3033]) ).
cnf(c_0_4458,plain,
( c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3034]) ).
cnf(c_0_4459,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3035]) ).
cnf(c_0_4460,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3036]) ).
cnf(c_0_4461,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3037]) ).
cnf(c_0_4462,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3038]) ).
cnf(c_0_4463,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X3
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3039]) ).
cnf(c_0_4464,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3040]) ).
cnf(c_0_4465,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2996]) ).
cnf(c_0_4466,plain,
( c_Polynomial_Opos__poly(X1,X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2963]) ).
cnf(c_0_4467,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3041]) ).
cnf(c_0_4468,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3041]) ).
cnf(c_0_4469,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,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)],[c_0_3042]) ).
cnf(c_0_4470,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
inference(split_conjunct,[status(thm)],[c_0_3043]) ).
cnf(c_0_4471,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[c_0_3044]) ).
cnf(c_0_4472,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3045]) ).
cnf(c_0_4473,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3046]) ).
cnf(c_0_4474,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3047]) ).
cnf(c_0_4475,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3048]) ).
cnf(c_0_4476,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3049]) ).
cnf(c_0_4477,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3050]) ).
cnf(c_0_4478,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),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)],[c_0_3051]) ).
cnf(c_0_4479,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),c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3052]) ).
cnf(c_0_4480,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),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)],[c_0_3053]) ).
cnf(c_0_4481,plain,
( c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3054]) ).
cnf(c_0_4482,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3055]) ).
cnf(c_0_4483,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2947]) ).
cnf(c_0_4484,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3056]) ).
cnf(c_0_4485,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3056]) ).
cnf(c_0_4486,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3057]) ).
cnf(c_0_4487,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3057]) ).
cnf(c_0_4488,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)),
inference(split_conjunct,[status(thm)],[c_0_3058]) ).
cnf(c_0_4489,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3059]) ).
cnf(c_0_4490,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3059]) ).
cnf(c_0_4491,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3060]) ).
cnf(c_0_4492,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3060]) ).
cnf(c_0_4493,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Omonom(X1,X2,X3)) = c_Polynomial_Omonom(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3061]) ).
cnf(c_0_4494,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3062]) ).
cnf(c_0_4495,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3063]) ).
cnf(c_0_4496,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_2966]) ).
cnf(c_0_4497,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3064]) ).
cnf(c_0_4498,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3065]) ).
cnf(c_0_4499,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2951]) ).
cnf(c_0_4500,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2951]) ).
cnf(c_0_4501,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3066]) ).
cnf(c_0_4502,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3067]) ).
cnf(c_0_4503,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3068]) ).
cnf(c_0_4504,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3069]) ).
cnf(c_0_4505,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3070]) ).
cnf(c_0_4506,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3071]) ).
cnf(c_0_4507,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3072]) ).
cnf(c_0_4508,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3073]) ).
cnf(c_0_4509,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2953]) ).
cnf(c_0_4510,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2953]) ).
cnf(c_0_4511,plain,
( c_Nat_OSuc(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)],[c_0_3074]) ).
cnf(c_0_4512,plain,
( X1 = c_Nat_OSuc(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)],[c_0_3075]) ).
cnf(c_0_4513,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3076]) ).
cnf(c_0_4514,plain,
( 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),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3077]) ).
cnf(c_0_4515,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = 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)],[c_0_3078]) ).
cnf(c_0_4516,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = 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)],[c_0_3079]) ).
cnf(c_0_4517,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_4518,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = 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)],[c_0_3080]) ).
cnf(c_0_4519,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3081]) ).
cnf(c_0_4520,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3028]) ).
cnf(c_0_4521,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3029]) ).
cnf(c_0_4522,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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)],[c_0_3082]) ).
cnf(c_0_4523,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2954]) ).
cnf(c_0_4524,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oplus__class_Oplus(X1,X2,X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3083]) ).
cnf(c_0_4525,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2)) = 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)],[c_0_3084]) ).
cnf(c_0_4526,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3085]) ).
cnf(c_0_4527,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3086]) ).
cnf(c_0_4528,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3087]) ).
cnf(c_0_4529,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3088]) ).
cnf(c_0_4530,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X2) = 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)],[c_0_3089]) ).
cnf(c_0_4531,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3039]) ).
cnf(c_0_4532,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3040]) ).
cnf(c_0_4533,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4534,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3090]) ).
cnf(c_0_4535,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3091]) ).
cnf(c_0_4536,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3092]) ).
cnf(c_0_4537,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X2,X3,X1) != c_Polynomial_OpCons(X2,X4,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3093]) ).
cnf(c_0_4538,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2972]) ).
cnf(c_0_4539,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2972]) ).
cnf(c_0_4540,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2973]) ).
cnf(c_0_4541,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2973]) ).
cnf(c_0_4542,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3066]) ).
cnf(c_0_4543,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3067]) ).
cnf(c_0_4544,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3068]) ).
cnf(c_0_4545,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3069]) ).
cnf(c_0_4546,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3070]) ).
cnf(c_0_4547,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3071]) ).
cnf(c_0_4548,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3072]) ).
cnf(c_0_4549,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3073]) ).
cnf(c_0_4550,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3094]) ).
cnf(c_0_4551,plain,
( c_Orderings_Oord__class_Oless(X1,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(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3095]) ).
cnf(c_0_4552,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3096]) ).
cnf(c_0_4553,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),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)],[c_0_3097]) ).
cnf(c_0_4554,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3098]) ).
cnf(c_0_4555,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3099]) ).
cnf(c_0_4556,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| X2 = X3
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3100]) ).
cnf(c_0_4557,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_4558,plain,
( c_Polynomial_Opos__poly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3101]) ).
cnf(c_0_4559,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3102]) ).
cnf(c_0_4560,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)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3012]) ).
cnf(c_0_4561,plain,
( X4 = X5
| ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3103]) ).
cnf(c_0_4562,plain,
( X2 = X3
| ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| X4 != X5 ),
inference(split_conjunct,[status(thm)],[c_0_3103]) ).
cnf(c_0_4563,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3085]) ).
cnf(c_0_4564,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3086]) ).
cnf(c_0_4565,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3087]) ).
cnf(c_0_4566,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3088]) ).
cnf(c_0_4567,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3104]) ).
cnf(c_0_4568,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,X3,X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3105]) ).
cnf(c_0_4569,plain,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3106]) ).
cnf(c_0_4570,plain,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3107]) ).
cnf(c_0_4571,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3108]) ).
cnf(c_0_4572,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3109]) ).
cnf(c_0_4573,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3110]) ).
cnf(c_0_4574,plain,
( X2 = X3
| ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X4) != c_Polynomial_Omonom(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3111]) ).
cnf(c_0_4575,plain,
( X2 = X4
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_3112]) ).
cnf(c_0_4576,plain,
( X3 = X5
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_3112]) ).
cnf(c_0_4577,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) != c_Groups_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3113]) ).
cnf(c_0_4578,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3114]) ).
cnf(c_0_4579,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3115]) ).
cnf(c_0_4580,plain,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3116]) ).
cnf(c_0_4581,plain,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X4,X2) != c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3117]) ).
cnf(c_0_4582,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
inference(split_conjunct,[status(thm)],[c_0_3118]) ).
cnf(c_0_4583,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3119]) ).
cnf(c_0_4584,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3120]) ).
cnf(c_0_4585,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3076]) ).
cnf(c_0_4586,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3121]) ).
cnf(c_0_4587,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3122]) ).
cnf(c_0_4588,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3123]) ).
cnf(c_0_4589,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3124]) ).
cnf(c_0_4590,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3125]) ).
cnf(c_0_4591,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3126]) ).
cnf(c_0_4592,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3127]) ).
cnf(c_0_4593,plain,
( X2 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3128]) ).
cnf(c_0_4594,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| 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) ),
inference(split_conjunct,[status(thm)],[c_0_3129]) ).
cnf(c_0_4595,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3130]) ).
cnf(c_0_4596,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3131]) ).
cnf(c_0_4597,plain,
( X1 = X2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3132]) ).
cnf(c_0_4598,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk10_2(X2,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3133]) ).
cnf(c_0_4599,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_2954]) ).
cnf(c_0_4600,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3098]) ).
cnf(c_0_4601,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3099]) ).
cnf(c_0_4602,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3134]) ).
cnf(c_0_4603,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3135]) ).
cnf(c_0_4604,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2985]) ).
cnf(c_0_4605,plain,
c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X2)),
inference(split_conjunct,[status(thm)],[c_0_3136]) ).
cnf(c_0_4606,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3137]) ).
cnf(c_0_4607,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = X2
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3138]) ).
cnf(c_0_4608,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3139]) ).
cnf(c_0_4609,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3140]) ).
cnf(c_0_4610,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3141]) ).
cnf(c_0_4611,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3142]) ).
cnf(c_0_4612,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3143]) ).
cnf(c_0_4613,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3144]) ).
cnf(c_0_4614,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3145]) ).
cnf(c_0_4615,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3091]) ).
cnf(c_0_4616,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3092]) ).
cnf(c_0_4617,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3146]) ).
cnf(c_0_4618,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3147]) ).
cnf(c_0_4619,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3148]) ).
cnf(c_0_4620,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3149]) ).
cnf(c_0_4621,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3150]) ).
cnf(c_0_4622,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3151]) ).
cnf(c_0_4623,plain,
( 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),X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_3152]) ).
cnf(c_0_4624,plain,
( 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)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_3152]) ).
cnf(c_0_4625,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3153]) ).
cnf(c_0_4626,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3154]) ).
cnf(c_0_4627,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk32_0),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)),
inference(split_conjunct,[status(thm)],[c_0_3155]) ).
cnf(c_0_4628,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk14_0),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)),
inference(split_conjunct,[status(thm)],[c_0_3156]) ).
cnf(c_0_4629,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)),
inference(split_conjunct,[status(thm)],[c_0_3157]) ).
cnf(c_0_4630,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_3158]) ).
cnf(c_0_4631,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_3159]) ).
cnf(c_0_4632,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_2925]) ).
cnf(c_0_4633,plain,
( 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)],[c_0_3160]) ).
cnf(c_0_4634,plain,
( 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)],[c_0_3161]) ).
cnf(c_0_4635,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk23_2(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3162]) ).
cnf(c_0_4636,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk9_2(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3163]) ).
cnf(c_0_4637,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[c_0_3164]) ).
cnf(c_0_4638,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3134]) ).
cnf(c_0_4639,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3135]) ).
cnf(c_0_4640,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3165]) ).
cnf(c_0_4641,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_3166]) ).
cnf(c_0_4642,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_3167]) ).
cnf(c_0_4643,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_3168]) ).
cnf(c_0_4644,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_3169]) ).
cnf(c_0_4645,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_3170]) ).
cnf(c_0_4646,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3171]) ).
cnf(c_0_4647,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3172]) ).
cnf(c_0_4648,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3173]) ).
cnf(c_0_4649,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))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2948]) ).
cnf(c_0_4650,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))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2949]) ).
cnf(c_0_4651,plain,
( X1 = c_Nat_OSuc(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3174]) ).
cnf(c_0_4652,plain,
( X1 = c_Nat_OSuc(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3175]) ).
cnf(c_0_4653,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X4 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3176]) ).
cnf(c_0_4654,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X4 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3177]) ).
cnf(c_0_4655,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3178]) ).
cnf(c_0_4656,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3179]) ).
cnf(c_0_4657,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3180]) ).
cnf(c_0_4658,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3107]) ).
cnf(c_0_4659,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3181]) ).
cnf(c_0_4660,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3182]) ).
cnf(c_0_4661,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X4 != X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3183]) ).
cnf(c_0_4662,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X4 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3184]) ).
cnf(c_0_4663,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| X1 != c_Nat_OSuc(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3133]) ).
cnf(c_0_4664,plain,
( c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2963]) ).
cnf(c_0_4665,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3185]) ).
cnf(c_0_4666,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_1(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3185]) ).
cnf(c_0_4667,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X3
| 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)],[c_0_3186]) ).
cnf(c_0_4668,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)],[c_0_3187]) ).
cnf(c_0_4669,plain,
( X1 = X2
| X3 = c_Groups_Ozero__class_Ozero(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)],[c_0_3188]) ).
cnf(c_0_4670,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3189]) ).
cnf(c_0_4671,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3190]) ).
cnf(c_0_4672,plain,
( c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3191]) ).
cnf(c_0_4673,plain,
( c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3192]) ).
cnf(c_0_4674,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3193]) ).
cnf(c_0_4675,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3194]) ).
cnf(c_0_4676,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3195]) ).
cnf(c_0_4677,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3196]) ).
cnf(c_0_4678,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3197]) ).
cnf(c_0_4679,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3104]) ).
cnf(c_0_4680,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3198]) ).
cnf(c_0_4681,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3199]) ).
cnf(c_0_4682,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3200]) ).
cnf(c_0_4683,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3011]) ).
cnf(c_0_4684,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3201]) ).
cnf(c_0_4685,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3171]) ).
cnf(c_0_4686,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3173]) ).
cnf(c_0_4687,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3202]) ).
cnf(c_0_4688,plain,
( 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)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_3152]) ).
cnf(c_0_4689,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3203]) ).
cnf(c_0_4690,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3204]) ).
cnf(c_0_4691,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3205]) ).
cnf(c_0_4692,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3206]) ).
cnf(c_0_4693,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Nat_OSuc(X1) = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3207]) ).
cnf(c_0_4694,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3193]) ).
cnf(c_0_4695,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3076]) ).
cnf(c_0_4696,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3194]) ).
cnf(c_0_4697,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3208]) ).
cnf(c_0_4698,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_1(X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3185]) ).
cnf(c_0_4699,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_3128]) ).
cnf(c_0_4700,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3209]) ).
cnf(c_0_4701,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3210]) ).
cnf(c_0_4702,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3211]) ).
cnf(c_0_4703,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3212]) ).
cnf(c_0_4704,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3213]) ).
cnf(c_0_4705,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3214]) ).
cnf(c_0_4706,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3215]) ).
cnf(c_0_4707,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3216]) ).
cnf(c_0_4708,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3216]) ).
cnf(c_0_4709,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3217]) ).
cnf(c_0_4710,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(split_conjunct,[status(thm)],[c_0_3218]) ).
cnf(c_0_4711,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[c_0_3219]) ).
cnf(c_0_4712,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_3220]) ).
cnf(c_0_4713,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3203]) ).
cnf(c_0_4714,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3221]) ).
cnf(c_0_4715,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3222]) ).
cnf(c_0_4716,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3175]) ).
cnf(c_0_4717,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3223]) ).
cnf(c_0_4718,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3224]) ).
cnf(c_0_4719,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3212]) ).
cnf(c_0_4720,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3213]) ).
cnf(c_0_4721,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3214]) ).
cnf(c_0_4722,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3225]) ).
cnf(c_0_4723,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3226]) ).
cnf(c_0_4724,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3227]) ).
cnf(c_0_4725,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,X2,X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3228]) ).
cnf(c_0_4726,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_3229]) ).
cnf(c_0_4727,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3230]) ).
cnf(c_0_4728,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3231]) ).
cnf(c_0_4729,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3232]) ).
cnf(c_0_4730,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X3 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3233]) ).
cnf(c_0_4731,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3234]) ).
cnf(c_0_4732,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_3144]) ).
cnf(c_0_4733,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_3091]) ).
cnf(c_0_4734,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3235]) ).
cnf(c_0_4735,plain,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3142]) ).
cnf(c_0_4736,plain,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3143]) ).
cnf(c_0_4737,plain,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3145]) ).
cnf(c_0_4738,plain,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3091]) ).
cnf(c_0_4739,plain,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3092]) ).
cnf(c_0_4740,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3236]) ).
cnf(c_0_4741,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3235]) ).
cnf(c_0_4742,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3237]) ).
cnf(c_0_4743,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3238]) ).
cnf(c_0_4744,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3239]) ).
cnf(c_0_4745,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3240]) ).
cnf(c_0_4746,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3241]) ).
cnf(c_0_4747,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3242]) ).
cnf(c_0_4748,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),
inference(split_conjunct,[status(thm)],[c_0_3243]) ).
cnf(c_0_4749,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3162]) ).
cnf(c_0_4750,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3163]) ).
cnf(c_0_4751,plain,
( c_Polynomial_Omonom(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3244]) ).
cnf(c_0_4752,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3237]) ).
cnf(c_0_4753,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3238]) ).
cnf(c_0_4754,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3239]) ).
cnf(c_0_4755,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3240]) ).
cnf(c_0_4756,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3245]) ).
cnf(c_0_4757,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3246]) ).
cnf(c_0_4758,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3247]) ).
cnf(c_0_4759,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3242]) ).
cnf(c_0_4760,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3248]) ).
cnf(c_0_4761,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3100]) ).
cnf(c_0_4762,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)],[c_0_3249]) ).
cnf(c_0_4763,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)),
inference(split_conjunct,[status(thm)],[c_0_3250]) ).
cnf(c_0_4764,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3251]) ).
cnf(c_0_4765,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[c_0_3252]) ).
cnf(c_0_4766,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[c_0_3253]) ).
cnf(c_0_4767,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),
inference(split_conjunct,[status(thm)],[c_0_3254]) ).
cnf(c_0_4768,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(esk10_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3133]) ).
cnf(c_0_4769,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3255]) ).
cnf(c_0_4770,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,X3,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3256]) ).
cnf(c_0_4771,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3257]) ).
cnf(c_0_4772,plain,
( c_Polynomial_OpCons(X1,X2,X3) = c_Polynomial_OpCons(X1,X4,X5)
| ~ class_Groups_Ozero(X1)
| X3 != X5
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_3112]) ).
cnf(c_0_4773,plain,
( ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3258]) ).
cnf(c_0_4774,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3258]) ).
cnf(c_0_4775,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| X2 = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3259]) ).
cnf(c_0_4776,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3260]) ).
cnf(c_0_4777,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3261]) ).
cnf(c_0_4778,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3195]) ).
cnf(c_0_4779,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3262]) ).
cnf(c_0_4780,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3102]) ).
cnf(c_0_4781,plain,
( c_Polynomial_Omonom(X1,X2,X3) = c_Polynomial_Omonom(X1,X4,X3)
| ~ class_Groups_Ozero(X1)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_3111]) ).
cnf(c_0_4782,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X4,X3)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_3116]) ).
cnf(c_0_4783,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_3117]) ).
cnf(c_0_4784,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3263]) ).
cnf(c_0_4785,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3264]) ).
cnf(c_0_4786,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3180]) ).
cnf(c_0_4787,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3265]) ).
cnf(c_0_4788,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3127]) ).
cnf(c_0_4789,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3266]) ).
cnf(c_0_4790,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3267]) ).
cnf(c_0_4791,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,X3)
| hAPP(X3,esk16_1(X3)) != hAPP(X3,esk17_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3268]) ).
cnf(c_0_4792,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3269]) ).
cnf(c_0_4793,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
inference(split_conjunct,[status(thm)],[c_0_3270]) ).
cnf(c_0_4794,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3119]) ).
cnf(c_0_4795,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3120]) ).
cnf(c_0_4796,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3271]) ).
cnf(c_0_4797,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3272]) ).
cnf(c_0_4798,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3273]) ).
cnf(c_0_4799,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3274]) ).
cnf(c_0_4800,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3275]) ).
cnf(c_0_4801,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3204]) ).
cnf(c_0_4802,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3276]) ).
cnf(c_0_4803,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3100]) ).
cnf(c_0_4804,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3277]) ).
cnf(c_0_4805,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3278]) ).
cnf(c_0_4806,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3279]) ).
cnf(c_0_4807,plain,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4,X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3268]) ).
cnf(c_0_4808,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3280]) ).
cnf(c_0_4809,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3262]) ).
cnf(c_0_4810,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3130]) ).
cnf(c_0_4811,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3131]) ).
cnf(c_0_4812,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3281]) ).
cnf(c_0_4813,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(split_conjunct,[status(thm)],[c_0_3282]) ).
cnf(c_0_4814,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(split_conjunct,[status(thm)],[c_0_3283]) ).
cnf(c_0_4815,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
inference(split_conjunct,[status(thm)],[c_0_3284]) ).
cnf(c_0_4816,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
inference(split_conjunct,[status(thm)],[c_0_3285]) ).
cnf(c_0_4817,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3286]) ).
cnf(c_0_4818,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)],[c_0_3287]) ).
cnf(c_0_4819,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)],[c_0_3288]) ).
cnf(c_0_4820,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[c_0_3289]) ).
cnf(c_0_4821,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3290]) ).
cnf(c_0_4822,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3291]) ).
cnf(c_0_4823,plain,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3292]) ).
cnf(c_0_4824,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3153]) ).
cnf(c_0_4825,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3154]) ).
cnf(c_0_4826,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X2 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3293]) ).
cnf(c_0_4827,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_3294]) ).
cnf(c_0_4828,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_3295]) ).
cnf(c_0_4829,plain,
( 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)],[c_0_3129]) ).
cnf(c_0_4830,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3296]) ).
cnf(c_0_4831,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3290]) ).
cnf(c_0_4832,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3290]) ).
cnf(c_0_4833,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3291]) ).
cnf(c_0_4834,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3291]) ).
cnf(c_0_4835,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[c_0_3297]) ).
cnf(c_0_4836,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3298]) ).
cnf(c_0_4837,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3299]) ).
cnf(c_0_4838,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3300]) ).
cnf(c_0_4839,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3301]) ).
cnf(c_0_4840,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3302]) ).
cnf(c_0_4841,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3303]) ).
cnf(c_0_4842,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3304]) ).
cnf(c_0_4843,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_3305]) ).
cnf(c_0_4844,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_3306]) ).
cnf(c_0_4845,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3307]) ).
cnf(c_0_4846,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3308]) ).
cnf(c_0_4847,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_3309]) ).
cnf(c_0_4848,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3290]) ).
cnf(c_0_4849,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3291]) ).
cnf(c_0_4850,plain,
( X2 = X3
| ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3310]) ).
cnf(c_0_4851,plain,
( X2 = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3311]) ).
cnf(c_0_4852,plain,
( X1 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3312]) ).
cnf(c_0_4853,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3313]) ).
cnf(c_0_4854,plain,
( X1 = 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)],[c_0_3314]) ).
cnf(c_0_4855,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != c_Groups_Oplus__class_Oplus(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3315]) ).
cnf(c_0_4856,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3189]) ).
cnf(c_0_4857,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3190]) ).
cnf(c_0_4858,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3316]) ).
cnf(c_0_4859,plain,
( c_Polynomial_OpCons(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3262]) ).
cnf(c_0_4860,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3317]) ).
cnf(c_0_4861,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3186]) ).
cnf(c_0_4862,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)],[c_0_3187]) ).
cnf(c_0_4863,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)],[c_0_3188]) ).
cnf(c_0_4864,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3229]) ).
cnf(c_0_4865,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3258]) ).
cnf(c_0_4866,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3259]) ).
cnf(c_0_4867,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3193]) ).
cnf(c_0_4868,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3318]) ).
cnf(c_0_4869,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3319]) ).
cnf(c_0_4870,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3320]) ).
cnf(c_0_4871,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3127]) ).
cnf(c_0_4872,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3266]) ).
cnf(c_0_4873,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3266]) ).
cnf(c_0_4874,plain,
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = 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)],[c_0_3321]) ).
cnf(c_0_4875,plain,
( 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)],[c_0_3322]) ).
cnf(c_0_4876,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3323]) ).
cnf(c_0_4877,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3186]) ).
cnf(c_0_4878,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)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3187]) ).
cnf(c_0_4879,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)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3188]) ).
cnf(c_0_4880,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3324]) ).
cnf(c_0_4881,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3217]) ).
cnf(c_0_4882,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)],[c_0_3325]) ).
cnf(c_0_4883,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3326]) ).
cnf(c_0_4884,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_3327]) ).
cnf(c_0_4885,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3328]) ).
cnf(c_0_4886,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3329]) ).
cnf(c_0_4887,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3330]) ).
cnf(c_0_4888,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3331]) ).
cnf(c_0_4889,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3332]) ).
cnf(c_0_4890,plain,
( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3332]) ).
cnf(c_0_4891,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)],[c_0_3333]) ).
cnf(c_0_4892,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)],[c_0_3334]) ).
cnf(c_0_4893,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_3335]) ).
cnf(c_0_4894,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3336]) ).
cnf(c_0_4895,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3337]) ).
cnf(c_0_4896,plain,
( c_Groups_Oplus__class_Oplus(X1,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)],[c_0_3338]) ).
cnf(c_0_4897,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3339]) ).
cnf(c_0_4898,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3339]) ).
cnf(c_0_4899,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3340]) ).
cnf(c_0_4900,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)],[c_0_3341]) ).
cnf(c_0_4901,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)],[c_0_3342]) ).
cnf(c_0_4902,plain,
( 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)],[c_0_3343]) ).
cnf(c_0_4903,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),esk15_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3344]) ).
cnf(c_0_4904,plain,
( c_Polynomial_Osmult(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3256]) ).
cnf(c_0_4905,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3345]) ).
cnf(c_0_4906,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3277]) ).
cnf(c_0_4907,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3279]) ).
cnf(c_0_4908,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk34_2(X2,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2646]) ).
cnf(c_0_4909,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_2(X2,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2647]) ).
cnf(c_0_4910,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3346]) ).
cnf(c_0_4911,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3347]) ).
cnf(c_0_4912,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3348]) ).
cnf(c_0_4913,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3349]) ).
cnf(c_0_4914,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_3350]) ).
cnf(c_0_4915,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_3351]) ).
cnf(c_0_4916,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_3352]) ).
cnf(c_0_4917,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)],[c_0_3353]) ).
cnf(c_0_4918,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)],[c_0_3354]) ).
cnf(c_0_4919,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3238]) ).
cnf(c_0_4920,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3239]) ).
cnf(c_0_4921,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3242]) ).
cnf(c_0_4922,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3294]) ).
cnf(c_0_4923,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3294]) ).
cnf(c_0_4924,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3355]) ).
cnf(c_0_4925,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3356]) ).
cnf(c_0_4926,plain,
( 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)],[c_0_3357]) ).
cnf(c_0_4927,plain,
( 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)],[c_0_3358]) ).
cnf(c_0_4928,plain,
( 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)],[c_0_3359]) ).
cnf(c_0_4929,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3360]) ).
cnf(c_0_4930,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3348]) ).
cnf(c_0_4931,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),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3361]) ).
cnf(c_0_4932,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_3362]) ).
cnf(c_0_4933,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_3363]) ).
cnf(c_0_4934,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3257]) ).
cnf(c_0_4935,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3364]) ).
cnf(c_0_4936,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3365]) ).
cnf(c_0_4937,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)],[c_0_3366]) ).
cnf(c_0_4938,plain,
( X2 = 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)],[c_0_3366]) ).
cnf(c_0_4939,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)],[c_0_3367]) ).
cnf(c_0_4940,plain,
( X2 = 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)],[c_0_3367]) ).
cnf(c_0_4941,plain,
( c_Polynomial_Omonom(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3280]) ).
cnf(c_0_4942,plain,
( c_Polynomial_Osmult(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3256]) ).
cnf(c_0_4943,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3332]) ).
cnf(c_0_4944,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3290]) ).
cnf(c_0_4945,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X2 != 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)],[c_0_3290]) ).
cnf(c_0_4946,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3291]) ).
cnf(c_0_4947,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != 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)],[c_0_3291]) ).
cnf(c_0_4948,plain,
( c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3316]) ).
cnf(c_0_4949,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3289]) ).
cnf(c_0_4950,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3368]) ).
cnf(c_0_4951,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)],[c_0_3369]) ).
cnf(c_0_4952,plain,
( 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)],[c_0_3370]) ).
cnf(c_0_4953,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)],[c_0_3371]) ).
cnf(c_0_4954,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_3372]) ).
cnf(c_0_4955,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3312]) ).
cnf(c_0_4956,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)],[c_0_3373]) ).
cnf(c_0_4957,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)],[c_0_3374]) ).
cnf(c_0_4958,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)],[c_0_3375]) ).
cnf(c_0_4959,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)],[c_0_3376]) ).
cnf(c_0_4960,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)],[c_0_3377]) ).
cnf(c_0_4961,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3378]) ).
cnf(c_0_4962,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3307]) ).
cnf(c_0_4963,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3308]) ).
cnf(c_0_4964,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)],[c_0_3379]) ).
cnf(c_0_4965,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)],[c_0_3380]) ).
cnf(c_0_4966,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)],[c_0_3381]) ).
cnf(c_0_4967,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)],[c_0_3382]) ).
cnf(c_0_4968,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)],[c_0_3383]) ).
cnf(c_0_4969,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)],[c_0_3384]) ).
cnf(c_0_4970,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3259]) ).
cnf(c_0_4971,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3301]) ).
cnf(c_0_4972,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3301]) ).
cnf(c_0_4973,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_2956]) ).
cnf(c_0_4974,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,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)],[c_0_3297]) ).
cnf(c_0_4975,plain,
( X2 = c_Groups_Oplus__class_Oplus(X1,X2,X3)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3315]) ).
cnf(c_0_4976,plain,
( c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3192]) ).
cnf(c_0_4977,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2549]) ).
cnf(c_0_4978,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)],[c_0_3385]) ).
cnf(c_0_4979,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)],[c_0_3386]) ).
cnf(c_0_4980,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)],[c_0_3387]) ).
cnf(c_0_4981,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)],[c_0_3388]) ).
cnf(c_0_4982,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2746]) ).
cnf(c_0_4983,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3310]) ).
cnf(c_0_4984,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3311]) ).
cnf(c_0_4985,plain,
( hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3129]) ).
cnf(c_0_4986,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[c_0_3389]) ).
cnf(c_0_4987,plain,
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3390]) ).
cnf(c_0_4988,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3391]) ).
cnf(c_0_4989,plain,
( 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)],[c_0_3392]) ).
cnf(c_0_4990,plain,
( 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)],[c_0_3393]) ).
cnf(c_0_4991,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3394]) ).
cnf(c_0_4992,plain,
( 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)],[c_0_3395]) ).
cnf(c_0_4993,plain,
( 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)],[c_0_3396]) ).
cnf(c_0_4994,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3397]) ).
cnf(c_0_4995,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3398]) ).
cnf(c_0_4996,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3399]) ).
cnf(c_0_4997,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3175]) ).
cnf(c_0_4998,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3339]) ).
cnf(c_0_4999,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)],[c_0_3400]) ).
cnf(c_0_5000,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)],[c_0_3401]) ).
cnf(c_0_5001,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)],[c_0_3402]) ).
cnf(c_0_5002,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)],[c_0_3403]) ).
cnf(c_0_5003,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)],[c_0_3404]) ).
cnf(c_0_5004,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3323]) ).
cnf(c_0_5005,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3405]) ).
cnf(c_0_5006,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3194]) ).
cnf(c_0_5007,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3106]) ).
cnf(c_0_5008,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3106]) ).
cnf(c_0_5009,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3406]) ).
cnf(c_0_5010,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(split_conjunct,[status(thm)],[c_0_3407]) ).
cnf(c_0_5011,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3133]) ).
cnf(c_0_5012,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3314]) ).
cnf(c_0_5013,plain,
( X1 = X2
| X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 = c_Groups_Ozero__class_Ozero(X3)
| c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| ~ class_Rings_Odivision__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3408]) ).
cnf(c_0_5014,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)],[c_0_3409]) ).
cnf(c_0_5015,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)],[c_0_3410]) ).
cnf(c_0_5016,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3411]) ).
cnf(c_0_5017,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3203]) ).
cnf(c_0_5018,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[c_0_3412]) ).
cnf(c_0_5019,plain,
( 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)],[c_0_3330]) ).
cnf(c_0_5020,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3331]) ).
cnf(c_0_5021,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3413]) ).
cnf(c_0_5022,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3414]) ).
cnf(c_0_5023,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3415]) ).
cnf(c_0_5024,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3416]) ).
cnf(c_0_5025,plain,
( X2 = X3
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3417]) ).
cnf(c_0_5026,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3366]) ).
cnf(c_0_5027,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3367]) ).
cnf(c_0_5028,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_3418]) ).
cnf(c_0_5029,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[c_0_3419]) ).
cnf(c_0_5030,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)],[c_0_3420]) ).
cnf(c_0_5031,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)],[c_0_3325]) ).
cnf(c_0_5032,plain,
( 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)],[c_0_2798]) ).
cnf(c_0_5033,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[c_0_3421]) ).
cnf(c_0_5034,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[c_0_3422]) ).
cnf(c_0_5035,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)],[c_0_3423]) ).
cnf(c_0_5036,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[c_0_3424]) ).
cnf(c_0_5037,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = 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)],[c_0_3323]) ).
cnf(c_0_5038,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)],[c_0_3425]) ).
cnf(c_0_5039,plain,
( ~ c_Polynomial_Opos__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3426]) ).
cnf(c_0_5040,plain,
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)],[c_0_3427]) ).
cnf(c_0_5041,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_3428]) ).
cnf(c_0_5042,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3429]) ).
cnf(c_0_5043,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[c_0_3430]) ).
cnf(c_0_5044,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3431]) ).
cnf(c_0_5045,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_3432]) ).
cnf(c_0_5046,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3433]) ).
cnf(c_0_5047,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3434]) ).
cnf(c_0_5048,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3092]) ).
cnf(c_0_5049,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3146]) ).
cnf(c_0_5050,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3146]) ).
cnf(c_0_5051,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3435]) ).
cnf(c_0_5052,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3237]) ).
cnf(c_0_5053,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3240]) ).
cnf(c_0_5054,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3246]) ).
cnf(c_0_5055,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[c_0_3436]) ).
cnf(c_0_5056,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_3437]) ).
cnf(c_0_5057,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[c_0_3438]) ).
cnf(c_0_5058,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[c_0_3439]) ).
cnf(c_0_5059,plain,
( 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)],[c_0_3440]) ).
cnf(c_0_5060,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3441]) ).
cnf(c_0_5061,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3442]) ).
cnf(c_0_5062,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk24_0),
inference(split_conjunct,[status(thm)],[c_0_2844]) ).
cnf(c_0_5063,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk19_0),
inference(split_conjunct,[status(thm)],[c_0_2845]) ).
cnf(c_0_5064,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)],[c_0_3443]) ).
cnf(c_0_5065,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(split_conjunct,[status(thm)],[c_0_3444]) ).
cnf(c_0_5066,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2784]) ).
cnf(c_0_5067,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)],[c_0_2602]) ).
cnf(c_0_5068,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)],[c_0_3361]) ).
cnf(c_0_5069,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3361]) ).
cnf(c_0_5070,plain,
( X2 = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3445]) ).
cnf(c_0_5071,plain,
( X2 = X3
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Rings_Oinverse__class_Oinverse(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3446]) ).
cnf(c_0_5072,plain,
( X1 = X2
| c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3447]) ).
cnf(c_0_5073,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3448]) ).
cnf(c_0_5074,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_3449]) ).
cnf(c_0_5075,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_3450]) ).
cnf(c_0_5076,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_3451]) ).
cnf(c_0_5077,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_3452]) ).
cnf(c_0_5078,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)],[c_0_3453]) ).
cnf(c_0_5079,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)],[c_0_3454]) ).
cnf(c_0_5080,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_3455]) ).
cnf(c_0_5081,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)],[c_0_3456]) ).
cnf(c_0_5082,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)],[c_0_3457]) ).
cnf(c_0_5083,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)],[c_0_3458]) ).
cnf(c_0_5084,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3459]) ).
cnf(c_0_5085,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3460]) ).
cnf(c_0_5086,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3461]) ).
cnf(c_0_5087,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3461]) ).
cnf(c_0_5088,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X3) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3462]) ).
cnf(c_0_5089,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X3) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3462]) ).
cnf(c_0_5090,plain,
( c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,X3)
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3417]) ).
cnf(c_0_5091,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3463]) ).
cnf(c_0_5092,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3463]) ).
cnf(c_0_5093,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3464]) ).
cnf(c_0_5094,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3465]) ).
cnf(c_0_5095,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3466]) ).
cnf(c_0_5096,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3467]) ).
cnf(c_0_5097,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3468]) ).
cnf(c_0_5098,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Oinverse(X2,X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3469]) ).
cnf(c_0_5099,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3445]) ).
cnf(c_0_5100,plain,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Oinverse(X1,X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3446]) ).
cnf(c_0_5101,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3470]) ).
cnf(c_0_5102,plain,
( class_Orderings_Oord(tc_fun(X1,X2))
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3471]) ).
cnf(c_0_5103,plain,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3472]) ).
cnf(c_0_5104,plain,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3473]) ).
cnf(c_0_5105,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3474]) ).
cnf(c_0_5106,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3475]) ).
cnf(c_0_5107,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3476]) ).
cnf(c_0_5108,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3464]) ).
cnf(c_0_5109,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3465]) ).
cnf(c_0_5110,plain,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3466]) ).
cnf(c_0_5111,plain,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3467]) ).
cnf(c_0_5112,plain,
( c_RealVector_Onorm__class_Onorm(X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3470]) ).
cnf(c_0_5113,plain,
( 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)],[c_0_3477]) ).
cnf(c_0_5114,plain,
( 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)],[c_0_3478]) ).
cnf(c_0_5115,plain,
( 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)],[c_0_3479]) ).
cnf(c_0_5116,plain,
( 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)],[c_0_3480]) ).
cnf(c_0_5117,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3475]) ).
cnf(c_0_5118,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3476]) ).
cnf(c_0_5119,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3481]) ).
cnf(c_0_5120,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3482]) ).
cnf(c_0_5121,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk32_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(split_conjunct,[status(thm)],[c_0_3155]) ).
cnf(c_0_5122,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk14_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(split_conjunct,[status(thm)],[c_0_3156]) ).
cnf(c_0_5123,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(split_conjunct,[status(thm)],[c_0_3483]) ).
cnf(c_0_5124,plain,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
inference(split_conjunct,[status(thm)],[c_0_3484]) ).
cnf(c_0_5125,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Oone(X1)
| c_Groups_Oone__class_Oone(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3485]) ).
cnf(c_0_5126,plain,
( c_Groups_Oone__class_Oone(X1) = X2
| ~ class_Groups_Oone(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3485]) ).
cnf(c_0_5127,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3486]) ).
cnf(c_0_5128,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| ~ class_Groups_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3486]) ).
cnf(c_0_5129,plain,
( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3487]) ).
cnf(c_0_5130,plain,
( c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3488]) ).
cnf(c_0_5131,plain,
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)],[c_0_3489]) ).
cnf(c_0_5132,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3490]) ).
cnf(c_0_5133,plain,
( class_Rings_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3491]) ).
cnf(c_0_5134,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3492]) ).
cnf(c_0_5135,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3493]) ).
cnf(c_0_5136,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3494]) ).
cnf(c_0_5137,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3495]) ).
cnf(c_0_5138,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3496]) ).
cnf(c_0_5139,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3497]) ).
cnf(c_0_5140,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3498]) ).
cnf(c_0_5141,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3499]) ).
cnf(c_0_5142,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3500]) ).
cnf(c_0_5143,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3501]) ).
cnf(c_0_5144,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3502]) ).
cnf(c_0_5145,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3503]) ).
cnf(c_0_5146,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3504]) ).
cnf(c_0_5147,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3505]) ).
cnf(c_0_5148,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3506]) ).
cnf(c_0_5149,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3507]) ).
cnf(c_0_5150,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3508]) ).
cnf(c_0_5151,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3509]) ).
cnf(c_0_5152,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3510]) ).
cnf(c_0_5153,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3511]) ).
cnf(c_0_5154,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3512]) ).
cnf(c_0_5155,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3513]) ).
cnf(c_0_5156,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3514]) ).
cnf(c_0_5157,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3515]) ).
cnf(c_0_5158,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3516]) ).
cnf(c_0_5159,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3517]) ).
cnf(c_0_5160,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3518]) ).
cnf(c_0_5161,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3519]) ).
cnf(c_0_5162,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3520]) ).
cnf(c_0_5163,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3521]) ).
cnf(c_0_5164,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3522]) ).
cnf(c_0_5165,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3523]) ).
cnf(c_0_5166,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3524]) ).
cnf(c_0_5167,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3525]) ).
cnf(c_0_5168,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3526]) ).
cnf(c_0_5169,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3527]) ).
cnf(c_0_5170,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3528]) ).
cnf(c_0_5171,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3529]) ).
cnf(c_0_5172,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3530]) ).
cnf(c_0_5173,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3531]) ).
cnf(c_0_5174,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3532]) ).
cnf(c_0_5175,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3533]) ).
cnf(c_0_5176,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3534]) ).
cnf(c_0_5177,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3535]) ).
cnf(c_0_5178,plain,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3536]) ).
cnf(c_0_5179,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3537]) ).
cnf(c_0_5180,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3538]) ).
cnf(c_0_5181,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3539]) ).
cnf(c_0_5182,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3540]) ).
cnf(c_0_5183,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3541]) ).
cnf(c_0_5184,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3542]) ).
cnf(c_0_5185,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3543]) ).
cnf(c_0_5186,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3544]) ).
cnf(c_0_5187,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3545]) ).
cnf(c_0_5188,plain,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3546]) ).
cnf(c_0_5189,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3547]) ).
cnf(c_0_5190,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3548]) ).
cnf(c_0_5191,plain,
( c_Nat_OSuc(X1) = c_Nat_OSuc(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3548]) ).
cnf(c_0_5192,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_3549]) ).
cnf(c_0_5193,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_3550]) ).
cnf(c_0_5194,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3551]) ).
cnf(c_0_5195,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3552]) ).
cnf(c_0_5196,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_3553]) ).
cnf(c_0_5197,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3554]) ).
cnf(c_0_5198,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_3555]) ).
cnf(c_0_5199,plain,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3556]) ).
cnf(c_0_5200,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3557]) ).
cnf(c_0_5201,plain,
c_Nat_OSuc(X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_3558]) ).
cnf(c_0_5202,plain,
X1 != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_3559]) ).
cnf(c_0_5203,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3560]) ).
cnf(c_0_5204,plain,
esk26_0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2514]) ).
cnf(c_0_5205,plain,
esk25_0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_2514]) ).
cnf(c_0_5206,plain,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3561]) ).
cnf(c_0_5207,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3562]) ).
cnf(c_0_5208,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3563]) ).
cnf(c_0_5209,plain,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3564]) ).
cnf(c_0_5210,plain,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3565]) ).
cnf(c_0_5211,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3566]) ).
cnf(c_0_5212,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3567]) ).
cnf(c_0_5213,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3568]) ).
cnf(c_0_5214,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3569]) ).
cnf(c_0_5215,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3570]) ).
cnf(c_0_5216,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3571]) ).
cnf(c_0_5217,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3572]) ).
cnf(c_0_5218,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3573]) ).
cnf(c_0_5219,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3574]) ).
cnf(c_0_5220,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3575]) ).
cnf(c_0_5221,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3576]) ).
cnf(c_0_5222,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3577]) ).
cnf(c_0_5223,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3578]) ).
cnf(c_0_5224,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3579]) ).
cnf(c_0_5225,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3580]) ).
cnf(c_0_5226,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3581]) ).
cnf(c_0_5227,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3582]) ).
cnf(c_0_5228,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3583]) ).
cnf(c_0_5229,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3584]) ).
cnf(c_0_5230,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3585]) ).
cnf(c_0_5231,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3586]) ).
cnf(c_0_5232,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3587]) ).
cnf(c_0_5233,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3588]) ).
cnf(c_0_5234,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3589]) ).
cnf(c_0_5235,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3590]) ).
cnf(c_0_5236,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3591]) ).
cnf(c_0_5237,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3592]) ).
cnf(c_0_5238,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3593]) ).
cnf(c_0_5239,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3594]) ).
cnf(c_0_5240,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3595]) ).
cnf(c_0_5241,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3596]) ).
cnf(c_0_5242,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3597]) ).
cnf(c_0_5243,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3598]) ).
cnf(c_0_5244,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3599]) ).
cnf(c_0_5245,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3600]) ).
cnf(c_0_5246,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3601]) ).
cnf(c_0_5247,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3602]) ).
cnf(c_0_5248,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3603]) ).
cnf(c_0_5249,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3604]) ).
cnf(c_0_5250,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3605]) ).
cnf(c_0_5251,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3606]) ).
cnf(c_0_5252,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3607]) ).
cnf(c_0_5253,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3608]) ).
cnf(c_0_5254,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3609]) ).
cnf(c_0_5255,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3610]) ).
cnf(c_0_5256,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3611]) ).
cnf(c_0_5257,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3612]) ).
cnf(c_0_5258,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3613]) ).
cnf(c_0_5259,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3614]) ).
cnf(c_0_5260,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3615]) ).
cnf(c_0_5261,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3616]) ).
cnf(c_0_5262,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3617]) ).
cnf(c_0_5263,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3618]) ).
cnf(c_0_5264,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3619]) ).
cnf(c_0_5265,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3620]) ).
cnf(c_0_5266,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3621]) ).
cnf(c_0_5267,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3622]) ).
cnf(c_0_5268,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3623]) ).
cnf(c_0_5269,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3624]) ).
cnf(c_0_5270,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3625]) ).
cnf(c_0_5271,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3626]) ).
cnf(c_0_5272,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3627]) ).
cnf(c_0_5273,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3628]) ).
cnf(c_0_5274,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3629]) ).
cnf(c_0_5275,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3630]) ).
cnf(c_0_5276,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3631]) ).
cnf(c_0_5277,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3632]) ).
cnf(c_0_5278,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3633]) ).
cnf(c_0_5279,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3634]) ).
cnf(c_0_5280,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3635]) ).
cnf(c_0_5281,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3636]) ).
cnf(c_0_5282,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3637]) ).
cnf(c_0_5283,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3638]) ).
cnf(c_0_5284,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3639]) ).
cnf(c_0_5285,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3640]) ).
cnf(c_0_5286,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3641]) ).
cnf(c_0_5287,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3642]) ).
cnf(c_0_5288,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3643]) ).
cnf(c_0_5289,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3644]) ).
cnf(c_0_5290,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3645]) ).
cnf(c_0_5291,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3646]) ).
cnf(c_0_5292,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3647]) ).
cnf(c_0_5293,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3648]) ).
cnf(c_0_5294,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3649]) ).
cnf(c_0_5295,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3650]) ).
cnf(c_0_5296,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3651]) ).
cnf(c_0_5297,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3652]) ).
cnf(c_0_5298,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3653]) ).
cnf(c_0_5299,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3654]) ).
cnf(c_0_5300,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3655]) ).
cnf(c_0_5301,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3656]) ).
cnf(c_0_5302,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3657]) ).
cnf(c_0_5303,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3658]) ).
cnf(c_0_5304,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3659]) ).
cnf(c_0_5305,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3660]) ).
cnf(c_0_5306,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3661]) ).
cnf(c_0_5307,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3662]) ).
cnf(c_0_5308,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3663]) ).
cnf(c_0_5309,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3664]) ).
cnf(c_0_5310,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3665]) ).
cnf(c_0_5311,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3666]) ).
cnf(c_0_5312,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3667]) ).
cnf(c_0_5313,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3668]) ).
cnf(c_0_5314,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[c_0_3669]) ).
cnf(c_0_5315,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[c_0_3670]) ).
cnf(c_0_5316,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[c_0_3671]) ).
cnf(c_0_5317,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3672]) ).
cnf(c_0_5318,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3673]) ).
cnf(c_0_5319,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3674]) ).
cnf(c_0_5320,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3675]) ).
cnf(c_0_5321,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3676]) ).
cnf(c_0_5322,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3677]) ).
cnf(c_0_5323,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3678]) ).
cnf(c_0_5324,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3679]) ).
cnf(c_0_5325,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3680]) ).
cnf(c_0_5326,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3681]) ).
cnf(c_0_5327,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3682]) ).
cnf(c_0_5328,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3683]) ).
cnf(c_0_5329,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3684]) ).
cnf(c_0_5330,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3685]) ).
cnf(c_0_5331,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3686]) ).
cnf(c_0_5332,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3687]) ).
cnf(c_0_5333,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3688]) ).
cnf(c_0_5334,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3689]) ).
cnf(c_0_5335,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3690]) ).
cnf(c_0_5336,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3691]) ).
cnf(c_0_5337,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3692]) ).
cnf(c_0_5338,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3693]) ).
cnf(c_0_5339,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3694]) ).
cnf(c_0_5340,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3695]) ).
cnf(c_0_5341,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3696]) ).
cnf(c_0_5342,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3697]) ).
cnf(c_0_5343,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3698]) ).
cnf(c_0_5344,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3699]) ).
cnf(c_0_5345,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3700]) ).
cnf(c_0_5346,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3701]) ).
cnf(c_0_5347,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3702]) ).
cnf(c_0_5348,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3703]) ).
cnf(c_0_5349,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3704]) ).
cnf(c_0_5350,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3705]) ).
cnf(c_0_5351,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3706]) ).
cnf(c_0_5352,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3707]) ).
cnf(c_0_5353,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3708]) ).
cnf(c_0_5354,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3709]) ).
cnf(c_0_5355,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3710]) ).
cnf(c_0_5356,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3711]) ).
cnf(c_0_5357,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3712]) ).
cnf(c_0_5358,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3713]) ).
cnf(c_0_5359,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3714]) ).
cnf(c_0_5360,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3715]) ).
cnf(c_0_5361,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3716]) ).
cnf(c_0_5362,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3717]) ).
cnf(c_0_5363,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3718]) ).
cnf(c_0_5364,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3719]) ).
cnf(c_0_5365,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3720]) ).
cnf(c_0_5366,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3721]) ).
cnf(c_0_5367,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3722]) ).
cnf(c_0_5368,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3723]) ).
cnf(c_0_5369,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3724]) ).
cnf(c_0_5370,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3725]) ).
cnf(c_0_5371,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3726]) ).
cnf(c_0_5372,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3727]) ).
cnf(c_0_5373,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3728]) ).
cnf(c_0_5374,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3729]) ).
cnf(c_0_5375,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3730]) ).
cnf(c_0_5376,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3731]) ).
cnf(c_0_5377,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3732]) ).
cnf(c_0_5378,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3733]) ).
cnf(c_0_5379,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3734]) ).
cnf(c_0_5380,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3735]) ).
cnf(c_0_5381,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3736]) ).
cnf(c_0_5382,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3737]) ).
cnf(c_0_5383,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3738]) ).
cnf(c_0_5384,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3739]) ).
cnf(c_0_5385,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3740]) ).
cnf(c_0_5386,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3741]) ).
cnf(c_0_5387,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3742]) ).
cnf(c_0_5388,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3743]) ).
cnf(c_0_5389,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3744]) ).
cnf(c_0_5390,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3745]) ).
cnf(c_0_5391,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3746]) ).
cnf(c_0_5392,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3747]) ).
cnf(c_0_5393,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3748]) ).
cnf(c_0_5394,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3749]) ).
cnf(c_0_5395,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3750]) ).
cnf(c_0_5396,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3751]) ).
cnf(c_0_5397,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3752]) ).
cnf(c_0_5398,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3753]) ).
cnf(c_0_5399,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3754]) ).
cnf(c_0_5400,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3755]) ).
cnf(c_0_5401,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3756]) ).
cnf(c_0_5402,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3757]) ).
cnf(c_0_5403,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3758]) ).
cnf(c_0_5404,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3759]) ).
cnf(c_0_5405,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3760]) ).
cnf(c_0_5406,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3761]) ).
cnf(c_0_5407,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3762]) ).
cnf(c_0_5408,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3763]) ).
cnf(c_0_5409,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3764]) ).
cnf(c_0_5410,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3765]) ).
cnf(c_0_5411,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3766]) ).
cnf(c_0_5412,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3767]) ).
cnf(c_0_5413,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| ~ class_Orderings_Oord(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,hAPP(X3,X5),hAPP(X3,esk31_4(X3,X5,X1,X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
c_0_3768,
[final] ).
cnf(c_0_5414,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
c_0_3769,
[final] ).
cnf(c_0_5415,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
c_0_3770,
[final] ).
cnf(c_0_5416,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),esk25_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk26_0,esk27_0)),X1))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1),
c_0_3771,
[final] ).
cnf(c_0_5417,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X1))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1),
c_0_3772,
[final] ).
cnf(c_0_5418,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X2,X3))),X3)
| ~ class_Rings_Oidom(X1) ),
c_0_3773,
[final] ).
cnf(c_0_5419,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X3,X2))),X2) ),
c_0_3774,
[final] ).
cnf(c_0_5420,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk18_0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) ),
c_0_3775,
[final] ).
cnf(c_0_5421,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
c_0_3776,
[final] ).
cnf(c_0_5422,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1),
c_0_3777,
[final] ).
cnf(c_0_5423,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,esk28_4(X4,X3,X2,X1)),hAPP(X4,esk28_4(X4,X3,X2,X1))) ),
c_0_3778,
[final] ).
cnf(c_0_5424,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
c_0_3779,
[final] ).
cnf(c_0_5425,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),c_Groups_Ominus__class_Ominus(X1,X3,X5))) = 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))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3780,
[final] ).
cnf(c_0_5426,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk22_0) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk21_0),
c_0_3781,
[final] ).
cnf(c_0_5427,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),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)),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) ),
c_0_3782,
[final] ).
cnf(c_0_5428,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6) ),
c_0_3783,
[final] ).
cnf(c_0_5429,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)) ),
c_0_3784,
[final] ).
cnf(c_0_5430,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)) ),
c_0_3785,
[final] ).
cnf(c_0_5431,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6) ),
c_0_3786,
[final] ).
cnf(c_0_5432,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5) ),
c_0_3787,
[final] ).
cnf(c_0_5433,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5)) ),
c_0_3788,
[final] ).
cnf(c_0_5434,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5) ),
c_0_3789,
[final] ).
cnf(c_0_5435,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5)) ),
c_0_3790,
[final] ).
cnf(c_0_5436,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
c_0_3791,
[final] ).
cnf(c_0_5437,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Oorder(X1,X3,X2)),X2)
| ~ class_Rings_Oidom(X1) ),
c_0_3792,
[final] ).
cnf(c_0_5438,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),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) ),
c_0_3793,
[final] ).
cnf(c_0_5439,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)) ),
c_0_3794,
[final] ).
cnf(c_0_5440,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6)) ),
c_0_3795,
[final] ).
cnf(c_0_5441,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6)) ),
c_0_3796,
[final] ).
cnf(c_0_5442,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)) ),
c_0_3797,
[final] ).
cnf(c_0_5443,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) ),
c_0_3798,
[final] ).
cnf(c_0_5444,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)) ),
c_0_3799,
[final] ).
cnf(c_0_5445,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) ),
c_0_3800,
[final] ).
cnf(c_0_5446,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)) ),
c_0_3801,
[final] ).
cnf(c_0_5447,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk4_2(X2,X1)),X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_3802,
[final] ).
cnf(c_0_5448,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3803,
[final] ).
cnf(c_0_5449,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3))) = c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_3804,
[final] ).
cnf(c_0_5450,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
c_0_3805,
[final] ).
cnf(c_0_5451,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
c_0_3806,
[final] ).
cnf(c_0_5452,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) ),
c_0_3807,
[final] ).
cnf(c_0_5453,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),esk13_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_3808,
[final] ).
cnf(c_0_5454,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
c_0_3809,
[final] ).
cnf(c_0_5455,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
c_0_3810,
[final] ).
cnf(c_0_5456,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
c_0_3811,
[final] ).
cnf(c_0_5457,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6) ),
c_0_3812,
[final] ).
cnf(c_0_5458,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5) ),
c_0_3813,
[final] ).
cnf(c_0_5459,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2)),X4)) ),
c_0_3814,
[final] ).
cnf(c_0_5460,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk35_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3815,
[final] ).
cnf(c_0_5461,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
c_0_3816,
[final] ).
cnf(c_0_5462,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X3)) ),
c_0_3817,
[final] ).
cnf(c_0_5463,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5)) ),
c_0_3818,
[final] ).
cnf(c_0_5464,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4) != X5 ),
c_0_3819,
[final] ).
cnf(c_0_5465,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X4 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5) ),
c_0_3820,
[final] ).
cnf(c_0_5466,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| ~ class_Rings_Oring(X1)
| X4 != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6) ),
c_0_3821,
[final] ).
cnf(c_0_5467,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4) != X6 ),
c_0_3822,
[final] ).
cnf(c_0_5468,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
c_0_3823,
[final] ).
cnf(c_0_5469,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)) = 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))
| ~ class_Rings_Oring(X1) ),
c_0_3824,
[final] ).
cnf(c_0_5470,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
c_0_3825,
[final] ).
cnf(c_0_5471,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
c_0_3826,
[final] ).
cnf(c_0_5472,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4) = X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5) ),
c_0_3827,
[final] ).
cnf(c_0_5473,plain,
( X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5) ),
c_0_3828,
[final] ).
cnf(c_0_5474,plain,
( X2 = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6)
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6) ),
c_0_3829,
[final] ).
cnf(c_0_5475,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5) = X6
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6) ),
c_0_3830,
[final] ).
cnf(c_0_5476,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3),X5)
| ~ class_Rings_Osemiring(X1) ),
c_0_3831,
[final] ).
cnf(c_0_5477,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X5))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X5)) ),
c_0_3832,
[final] ).
cnf(c_0_5478,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
c_0_3833,
[final] ).
cnf(c_0_5479,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| c_Orderings_Oord__class_Oless__eq(X1,X5,esk31_4(X3,X5,X1,X2))
| ~ class_Orderings_Oord(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4) ),
c_0_3834,
[final] ).
cnf(c_0_5480,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X3,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_3835,
[final] ).
cnf(c_0_5481,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Oplus__class_Oplus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_3836,
[final] ).
cnf(c_0_5482,plain,
( c_Orderings_Oord__class_Oless(X1,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)),X6)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
c_0_3837,
[final] ).
cnf(c_0_5483,plain,
( c_Orderings_Oord__class_Oless__eq(X1,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)),X6)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1(X1) ),
c_0_3838,
[final] ).
cnf(c_0_5484,plain,
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),esk30_3(X3,X2,X1))))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
c_0_3839,
[final] ).
cnf(c_0_5485,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X2),X4),
c_0_3840,
[final] ).
cnf(c_0_5486,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3)),X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
c_0_3841,
[final] ).
cnf(c_0_5487,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_3842,
[final] ).
cnf(c_0_5488,plain,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))) ),
c_0_3843,
[final] ).
cnf(c_0_5489,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) ),
c_0_3844,
[final] ).
cnf(c_0_5490,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,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)) ),
c_0_3845,
[final] ).
cnf(c_0_5491,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,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)) ),
c_0_3846,
[final] ).
cnf(c_0_5492,plain,
( ~ c_Orderings_Oord__class_Oless(X1,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))
| ~ class_Rings_Olinordered__ring(X1) ),
c_0_3847,
[final] ).
cnf(c_0_5493,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_3848,
[final] ).
cnf(c_0_5494,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_3849,
[final] ).
cnf(c_0_5495,plain,
( hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2) ),
c_0_3850,
[final] ).
cnf(c_0_5496,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
c_0_3851,
[final] ).
cnf(c_0_5497,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_3852,
[final] ).
cnf(c_0_5498,plain,
( hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X3,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2) ),
c_0_3853,
[final] ).
cnf(c_0_5499,plain,
( X2 = X3
| X4 = X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)) != 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)) ),
c_0_3854,
[final] ).
cnf(c_0_5500,plain,
( X3 = X5
| X2 = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) != 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)) ),
c_0_3855,
[final] ).
cnf(c_0_5501,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
c_0_3856,
[final] ).
cnf(c_0_5502,plain,
hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)) = hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Nat_OSuc(X5)),
c_0_3857,
[final] ).
cnf(c_0_5503,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(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)),X2),c_Polynomial_OpCons(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_3858,
[final] ).
cnf(c_0_5504,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_Rings_Oring__1(X1) ),
c_0_3859,
[final] ).
cnf(c_0_5505,plain,
( c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,esk29_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))) ),
c_0_3860,
[final] ).
cnf(c_0_5506,plain,
( c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
c_0_3861,
[final] ).
cnf(c_0_5507,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3)) ),
c_0_3862,
[final] ).
cnf(c_0_5508,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
c_0_3863,
[final] ).
cnf(c_0_5509,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),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))) = c_Polynomial_Opcompose(X1,c_Polynomial_OpCons(X1,X2,X3),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_3864,
[final] ).
cnf(c_0_5510,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) ),
c_0_3865,
[final] ).
cnf(c_0_5511,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) ),
c_0_3866,
[final] ).
cnf(c_0_5512,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)),
c_0_3867,
[final] ).
cnf(c_0_5513,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2))),
c_0_3868,
[final] ).
cnf(c_0_5514,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_3869,
[final] ).
cnf(c_0_5515,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,esk6_3(X3,X2,X1))) ),
c_0_3870,
[final] ).
cnf(c_0_5516,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,esk5_3(X3,X2,X1))) ),
c_0_3871,
[final] ).
cnf(c_0_5517,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X1,esk6_3(X3,X2,X1))) ),
c_0_3872,
[final] ).
cnf(c_0_5518,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X1,esk5_3(X3,X2,X1))) ),
c_0_3873,
[final] ).
cnf(c_0_5519,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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X5))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_3874,
[final] ).
cnf(c_0_5520,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))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_3875,
[final] ).
cnf(c_0_5521,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_Groups_Oplus__class_Oplus(tc_Int_Oint,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_0_3876,
[final] ).
cnf(c_0_5522,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X5))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3877,
[final] ).
cnf(c_0_5523,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk27_0),esk25_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
c_0_3878,
[final] ).
cnf(c_0_5524,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
c_0_3879,
[final] ).
cnf(c_0_5525,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_3880,
[final] ).
cnf(c_0_5526,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_3881,
[final] ).
cnf(c_0_5527,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
c_0_3882,
[final] ).
cnf(c_0_5528,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
c_0_3883,
[final] ).
cnf(c_0_5529,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),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(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,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_3884,
[final] ).
cnf(c_0_5530,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),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_3885,
[final] ).
cnf(c_0_5531,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),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_3886,
[final] ).
cnf(c_0_5532,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),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_3887,
[final] ).
cnf(c_0_5533,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
c_0_3888,
[final] ).
cnf(c_0_5534,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
c_0_3889,
[final] ).
cnf(c_0_5535,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X5))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3890,
[final] ).
cnf(c_0_5536,plain,
( hBOOL(hAPP(X2,esk29_3(X3,X2,X1)))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))) ),
c_0_3891,
[final] ).
cnf(c_0_5537,plain,
( c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3),c_Polynomial_Osynthetic__div(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,c_Polynomial_Osynthetic__div(X1,X2,X3)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_3892,
[final] ).
cnf(c_0_5538,plain,
( 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)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_3893,
[final] ).
cnf(c_0_5539,plain,
( 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)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
c_0_3894,
[final] ).
cnf(c_0_5540,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3)
| ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X3),X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_3895,
[final] ).
cnf(c_0_5541,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(X4)))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_3896,
[final] ).
cnf(c_0_5542,plain,
( c_Orderings_Oord__class_Oless__eq(X1,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_3897,
[final] ).
cnf(c_0_5543,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3)
| ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_3898,
[final] ).
cnf(c_0_5544,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
c_0_3899,
[final] ).
cnf(c_0_5545,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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)))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
c_0_3900,
[final] ).
cnf(c_0_5546,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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)))
| ~ class_Rings_Olinordered__ring(X1) ),
c_0_3901,
[final] ).
cnf(c_0_5547,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))) ),
c_0_3902,
[final] ).
cnf(c_0_5548,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1))) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1(X1) ),
c_0_3903,
[final] ).
cnf(c_0_5549,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_OpCons(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_3904,
[final] ).
cnf(c_0_5550,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)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_3905,
[final] ).
cnf(c_0_5551,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_3906,
[final] ).
cnf(c_0_5552,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(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_0_3907,
[final] ).
cnf(c_0_5553,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(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_0_3908,
[final] ).
cnf(c_0_5554,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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_0_3909,
[final] ).
cnf(c_0_5555,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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(X1) ),
c_0_3910,
[final] ).
cnf(c_0_5556,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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_0_3911,
[final] ).
cnf(c_0_5557,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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(X1) ),
c_0_3912,
[final] ).
cnf(c_0_5558,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
c_0_3913,
[final] ).
cnf(c_0_5559,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
c_0_3914,
[final] ).
cnf(c_0_5560,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(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)) ),
c_0_3915,
[final] ).
cnf(c_0_5561,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
c_0_3916,
[final] ).
cnf(c_0_5562,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(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(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
c_0_3917,
[final] ).
cnf(c_0_5563,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
c_0_3918,
[final] ).
cnf(c_0_5564,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)) ),
c_0_3919,
[final] ).
cnf(c_0_5565,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ 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(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
c_0_3920,
[final] ).
cnf(c_0_5566,plain,
( c_Polynomial_OpCons(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X5)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_3921,
[final] ).
cnf(c_0_5567,plain,
( c_Polynomial_OpCons(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X5)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_3922,
[final] ).
cnf(c_0_5568,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) ),
c_0_3923,
[final] ).
cnf(c_0_5569,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_3924,
[final] ).
cnf(c_0_5570,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_3925,
[final] ).
cnf(c_0_5571,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_3926,
[final] ).
cnf(c_0_5572,plain,
( 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,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_3927,
[final] ).
cnf(c_0_5573,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_3928,
[final] ).
cnf(c_0_5574,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
c_0_3929,
[final] ).
cnf(c_0_5575,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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_0_3930,
[final] ).
cnf(c_0_5576,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk34_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3931,
[final] ).
cnf(c_0_5577,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk33_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3932,
[final] ).
cnf(c_0_5578,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3933,
[final] ).
cnf(c_0_5579,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3934,
[final] ).
cnf(c_0_5580,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3935,
[final] ).
cnf(c_0_5581,plain,
( 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),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_3936,
[final] ).
cnf(c_0_5582,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_3937,
[final] ).
cnf(c_0_5583,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring(X1) ),
c_0_3938,
[final] ).
cnf(c_0_5584,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3939,
[final] ).
cnf(c_0_5585,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3940,
[final] ).
cnf(c_0_5586,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
c_0_3941,
[final] ).
cnf(c_0_5587,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
c_0_3942,
[final] ).
cnf(c_0_5588,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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_0_3943,
[final] ).
cnf(c_0_5589,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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_0_3944,
[final] ).
cnf(c_0_5590,plain,
( 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)) = 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)
| X2 != X4 ),
c_0_3945,
[final] ).
cnf(c_0_5591,plain,
( 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)) = 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)
| X3 != X5 ),
c_0_3946,
[final] ).
cnf(c_0_5592,plain,
( 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)) = 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)
| X2 != X4 ),
c_0_3947,
[final] ).
cnf(c_0_5593,plain,
( 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)) = 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)
| X3 != X5 ),
c_0_3948,
[final] ).
cnf(c_0_5594,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
c_0_3949,
[final] ).
cnf(c_0_5595,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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_0_3950,
[final] ).
cnf(c_0_5596,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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_3951,
[final] ).
cnf(c_0_5597,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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_3952,
[final] ).
cnf(c_0_5598,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) ),
c_0_3953,
[final] ).
cnf(c_0_5599,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
c_0_3954,
[final] ).
cnf(c_0_5600,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
c_0_3955,
[final] ).
cnf(c_0_5601,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
c_0_3956,
[final] ).
cnf(c_0_5602,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
c_0_3957,
[final] ).
cnf(c_0_5603,plain,
( X4 = X6
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != c_Groups_Oplus__class_Oplus(X1,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X6))
| X2 != X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
c_0_3958,
[final] ).
cnf(c_0_5604,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2)) ),
c_0_3959,
[final] ).
cnf(c_0_5605,plain,
( 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)
| ~ 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)) ),
c_0_3960,
[final] ).
cnf(c_0_5606,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ 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_0_3961,
[final] ).
cnf(c_0_5607,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)) ),
c_0_3962,
[final] ).
cnf(c_0_5608,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)) ),
c_0_3963,
[final] ).
cnf(c_0_5609,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(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_0_3964,
[final] ).
cnf(c_0_5610,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(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_0_3965,
[final] ).
cnf(c_0_5611,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(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_0_3966,
[final] ).
cnf(c_0_5612,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_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) ),
c_0_3967,
[final] ).
cnf(c_0_5613,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)) ),
c_0_3968,
[final] ).
cnf(c_0_5614,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
c_0_3969,
[final] ).
cnf(c_0_5615,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3970,
[final] ).
cnf(c_0_5616,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3971,
[final] ).
cnf(c_0_5617,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3972,
[final] ).
cnf(c_0_5618,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3973,
[final] ).
cnf(c_0_5619,plain,
( c_Polynomial_Osmult(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_3974,
[final] ).
cnf(c_0_5620,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),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2)) ),
c_0_3975,
[final] ).
cnf(c_0_5621,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2)) ),
c_0_3976,
[final] ).
cnf(c_0_5622,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_3977,
[final] ).
cnf(c_0_5623,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)),X4)
| ~ class_Rings_Ocomm__ring(X1) ),
c_0_3978,
[final] ).
cnf(c_0_5624,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X5),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_3979,
[final] ).
cnf(c_0_5625,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
c_0_3980,
[final] ).
cnf(c_0_5626,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
c_0_3981,
[final] ).
cnf(c_0_5627,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
c_0_3982,
[final] ).
cnf(c_0_5628,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
c_0_3983,
[final] ).
cnf(c_0_5629,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
c_0_3984,
[final] ).
cnf(c_0_5630,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
c_0_3985,
[final] ).
cnf(c_0_5631,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
c_0_3986,
[final] ).
cnf(c_0_5632,plain,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3),
c_0_3987,
[final] ).
cnf(c_0_5633,plain,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),X3),
c_0_3988,
[final] ).
cnf(c_0_5634,plain,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),
c_0_3989,
[final] ).
cnf(c_0_5635,plain,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3),
c_0_3990,
[final] ).
cnf(c_0_5636,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),X3),
c_0_3991,
[final] ).
cnf(c_0_5637,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
c_0_3992,
[final] ).
cnf(c_0_5638,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
c_0_3993,
[final] ).
cnf(c_0_5639,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
c_0_3994,
[final] ).
cnf(c_0_5640,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
c_0_3995,
[final] ).
cnf(c_0_5641,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
c_0_3996,
[final] ).
cnf(c_0_5642,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
c_0_3997,
[final] ).
cnf(c_0_5643,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
c_0_3998,
[final] ).
cnf(c_0_5644,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
c_0_3999,
[final] ).
cnf(c_0_5645,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
c_0_4000,
[final] ).
cnf(c_0_5646,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
c_0_4001,
[final] ).
cnf(c_0_5647,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ 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)) ),
c_0_4002,
[final] ).
cnf(c_0_5648,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ 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)) ),
c_0_4003,
[final] ).
cnf(c_0_5649,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_4004,
[final] ).
cnf(c_0_5650,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)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4005,
[final] ).
cnf(c_0_5651,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk3_0),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_4006,
[final] ).
cnf(c_0_5652,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_4007,
[final] ).
cnf(c_0_5653,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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)) ),
c_0_4008,
[final] ).
cnf(c_0_5654,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
c_0_4009,
[final] ).
cnf(c_0_5655,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
c_0_4010,
[final] ).
cnf(c_0_5656,plain,
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)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
c_0_4011,
[final] ).
cnf(c_0_5657,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_OpCons(X2,X4,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
c_0_4012,
[final] ).
cnf(c_0_5658,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
c_0_4013,
[final] ).
cnf(c_0_5659,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
c_0_4014,
[final] ).
cnf(c_0_5660,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
c_0_4015,
[final] ).
cnf(c_0_5661,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____),
c_0_4016,
[final] ).
cnf(c_0_5662,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk6_3(X3,X2,X1)) = X2
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
c_0_4017,
[final] ).
cnf(c_0_5663,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk5_3(X3,X2,X1)) = X2
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
c_0_4018,
[final] ).
cnf(c_0_5664,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
c_0_4019,
[final] ).
cnf(c_0_5665,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_4020,
[final] ).
cnf(c_0_5666,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X4))
| ~ class_Rings_Ocomm__ring(X1) ),
c_0_4021,
[final] ).
cnf(c_0_5667,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X3)
| ~ class_Rings_Olinordered__semidom(X4) ),
c_0_4022,
[final] ).
cnf(c_0_5668,plain,
( 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),c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4023,
[final] ).
cnf(c_0_5669,plain,
( 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),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4024,
[final] ).
cnf(c_0_5670,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk6_3(X3,X2,X1)) = X2 ),
c_0_4025,
[final] ).
cnf(c_0_5671,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk5_3(X3,X2,X1)) = X2 ),
c_0_4026,
[final] ).
cnf(c_0_5672,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4027,
[final] ).
cnf(c_0_5673,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4028,
[final] ).
cnf(c_0_5674,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_RealVector_Onorm__class_Onorm(X2,X4)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
c_0_4029,
[final] ).
cnf(c_0_5675,plain,
( c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
c_0_4030,
[final] ).
cnf(c_0_5676,plain,
( c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
c_0_4031,
[final] ).
cnf(c_0_5677,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4032,
[final] ).
cnf(c_0_5678,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Rings_Oordered__ring(X1) ),
c_0_4033,
[final] ).
cnf(c_0_5679,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ class_Rings_Oordered__ring(X1) ),
c_0_4034,
[final] ).
cnf(c_0_5680,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Oordered__comm__semiring(X1) ),
c_0_4035,
[final] ).
cnf(c_0_5681,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
c_0_4036,
[final] ).
cnf(c_0_5682,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
c_0_4037,
[final] ).
cnf(c_0_5683,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),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
c_0_4038,
[final] ).
cnf(c_0_5684,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),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4039,
[final] ).
cnf(c_0_5685,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4040,
[final] ).
cnf(c_0_5686,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4041,
[final] ).
cnf(c_0_5687,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
c_0_4042,
[final] ).
cnf(c_0_5688,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))
| ~ 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,X4,X3) ),
c_0_4043,
[final] ).
cnf(c_0_5689,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),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4044,
[final] ).
cnf(c_0_5690,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__semiring__strict(X1) ),
c_0_4045,
[final] ).
cnf(c_0_5691,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__comm__semiring__strict(X1) ),
c_0_4046,
[final] ).
cnf(c_0_5692,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),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
c_0_4047,
[final] ).
cnf(c_0_5693,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,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
c_0_4048,
[final] ).
cnf(c_0_5694,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
c_0_4049,
[final] ).
cnf(c_0_5695,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
c_0_4050,
[final] ).
cnf(c_0_5696,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
c_0_4051,
[final] ).
cnf(c_0_5697,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
c_0_4052,
[final] ).
cnf(c_0_5698,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
c_0_4053,
[final] ).
cnf(c_0_5699,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
c_0_4054,
[final] ).
cnf(c_0_5700,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4055,
[final] ).
cnf(c_0_5701,plain,
( 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))
| ~ 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,X3,X4) ),
c_0_4056,
[final] ).
cnf(c_0_5702,plain,
( 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)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4057,
[final] ).
cnf(c_0_5703,plain,
( 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,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_4058,
[final] ).
cnf(c_0_5704,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_4059,
[final] ).
cnf(c_0_5705,plain,
( 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,c_Groups_Ominus__class_Ominus(X1,X2,X4),X3)
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4060,
[final] ).
cnf(c_0_5706,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
| ~ class_Rings_Ocomm__ring(X1) ),
c_0_4061,
[final] ).
cnf(c_0_5707,plain,
( 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),X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4062,
[final] ).
cnf(c_0_5708,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X1) ),
c_0_4063,
[final] ).
cnf(c_0_5709,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4064,
[final] ).
cnf(c_0_5710,plain,
( c_Polynomial_OpCons(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Polynomial_OpCons(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_4065,
[final] ).
cnf(c_0_5711,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
c_0_4066,
[final] ).
cnf(c_0_5712,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
c_0_4067,
[final] ).
cnf(c_0_5713,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
c_0_4068,
[final] ).
cnf(c_0_5714,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
c_0_4069,
[final] ).
cnf(c_0_5715,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
c_0_4070,
[final] ).
cnf(c_0_5716,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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) ),
c_0_4071,
[final] ).
cnf(c_0_5717,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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) ),
c_0_4072,
[final] ).
cnf(c_0_5718,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4073,
[final] ).
cnf(c_0_5719,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4074,
[final] ).
cnf(c_0_5720,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4075,
[final] ).
cnf(c_0_5721,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4076,
[final] ).
cnf(c_0_5722,plain,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4077,
[final] ).
cnf(c_0_5723,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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)) ),
c_0_4078,
[final] ).
cnf(c_0_5724,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X1)) ),
c_0_4079,
[final] ).
cnf(c_0_5725,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1)) ),
c_0_4080,
[final] ).
cnf(c_0_5726,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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)) ),
c_0_4081,
[final] ).
cnf(c_0_5727,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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)) ),
c_0_4082,
[final] ).
cnf(c_0_5728,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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)) ),
c_0_4083,
[final] ).
cnf(c_0_5729,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| ~ 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)) ),
c_0_4084,
[final] ).
cnf(c_0_5730,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)) ),
c_0_4085,
[final] ).
cnf(c_0_5731,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)) ),
c_0_4086,
[final] ).
cnf(c_0_5732,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
c_0_4087,
[final] ).
cnf(c_0_5733,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,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4088,
[final] ).
cnf(c_0_5734,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,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4089,
[final] ).
cnf(c_0_5735,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,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),X3),X2)) ),
c_0_4090,
[final] ).
cnf(c_0_5736,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_0_4091,
[final] ).
cnf(c_0_5737,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) ),
c_0_4092,
[final] ).
cnf(c_0_5738,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) ),
c_0_4093,
[final] ).
cnf(c_0_5739,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) ),
c_0_4094,
[final] ).
cnf(c_0_5740,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) ),
c_0_4095,
[final] ).
cnf(c_0_5741,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4096,
[final] ).
cnf(c_0_5742,plain,
( X4 = c_Polynomial_Osynthetic__div(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) != c_Polynomial_OpCons(X1,X5,X4) ),
c_0_4097,
[final] ).
cnf(c_0_5743,plain,
( c_Polynomial_Osynthetic__div(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X3),X4),c_Polynomial_Osynthetic__div(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_4098,
[final] ).
cnf(c_0_5744,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) ),
c_0_4099,
[final] ).
cnf(c_0_5745,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_Groups_Omonoid__mult(X1) ),
c_0_4100,
[final] ).
cnf(c_0_5746,plain,
( 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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
c_0_4101,
[final] ).
cnf(c_0_5747,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
c_0_4102,
[final] ).
cnf(c_0_5748,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
c_0_4103,
[final] ).
cnf(c_0_5749,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
c_0_4104,
[final] ).
cnf(c_0_5750,plain,
( c_Orderings_Oord__class_Oless(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))
| ~ 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,X3) ),
c_0_4105,
[final] ).
cnf(c_0_5751,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),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
c_0_4106,
[final] ).
cnf(c_0_5752,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,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
c_0_4107,
[final] ).
cnf(c_0_5753,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) ),
c_0_4108,
[final] ).
cnf(c_0_5754,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),X3),X2))
| ~ 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,X1,X3) ),
c_0_4109,
[final] ).
cnf(c_0_5755,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) ),
c_0_4110,
[final] ).
cnf(c_0_5756,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
c_0_4111,
[final] ).
cnf(c_0_5757,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
c_0_4112,
[final] ).
cnf(c_0_5758,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4113,
[final] ).
cnf(c_0_5759,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
c_0_4114,
[final] ).
cnf(c_0_5760,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
c_0_4115,
[final] ).
cnf(c_0_5761,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
c_0_4116,
[final] ).
cnf(c_0_5762,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
c_0_4117,
[final] ).
cnf(c_0_5763,plain,
( c_Orderings_Oord__class_Oless__eq(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),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
c_0_4118,
[final] ).
cnf(c_0_5764,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
c_0_4119,
[final] ).
cnf(c_0_5765,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
c_0_4120,
[final] ).
cnf(c_0_5766,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
c_0_4121,
[final] ).
cnf(c_0_5767,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
c_0_4122,
[final] ).
cnf(c_0_5768,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
c_0_4123,
[final] ).
cnf(c_0_5769,plain,
( X5 = hAPP(c_Polynomial_Opoly(X1,X2),X3)
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) != c_Polynomial_OpCons(X1,X5,X4) ),
c_0_4124,
[final] ).
cnf(c_0_5770,plain,
( c_Polynomial_Osmult(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_4125,
[final] ).
cnf(c_0_5771,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
c_0_4126,
[final] ).
cnf(c_0_5772,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_4127,
[final] ).
cnf(c_0_5773,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Osmult(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_4128,
[final] ).
cnf(c_0_5774,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4129,
[final] ).
cnf(c_0_5775,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4130,
[final] ).
cnf(c_0_5776,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4131,
[final] ).
cnf(c_0_5777,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4132,
[final] ).
cnf(c_0_5778,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
c_0_4133,
[final] ).
cnf(c_0_5779,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
c_0_4134,
[final] ).
cnf(c_0_5780,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
c_0_4135,
[final] ).
cnf(c_0_5781,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
c_0_4136,
[final] ).
cnf(c_0_5782,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),c_Nat_OSuc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X4))
| ~ class_Rings_Olinordered__semidom(X3) ),
c_0_4137,
[final] ).
cnf(c_0_5783,plain,
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4138,
[final] ).
cnf(c_0_5784,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
c_0_4139,
[final] ).
cnf(c_0_5785,plain,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)),
c_0_4140,
[final] ).
cnf(c_0_5786,plain,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
c_0_4141,
[final] ).
cnf(c_0_5787,plain,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),
c_0_4142,
[final] ).
cnf(c_0_5788,plain,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
c_0_4143,
[final] ).
cnf(c_0_5789,plain,
( hAPP(c_Polynomial_Opoly(X1,X2),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Opcompose(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_4144,
[final] ).
cnf(c_0_5790,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),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) ),
c_0_4145,
[final] ).
cnf(c_0_5791,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
c_0_4146,
[final] ).
cnf(c_0_5792,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4147,
[final] ).
cnf(c_0_5793,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_4148,
[final] ).
cnf(c_0_5794,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_4149,
[final] ).
cnf(c_0_5795,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
c_0_4150,
[final] ).
cnf(c_0_5796,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4151,
[final] ).
cnf(c_0_5797,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4152,
[final] ).
cnf(c_0_5798,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4153,
[final] ).
cnf(c_0_5799,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4154,
[final] ).
cnf(c_0_5800,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4155,
[final] ).
cnf(c_0_5801,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4156,
[final] ).
cnf(c_0_5802,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4157,
[final] ).
cnf(c_0_5803,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ 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)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4158,
[final] ).
cnf(c_0_5804,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),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,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4159,
[final] ).
cnf(c_0_5805,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
c_0_4160,
[final] ).
cnf(c_0_5806,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
c_0_4161,
[final] ).
cnf(c_0_5807,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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
c_0_4162,
[final] ).
cnf(c_0_5808,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)),
c_0_4163,
[final] ).
cnf(c_0_5809,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)),
c_0_4164,
[final] ).
cnf(c_0_5810,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)),
c_0_4165,
[final] ).
cnf(c_0_5811,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
c_0_4166,
[final] ).
cnf(c_0_5812,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4167,
[final] ).
cnf(c_0_5813,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4168,
[final] ).
cnf(c_0_5814,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4169,
[final] ).
cnf(c_0_5815,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4170,
[final] ).
cnf(c_0_5816,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring(X1) ),
c_0_4171,
[final] ).
cnf(c_0_5817,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
c_0_4172,
[final] ).
cnf(c_0_5818,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
c_0_4173,
[final] ).
cnf(c_0_5819,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
c_0_4174,
[final] ).
cnf(c_0_5820,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
c_0_4175,
[final] ).
cnf(c_0_5821,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4176,
[final] ).
cnf(c_0_5822,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4177,
[final] ).
cnf(c_0_5823,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4178,
[final] ).
cnf(c_0_5824,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4179,
[final] ).
cnf(c_0_5825,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4180,
[final] ).
cnf(c_0_5826,plain,
( 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)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4181,
[final] ).
cnf(c_0_5827,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),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)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4182,
[final] ).
cnf(c_0_5828,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Rings_Olinordered__semiring__strict(X1) ),
c_0_4183,
[final] ).
cnf(c_0_5829,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),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,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4184,
[final] ).
cnf(c_0_5830,plain,
( 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,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
c_0_4185,
[final] ).
cnf(c_0_5831,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
c_0_4186,
[final] ).
cnf(c_0_5832,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
c_0_4187,
[final] ).
cnf(c_0_5833,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
c_0_4188,
[final] ).
cnf(c_0_5834,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
c_0_4189,
[final] ).
cnf(c_0_5835,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
c_0_4190,
[final] ).
cnf(c_0_5836,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
c_0_4191,
[final] ).
cnf(c_0_5837,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
c_0_4192,
[final] ).
cnf(c_0_5838,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
c_0_4193,
[final] ).
cnf(c_0_5839,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
c_0_4194,
[final] ).
cnf(c_0_5840,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
c_0_4195,
[final] ).
cnf(c_0_5841,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
c_0_4196,
[final] ).
cnf(c_0_5842,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),esk24_0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
c_0_4197,
[final] ).
cnf(c_0_5843,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),esk19_0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
c_0_4198,
[final] ).
cnf(c_0_5844,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
c_0_4199,
[final] ).
cnf(c_0_5845,plain,
( X3 = esk8_2(X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X1) != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
c_0_4200,
[final] ).
cnf(c_0_5846,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
c_0_4201,
[final] ).
cnf(c_0_5847,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4202,
[final] ).
cnf(c_0_5848,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4203,
[final] ).
cnf(c_0_5849,plain,
( 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)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
c_0_4204,
[final] ).
cnf(c_0_5850,plain,
( 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)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
c_0_4205,
[final] ).
cnf(c_0_5851,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4206,
[final] ).
cnf(c_0_5852,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4207,
[final] ).
cnf(c_0_5853,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4208,
[final] ).
cnf(c_0_5854,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4209,
[final] ).
cnf(c_0_5855,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4210,
[final] ).
cnf(c_0_5856,plain,
( c_Rings_Odvd__class_Odvd(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__eq(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4211,
[final] ).
cnf(c_0_5857,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,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
c_0_4212,
[final] ).
cnf(c_0_5858,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,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
c_0_4213,
[final] ).
cnf(c_0_5859,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
c_0_4214,
[final] ).
cnf(c_0_5860,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)),
c_0_4215,
[final] ).
cnf(c_0_5861,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
c_0_4216,
[final] ).
cnf(c_0_5862,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
c_0_4217,
[final] ).
cnf(c_0_5863,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
c_0_4218,
[final] ).
cnf(c_0_5864,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
c_0_4219,
[final] ).
cnf(c_0_5865,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
c_0_4220,
[final] ).
cnf(c_0_5866,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
c_0_4221,
[final] ).
cnf(c_0_5867,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
c_0_4222,
[final] ).
cnf(c_0_5868,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
c_0_4223,
[final] ).
cnf(c_0_5869,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
c_0_4224,
[final] ).
cnf(c_0_5870,plain,
( X3 = X2
| hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_4225,
[final] ).
cnf(c_0_5871,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
c_0_4226,
[final] ).
cnf(c_0_5872,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4227,
[final] ).
cnf(c_0_5873,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
c_0_4228,
[final] ).
cnf(c_0_5874,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
c_0_4229,
[final] ).
cnf(c_0_5875,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
c_0_4230,
[final] ).
cnf(c_0_5876,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4)) ),
c_0_4231,
[final] ).
cnf(c_0_5877,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| ~ class_Fields_Ofield(X1) ),
c_0_4232,
[final] ).
cnf(c_0_5878,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
c_0_4233,
[final] ).
cnf(c_0_5879,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
c_0_4234,
[final] ).
cnf(c_0_5880,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4235,
[final] ).
cnf(c_0_5881,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4236,
[final] ).
cnf(c_0_5882,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
c_0_4237,
[final] ).
cnf(c_0_5883,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4238,
[final] ).
cnf(c_0_5884,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4239,
[final] ).
cnf(c_0_5885,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
c_0_4240,
[final] ).
cnf(c_0_5886,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Nat_OSuc(X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
c_0_4241,
[final] ).
cnf(c_0_5887,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4242,
[final] ).
cnf(c_0_5888,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
c_0_4243,
[final] ).
cnf(c_0_5889,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4244,
[final] ).
cnf(c_0_5890,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4245,
[final] ).
cnf(c_0_5891,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4246,
[final] ).
cnf(c_0_5892,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
c_0_4247,
[final] ).
cnf(c_0_5893,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
c_0_4248,
[final] ).
cnf(c_0_5894,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
c_0_4249,
[final] ).
cnf(c_0_5895,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
c_0_4250,
[final] ).
cnf(c_0_5896,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
c_0_4251,
[final] ).
cnf(c_0_5897,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = c_Divides_Odiv__class_Odiv(X1,X2,X4)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_4252,
[final] ).
cnf(c_0_5898,plain,
( 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)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_4253,
[final] ).
cnf(c_0_5899,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4254,
[final] ).
cnf(c_0_5900,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4255,
[final] ).
cnf(c_0_5901,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4256,
[final] ).
cnf(c_0_5902,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4257,
[final] ).
cnf(c_0_5903,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4258,
[final] ).
cnf(c_0_5904,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4259,
[final] ).
cnf(c_0_5905,plain,
( c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Polynomial_Osmult(X1,X2,c_Polynomial_Omonom(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_4260,
[final] ).
cnf(c_0_5906,plain,
( c_Polynomial_Osmult(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Polynomial_Osmult(X1,X2,c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_4261,
[final] ).
cnf(c_0_5907,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4262,
[final] ).
cnf(c_0_5908,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
c_0_4263,
[final] ).
cnf(c_0_5909,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),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
c_0_4264,
[final] ).
cnf(c_0_5910,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
c_0_4265,
[final] ).
cnf(c_0_5911,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))),
c_0_4266,
[final] ).
cnf(c_0_5912,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),c_Nat_OSuc(X3))
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_4267,
[final] ).
cnf(c_0_5913,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),c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4268,
[final] ).
cnf(c_0_5914,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
c_0_4269,
[final] ).
cnf(c_0_5915,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
c_0_4270,
[final] ).
cnf(c_0_5916,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| 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))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
c_0_4271,
[final] ).
cnf(c_0_5917,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
c_0_4272,
[final] ).
cnf(c_0_5918,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
c_0_4273,
[final] ).
cnf(c_0_5919,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
c_0_4274,
[final] ).
cnf(c_0_5920,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
c_0_4275,
[final] ).
cnf(c_0_5921,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
c_0_4276,
[final] ).
cnf(c_0_5922,plain,
( X2 = 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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1) ),
c_0_4277,
[final] ).
cnf(c_0_5923,plain,
( X2 = 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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) ),
c_0_4278,
[final] ).
cnf(c_0_5924,plain,
( 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_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
c_0_4279,
[final] ).
cnf(c_0_5925,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
c_0_4280,
[final] ).
cnf(c_0_5926,plain,
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
c_0_4281,
[final] ).
cnf(c_0_5927,plain,
( c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
c_0_4282,
[final] ).
cnf(c_0_5928,plain,
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
c_0_4283,
[final] ).
cnf(c_0_5929,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) ),
c_0_4284,
[final] ).
cnf(c_0_5930,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
c_0_4285,
[final] ).
cnf(c_0_5931,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)),
c_0_4286,
[final] ).
cnf(c_0_5932,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2),
c_0_4287,
[final] ).
cnf(c_0_5933,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
c_0_4288,
[final] ).
cnf(c_0_5934,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
c_0_4289,
[final] ).
cnf(c_0_5935,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
c_0_4290,
[final] ).
cnf(c_0_5936,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
c_0_4291,
[final] ).
cnf(c_0_5937,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
c_0_4292,
[final] ).
cnf(c_0_5938,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
c_0_4293,
[final] ).
cnf(c_0_5939,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
c_0_4294,
[final] ).
cnf(c_0_5940,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
c_0_4295,
[final] ).
cnf(c_0_5941,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
c_0_4296,
[final] ).
cnf(c_0_5942,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
c_0_4297,
[final] ).
cnf(c_0_5943,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
c_0_4298,
[final] ).
cnf(c_0_5944,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4299,
[final] ).
cnf(c_0_5945,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4300,
[final] ).
cnf(c_0_5946,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
c_0_4301,
[final] ).
cnf(c_0_5947,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
c_0_4302,
[final] ).
cnf(c_0_5948,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
c_0_4303,
[final] ).
cnf(c_0_5949,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
c_0_4304,
[final] ).
cnf(c_0_5950,plain,
( 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
c_0_4305,
[final] ).
cnf(c_0_5951,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
c_0_4306,
[final] ).
cnf(c_0_5952,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
c_0_4307,
[final] ).
cnf(c_0_5953,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
c_0_4308,
[final] ).
cnf(c_0_5954,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
c_0_4309,
[final] ).
cnf(c_0_5955,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
c_0_4310,
[final] ).
cnf(c_0_5956,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
c_0_4311,
[final] ).
cnf(c_0_5957,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
c_0_4312,
[final] ).
cnf(c_0_5958,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4313,
[final] ).
cnf(c_0_5959,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4314,
[final] ).
cnf(c_0_5960,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4315,
[final] ).
cnf(c_0_5961,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4316,
[final] ).
cnf(c_0_5962,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4317,
[final] ).
cnf(c_0_5963,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4318,
[final] ).
cnf(c_0_5964,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
c_0_4319,
[final] ).
cnf(c_0_5965,plain,
( X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4320,
[final] ).
cnf(c_0_5966,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)) ),
c_0_4321,
[final] ).
cnf(c_0_5967,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),X2)
| ~ 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)) ),
c_0_4322,
[final] ).
cnf(c_0_5968,plain,
( c_Orderings_Oord__class_Oless__eq(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_0_4323,
[final] ).
cnf(c_0_5969,plain,
( c_Orderings_Oord__class_Oless__eq(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))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
c_0_4324,
[final] ).
cnf(c_0_5970,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
c_0_4325,
[final] ).
cnf(c_0_5971,plain,
( 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)
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4326,
[final] ).
cnf(c_0_5972,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)) ),
c_0_4327,
[final] ).
cnf(c_0_5973,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
c_0_4328,
[final] ).
cnf(c_0_5974,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4329,
[final] ).
cnf(c_0_5975,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4330,
[final] ).
cnf(c_0_5976,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4331,
[final] ).
cnf(c_0_5977,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4332,
[final] ).
cnf(c_0_5978,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| X2 = X3
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
c_0_4333,
[final] ).
cnf(c_0_5979,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
c_0_4334,
[final] ).
cnf(c_0_5980,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
c_0_4335,
[final] ).
cnf(c_0_5981,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
c_0_4336,
[final] ).
cnf(c_0_5982,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
c_0_4337,
[final] ).
cnf(c_0_5983,plain,
( 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_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4338,
[final] ).
cnf(c_0_5984,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4339,
[final] ).
cnf(c_0_5985,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2)) ),
c_0_4340,
[final] ).
cnf(c_0_5986,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| X2 != X3 ),
c_0_4341,
[final] ).
cnf(c_0_5987,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk8_2(X2,X1)),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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
c_0_4342,
[final] ).
cnf(c_0_5988,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk7_2(X2,X1)),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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
c_0_4343,
[final] ).
cnf(c_0_5989,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
c_0_4344,
[final] ).
cnf(c_0_5990,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
c_0_4345,
[final] ).
cnf(c_0_5991,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1) ),
c_0_4346,
[final] ).
cnf(c_0_5992,plain,
( 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)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4347,
[final] ).
cnf(c_0_5993,plain,
( 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)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4348,
[final] ).
cnf(c_0_5994,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4349,
[final] ).
cnf(c_0_5995,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4350,
[final] ).
cnf(c_0_5996,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
c_0_4351,
[final] ).
cnf(c_0_5997,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4352,
[final] ).
cnf(c_0_5998,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4353,
[final] ).
cnf(c_0_5999,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
c_0_4354,
[final] ).
cnf(c_0_6000,plain,
( 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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4355,
[final] ).
cnf(c_0_6001,plain,
( c_Polynomial_Opos__poly(X1,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
c_0_4356,
[final] ).
cnf(c_0_6002,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),esk20_1(X1)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X1),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)) ),
c_0_4357,
[final] ).
cnf(c_0_6003,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4358,
[final] ).
cnf(c_0_6004,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4359,
[final] ).
cnf(c_0_6005,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4360,
[final] ).
cnf(c_0_6006,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4361,
[final] ).
cnf(c_0_6007,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4362,
[final] ).
cnf(c_0_6008,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4363,
[final] ).
cnf(c_0_6009,plain,
( X3 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4) ),
c_0_4364,
[final] ).
cnf(c_0_6010,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
c_0_4365,
[final] ).
cnf(c_0_6011,plain,
( X3 = X2
| hBOOL(hAPP(hAPP(X1,X2),X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_4366,
[final] ).
cnf(c_0_6012,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
c_0_4367,
[final] ).
cnf(c_0_6013,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
c_0_4368,
[final] ).
cnf(c_0_6014,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4369,
[final] ).
cnf(c_0_6015,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4370,
[final] ).
cnf(c_0_6016,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4371,
[final] ).
cnf(c_0_6017,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
c_0_4372,
[final] ).
cnf(c_0_6018,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
c_0_4373,
[final] ).
cnf(c_0_6019,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_4374,
[final] ).
cnf(c_0_6020,plain,
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring(X1) ),
c_0_4375,
[final] ).
cnf(c_0_6021,plain,
( ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3) ),
c_0_4376,
[final] ).
cnf(c_0_6022,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
c_0_4377,
[final] ).
cnf(c_0_6023,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
c_0_4378,
[final] ).
cnf(c_0_6024,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,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_0_4379,
[final] ).
cnf(c_0_6025,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
c_0_4380,
[final] ).
cnf(c_0_6026,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk8_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
c_0_4381,
[final] ).
cnf(c_0_6027,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk7_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
c_0_4382,
[final] ).
cnf(c_0_6028,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
c_0_4383,
[final] ).
cnf(c_0_6029,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
c_0_4384,
[final] ).
cnf(c_0_6030,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
c_0_4385,
[final] ).
cnf(c_0_6031,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ 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),X2) ),
c_0_4386,
[final] ).
cnf(c_0_6032,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
c_0_4387,
[final] ).
cnf(c_0_6033,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
c_0_4388,
[final] ).
cnf(c_0_6034,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
c_0_4389,
[final] ).
cnf(c_0_6035,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
c_0_4390,
[final] ).
cnf(c_0_6036,plain,
( c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4391,
[final] ).
cnf(c_0_6037,plain,
( c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4392,
[final] ).
cnf(c_0_6038,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
c_0_4393,
[final] ).
cnf(c_0_6039,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4394,
[final] ).
cnf(c_0_6040,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4395,
[final] ).
cnf(c_0_6041,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_4396,
[final] ).
cnf(c_0_6042,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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) ),
c_0_4397,
[final] ).
cnf(c_0_6043,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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),X2) ),
c_0_4398,
[final] ).
cnf(c_0_6044,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_4399,
[final] ).
cnf(c_0_6045,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)) = c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
c_0_4400,
[final] ).
cnf(c_0_6046,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
c_0_4401,
[final] ).
cnf(c_0_6047,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,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) ),
c_0_4402,
[final] ).
cnf(c_0_6048,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
c_0_4403,
[final] ).
cnf(c_0_6049,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
c_0_4404,
[final] ).
cnf(c_0_6050,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
c_0_4405,
[final] ).
cnf(c_0_6051,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
c_0_4406,
[final] ).
cnf(c_0_6052,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
c_0_4407,
[final] ).
cnf(c_0_6053,plain,
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk12_2(X1,X2))) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
c_0_4408,
[final] ).
cnf(c_0_6054,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
c_0_4409,
[final] ).
cnf(c_0_6055,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,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) ),
c_0_4410,
[final] ).
cnf(c_0_6056,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
c_0_4411,
[final] ).
cnf(c_0_6057,plain,
( c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_4412,
[final] ).
cnf(c_0_6058,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4413,
[final] ).
cnf(c_0_6059,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
c_0_4414,
[final] ).
cnf(c_0_6060,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
c_0_4415,
[final] ).
cnf(c_0_6061,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4416,
[final] ).
cnf(c_0_6062,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4) ),
c_0_4417,
[final] ).
cnf(c_0_6063,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| ~ class_Orderings_Oord(X1) ),
c_0_4418,
[final] ).
cnf(c_0_6064,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| ~ class_Orderings_Oord(X1) ),
c_0_4419,
[final] ).
cnf(c_0_6065,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4420,
[final] ).
cnf(c_0_6066,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
c_0_4421,
[final] ).
cnf(c_0_6067,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
c_0_4422,
[final] ).
cnf(c_0_6068,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4423,
[final] ).
cnf(c_0_6069,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4424,
[final] ).
cnf(c_0_6070,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
c_0_4425,
[final] ).
cnf(c_0_6071,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
c_0_4426,
[final] ).
cnf(c_0_6072,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4427,
[final] ).
cnf(c_0_6073,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
c_0_4428,
[final] ).
cnf(c_0_6074,plain,
( 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) ),
c_0_4429,
[final] ).
cnf(c_0_6075,plain,
( c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X3,X2) ),
c_0_4430,
[final] ).
cnf(c_0_6076,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
c_0_4431,
[final] ).
cnf(c_0_6077,plain,
( 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)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
c_0_4432,
[final] ).
cnf(c_0_6078,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_4433,
[final] ).
cnf(c_0_6079,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| 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_0_4434,
[final] ).
cnf(c_0_6080,plain,
( c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),c_Polynomial_Omonom(X1,X2,X3)) = c_Polynomial_Omonom(X1,X2,c_Nat_OSuc(X3))
| ~ class_Groups_Ozero(X1) ),
c_0_4435,
[final] ).
cnf(c_0_6081,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
c_0_4436,
[final] ).
cnf(c_0_6082,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) ),
c_0_4437,
[final] ).
cnf(c_0_6083,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) ),
c_0_4438,
[final] ).
cnf(c_0_6084,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
c_0_4439,
[final] ).
cnf(c_0_6085,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
c_0_4440,
[final] ).
cnf(c_0_6086,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
c_0_4441,
[final] ).
cnf(c_0_6087,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
c_0_4442,
[final] ).
cnf(c_0_6088,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
c_0_4443,
[final] ).
cnf(c_0_6089,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
c_0_4444,
[final] ).
cnf(c_0_6090,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
c_0_4445,
[final] ).
cnf(c_0_6091,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
c_0_4446,
[final] ).
cnf(c_0_6092,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4447,
[final] ).
cnf(c_0_6093,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4448,
[final] ).
cnf(c_0_6094,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4449,
[final] ).
cnf(c_0_6095,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4450,
[final] ).
cnf(c_0_6096,plain,
( c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_4451,
[final] ).
cnf(c_0_6097,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
c_0_4452,
[final] ).
cnf(c_0_6098,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
c_0_4453,
[final] ).
cnf(c_0_6099,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ 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),X2) ),
c_0_4454,
[final] ).
cnf(c_0_6100,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_Rings_Oring(X1) ),
c_0_4455,
[final] ).
cnf(c_0_6101,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4456,
[final] ).
cnf(c_0_6102,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4457,
[final] ).
cnf(c_0_6103,plain,
( c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
c_0_4458,
[final] ).
cnf(c_0_6104,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
c_0_4459,
[final] ).
cnf(c_0_6105,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3))
| ~ class_Rings_Ocomm__ring(X1) ),
c_0_4460,
[final] ).
cnf(c_0_6106,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4461,
[final] ).
cnf(c_0_6107,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
c_0_4462,
[final] ).
cnf(c_0_6108,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X3
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
c_0_4463,
[final] ).
cnf(c_0_6109,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
c_0_4464,
[final] ).
cnf(c_0_6110,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
c_0_4465,
[final] ).
cnf(c_0_6111,plain,
( c_Polynomial_Opos__poly(X1,X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
c_0_4466,
[final] ).
cnf(c_0_6112,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3 ),
c_0_4467,
[final] ).
cnf(c_0_6113,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) ),
c_0_4468,
[final] ).
cnf(c_0_6114,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,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) ),
c_0_4469,
[final] ).
cnf(c_0_6115,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
c_0_4470,
[final] ).
cnf(c_0_6116,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
c_0_4471,
[final] ).
cnf(c_0_6117,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4472,
[final] ).
cnf(c_0_6118,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
c_0_4473,
[final] ).
cnf(c_0_6119,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
c_0_4474,
[final] ).
cnf(c_0_6120,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
c_0_4475,
[final] ).
cnf(c_0_6121,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
c_0_4476,
[final] ).
cnf(c_0_6122,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
c_0_4477,
[final] ).
cnf(c_0_6123,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),c_Nat_OSuc(X3))
| ~ class_Power_Opower(X1) ),
c_0_4478,
[final] ).
cnf(c_0_6124,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),c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4479,
[final] ).
cnf(c_0_6125,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),c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4480,
[final] ).
cnf(c_0_6126,plain,
( c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4481,
[final] ).
cnf(c_0_6127,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3))
| ~ class_Rings_Ocomm__ring(X1) ),
c_0_4482,
[final] ).
cnf(c_0_6128,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4) ),
c_0_4483,
[final] ).
cnf(c_0_6129,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
c_0_4484,
[final] ).
cnf(c_0_6130,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
c_0_4485,
[final] ).
cnf(c_0_6131,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
c_0_4486,
[final] ).
cnf(c_0_6132,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
c_0_4487,
[final] ).
cnf(c_0_6133,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
c_0_4488,
[final] ).
cnf(c_0_6134,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
c_0_4489,
[final] ).
cnf(c_0_6135,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
c_0_4490,
[final] ).
cnf(c_0_6136,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
c_0_4491,
[final] ).
cnf(c_0_6137,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
c_0_4492,
[final] ).
cnf(c_0_6138,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Omonom(X1,X2,X3)) = c_Polynomial_Omonom(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4493,
[final] ).
cnf(c_0_6139,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3)) = c_Polynomial_Osmult(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Ocomm__ring(X1) ),
c_0_4494,
[final] ).
cnf(c_0_6140,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
c_0_4495,
[final] ).
cnf(c_0_6141,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| X3 != X4 ),
c_0_4496,
[final] ).
cnf(c_0_6142,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4497,
[final] ).
cnf(c_0_6143,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4498,
[final] ).
cnf(c_0_6144,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
c_0_4499,
[final] ).
cnf(c_0_6145,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
c_0_4500,
[final] ).
cnf(c_0_6146,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4501,
[final] ).
cnf(c_0_6147,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
c_0_4502,
[final] ).
cnf(c_0_6148,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
c_0_4503,
[final] ).
cnf(c_0_6149,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4504,
[final] ).
cnf(c_0_6150,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
c_0_4505,
[final] ).
cnf(c_0_6151,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4506,
[final] ).
cnf(c_0_6152,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
c_0_4507,
[final] ).
cnf(c_0_6153,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4508,
[final] ).
cnf(c_0_6154,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
c_0_4509,
[final] ).
cnf(c_0_6155,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
c_0_4510,
[final] ).
cnf(c_0_6156,plain,
( c_Nat_OSuc(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) ),
c_0_4511,
[final] ).
cnf(c_0_6157,plain,
( c_Nat_OSuc(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) ),
c_0_4512,
[final] ).
cnf(c_0_6158,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
c_0_4513,
[final] ).
cnf(c_0_6159,plain,
( 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),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
c_0_4514,
[final] ).
cnf(c_0_6160,plain,
( 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),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4515,
[final] ).
cnf(c_0_6161,plain,
( 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),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4516,
[final] ).
cnf(c_0_6162,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4517,
[final] ).
cnf(c_0_6163,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),
c_0_4518,
[final] ).
cnf(c_0_6164,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
c_0_4519,
[final] ).
cnf(c_0_6165,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
c_0_4520,
[final] ).
cnf(c_0_6166,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
c_0_4521,
[final] ).
cnf(c_0_6167,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4522,
[final] ).
cnf(c_0_6168,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
c_0_4523,
[final] ).
cnf(c_0_6169,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oplus__class_Oplus(X1,X2,X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4524,
[final] ).
cnf(c_0_6170,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2)),
c_0_4525,
[final] ).
cnf(c_0_6171,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
c_0_4526,
[final] ).
cnf(c_0_6172,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
c_0_4527,
[final] ).
cnf(c_0_6173,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
c_0_4528,
[final] ).
cnf(c_0_6174,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
c_0_4529,
[final] ).
cnf(c_0_6175,plain,
c_Groups_Ouminus__class_Ouminus(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),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X2),
c_0_4530,
[final] ).
cnf(c_0_6176,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X3 ),
c_0_4531,
[final] ).
cnf(c_0_6177,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
c_0_4532,
[final] ).
cnf(c_0_6178,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
c_0_4533,
[final] ).
cnf(c_0_6179,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4534,
[final] ).
cnf(c_0_6180,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
c_0_4535,
[final] ).
cnf(c_0_6181,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4536,
[final] ).
cnf(c_0_6182,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X2,X3,X1) != c_Polynomial_OpCons(X2,X4,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
c_0_4537,
[final] ).
cnf(c_0_6183,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4538,
[final] ).
cnf(c_0_6184,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
c_0_4539,
[final] ).
cnf(c_0_6185,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4540,
[final] ).
cnf(c_0_6186,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2) ),
c_0_4541,
[final] ).
cnf(c_0_6187,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4542,
[final] ).
cnf(c_0_6188,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4543,
[final] ).
cnf(c_0_6189,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4544,
[final] ).
cnf(c_0_6190,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4545,
[final] ).
cnf(c_0_6191,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4546,
[final] ).
cnf(c_0_6192,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4547,
[final] ).
cnf(c_0_6193,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4548,
[final] ).
cnf(c_0_6194,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4549,
[final] ).
cnf(c_0_6195,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
c_0_4550,
[final] ).
cnf(c_0_6196,plain,
( c_Orderings_Oord__class_Oless(X1,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(X1) ),
c_0_4551,
[final] ).
cnf(c_0_6197,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
c_0_4552,
[final] ).
cnf(c_0_6198,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Rings_Oring(X1) ),
c_0_4553,
[final] ).
cnf(c_0_6199,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
c_0_4554,
[final] ).
cnf(c_0_6200,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
c_0_4555,
[final] ).
cnf(c_0_6201,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| X2 = X3
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3) ),
c_0_4556,
[final] ).
cnf(c_0_6202,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4557,
[final] ).
cnf(c_0_6203,plain,
( c_Polynomial_Opos__poly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4558,
[final] ).
cnf(c_0_6204,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2) ),
c_0_4559,
[final] ).
cnf(c_0_6205,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)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 != X3 ),
c_0_4560,
[final] ).
cnf(c_0_6206,plain,
( X4 = X5
| ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| X2 != X3 ),
c_0_4561,
[final] ).
cnf(c_0_6207,plain,
( X2 = X3
| ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| X4 != X5 ),
c_0_4562,
[final] ).
cnf(c_0_6208,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4563,
[final] ).
cnf(c_0_6209,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4564,
[final] ).
cnf(c_0_6210,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
c_0_4565,
[final] ).
cnf(c_0_6211,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
c_0_4566,
[final] ).
cnf(c_0_6212,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
c_0_4567,
[final] ).
cnf(c_0_6213,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,X3,X2)
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4568,
[final] ).
cnf(c_0_6214,plain,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
c_0_4569,
[final] ).
cnf(c_0_6215,plain,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
c_0_4570,
[final] ).
cnf(c_0_6216,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
c_0_4571,
[final] ).
cnf(c_0_6217,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
c_0_4572,
[final] ).
cnf(c_0_6218,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4573,
[final] ).
cnf(c_0_6219,plain,
( X2 = X3
| ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X4) != c_Polynomial_Omonom(X1,X3,X4) ),
c_0_4574,
[final] ).
cnf(c_0_6220,plain,
( X2 = X4
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5) ),
c_0_4575,
[final] ).
cnf(c_0_6221,plain,
( X3 = X5
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5) ),
c_0_4576,
[final] ).
cnf(c_0_6222,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) != c_Groups_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
c_0_4577,
[final] ).
cnf(c_0_6223,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
c_0_4578,
[final] ).
cnf(c_0_6224,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
c_0_4579,
[final] ).
cnf(c_0_6225,plain,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4) ),
c_0_4580,
[final] ).
cnf(c_0_6226,plain,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X4,X2) != c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
c_0_4581,
[final] ).
cnf(c_0_6227,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
c_0_4582,
[final] ).
cnf(c_0_6228,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
c_0_4583,
[final] ).
cnf(c_0_6229,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
c_0_4584,
[final] ).
cnf(c_0_6230,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
c_0_4585,
[final] ).
cnf(c_0_6231,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4586,
[final] ).
cnf(c_0_6232,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
c_0_4587,
[final] ).
cnf(c_0_6233,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Oorder(X1) ),
c_0_4588,
[final] ).
cnf(c_0_6234,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
c_0_4589,
[final] ).
cnf(c_0_6235,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
c_0_4590,
[final] ).
cnf(c_0_6236,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
c_0_4591,
[final] ).
cnf(c_0_6237,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
c_0_4592,
[final] ).
cnf(c_0_6238,plain,
( X2 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
c_0_4593,
[final] ).
cnf(c_0_6239,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| 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) ),
c_0_4594,
[final] ).
cnf(c_0_6240,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
c_0_4595,
[final] ).
cnf(c_0_6241,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1) ),
c_0_4596,
[final] ).
cnf(c_0_6242,plain,
( X1 = X2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4597,
[final] ).
cnf(c_0_6243,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk10_2(X2,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
c_0_4598,
[final] ).
cnf(c_0_6244,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X1)
| X2 != X3 ),
c_0_4599,
[final] ).
cnf(c_0_6245,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
c_0_4600,
[final] ).
cnf(c_0_6246,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
c_0_4601,
[final] ).
cnf(c_0_6247,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2) ),
c_0_4602,
[final] ).
cnf(c_0_6248,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) ),
c_0_4603,
[final] ).
cnf(c_0_6249,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
c_0_4604,
[final] ).
cnf(c_0_6250,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X2)) = c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),
c_0_4605,
[final] ).
cnf(c_0_6251,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_4606,
[final] ).
cnf(c_0_6252,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = X2
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_4607,
[final] ).
cnf(c_0_6253,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))
| ~ class_Rings_Olinordered__ring(X1) ),
c_0_4608,
[final] ).
cnf(c_0_6254,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4609,
[final] ).
cnf(c_0_6255,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4610,
[final] ).
cnf(c_0_6256,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
c_0_4611,
[final] ).
cnf(c_0_6257,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
c_0_4612,
[final] ).
cnf(c_0_6258,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
c_0_4613,
[final] ).
cnf(c_0_6259,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
c_0_4614,
[final] ).
cnf(c_0_6260,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
c_0_4615,
[final] ).
cnf(c_0_6261,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
c_0_4616,
[final] ).
cnf(c_0_6262,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4617,
[final] ).
cnf(c_0_6263,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
c_0_4618,
[final] ).
cnf(c_0_6264,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
c_0_4619,
[final] ).
cnf(c_0_6265,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4620,
[final] ).
cnf(c_0_6266,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4621,
[final] ).
cnf(c_0_6267,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4622,
[final] ).
cnf(c_0_6268,plain,
( 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),X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
c_0_4623,
[final] ).
cnf(c_0_6269,plain,
( 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)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
c_0_4624,
[final] ).
cnf(c_0_6270,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ),
c_0_4625,
[final] ).
cnf(c_0_6271,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) ),
c_0_4626,
[final] ).
cnf(c_0_6272,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk32_0),X1),
c_0_4627,
[final] ).
cnf(c_0_6273,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk14_0),X1),
c_0_4628,
[final] ).
cnf(c_0_6274,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1),
c_0_4629,
[final] ).
cnf(c_0_6275,plain,
c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
c_0_4630,
[final] ).
cnf(c_0_6276,plain,
c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),
c_0_4631,
[final] ).
cnf(c_0_6277,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != X2 ),
c_0_4632,
[final] ).
cnf(c_0_6278,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4633,
[final] ).
cnf(c_0_6279,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4634,
[final] ).
cnf(c_0_6280,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk23_2(X1,X2)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
c_0_4635,
[final] ).
cnf(c_0_6281,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk9_2(X1,X2)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
c_0_4636,
[final] ).
cnf(c_0_6282,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Nat_OSuc(X1)),
c_0_4637,
[final] ).
cnf(c_0_6283,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
c_0_4638,
[final] ).
cnf(c_0_6284,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
c_0_4639,
[final] ).
cnf(c_0_6285,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_4640,
[final] ).
cnf(c_0_6286,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = X1,
c_0_4641,
[final] ).
cnf(c_0_6287,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
c_0_4642,
[final] ).
cnf(c_0_6288,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
c_0_4643,
[final] ).
cnf(c_0_6289,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
c_0_4644,
[final] ).
cnf(c_0_6290,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
c_0_4645,
[final] ).
cnf(c_0_6291,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
c_0_4646,
[final] ).
cnf(c_0_6292,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
c_0_4647,
[final] ).
cnf(c_0_6293,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
c_0_4648,
[final] ).
cnf(c_0_6294,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))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4649,
[final] ).
cnf(c_0_6295,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))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4650,
[final] ).
cnf(c_0_6296,plain,
( X1 = c_Nat_OSuc(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
c_0_4651,
[final] ).
cnf(c_0_6297,plain,
( X1 = c_Nat_OSuc(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
c_0_4652,
[final] ).
cnf(c_0_6298,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X4 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
c_0_4653,
[final] ).
cnf(c_0_6299,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X4 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Oord(X1) ),
c_0_4654,
[final] ).
cnf(c_0_6300,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
c_0_4655,
[final] ).
cnf(c_0_6301,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
c_0_4656,
[final] ).
cnf(c_0_6302,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 != X2 ),
c_0_4657,
[final] ).
cnf(c_0_6303,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2 ),
c_0_4658,
[final] ).
cnf(c_0_6304,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
c_0_4659,
[final] ).
cnf(c_0_6305,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
c_0_4660,
[final] ).
cnf(c_0_6306,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X4 != X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Oord(X1) ),
c_0_4661,
[final] ).
cnf(c_0_6307,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X4 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
c_0_4662,
[final] ).
cnf(c_0_6308,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| X1 != c_Nat_OSuc(X3) ),
c_0_4663,
[final] ).
cnf(c_0_6309,plain,
( c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X3) ),
c_0_4664,
[final] ).
cnf(c_0_6310,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
c_0_4665,
[final] ).
cnf(c_0_6311,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_1(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
c_0_4666,
[final] ).
cnf(c_0_6312,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X3
| 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_0_4667,
[final] ).
cnf(c_0_6313,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) ),
c_0_4668,
[final] ).
cnf(c_0_6314,plain,
( X1 = X2
| X3 = c_Groups_Ozero__class_Ozero(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_0_4669,
[final] ).
cnf(c_0_6315,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1) ),
c_0_4670,
[final] ).
cnf(c_0_6316,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3) ),
c_0_4671,
[final] ).
cnf(c_0_6317,plain,
( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Nat__Transfer_Otsub(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
c_0_4672,
[final] ).
cnf(c_0_6318,plain,
( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Nat__Transfer_Otsub(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
c_0_4673,
[final] ).
cnf(c_0_6319,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
c_0_4674,
[final] ).
cnf(c_0_6320,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
c_0_4675,
[final] ).
cnf(c_0_6321,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
c_0_4676,
[final] ).
cnf(c_0_6322,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
c_0_4677,
[final] ).
cnf(c_0_6323,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
c_0_4678,
[final] ).
cnf(c_0_6324,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
c_0_4679,
[final] ).
cnf(c_0_6325,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
c_0_4680,
[final] ).
cnf(c_0_6326,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
c_0_4681,
[final] ).
cnf(c_0_6327,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
c_0_4682,
[final] ).
cnf(c_0_6328,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) ),
c_0_4683,
[final] ).
cnf(c_0_6329,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Rings_Ocomm__ring__1(X1) ),
c_0_4684,
[final] ).
cnf(c_0_6330,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4685,
[final] ).
cnf(c_0_6331,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4686,
[final] ).
cnf(c_0_6332,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4687,
[final] ).
cnf(c_0_6333,plain,
( 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)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
c_0_4688,
[final] ).
cnf(c_0_6334,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
c_0_4689,
[final] ).
cnf(c_0_6335,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
c_0_4690,
[final] ).
cnf(c_0_6336,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
c_0_4691,
[final] ).
cnf(c_0_6337,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
c_0_4692,
[final] ).
cnf(c_0_6338,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Nat_OSuc(X1) = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4693,
[final] ).
cnf(c_0_6339,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
c_0_4694,
[final] ).
cnf(c_0_6340,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
c_0_4695,
[final] ).
cnf(c_0_6341,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
c_0_4696,
[final] ).
cnf(c_0_6342,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
c_0_4697,
[final] ).
cnf(c_0_6343,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_1(X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
c_0_4698,
[final] ).
cnf(c_0_6344,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
c_0_4699,
[final] ).
cnf(c_0_6345,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
c_0_4700,
[final] ).
cnf(c_0_6346,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
c_0_4701,
[final] ).
cnf(c_0_6347,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
c_0_4702,
[final] ).
cnf(c_0_6348,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
c_0_4703,
[final] ).
cnf(c_0_6349,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
c_0_4704,
[final] ).
cnf(c_0_6350,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
c_0_4705,
[final] ).
cnf(c_0_6351,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)
| ~ class_Rings_Odvd(X1) ),
c_0_4706,
[final] ).
cnf(c_0_6352,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
c_0_4707,
[final] ).
cnf(c_0_6353,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
c_0_4708,
[final] ).
cnf(c_0_6354,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)) ),
c_0_4709,
[final] ).
cnf(c_0_6355,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
c_0_4710,
[final] ).
cnf(c_0_6356,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
c_0_4711,
[final] ).
cnf(c_0_6357,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)),
c_0_4712,
[final] ).
cnf(c_0_6358,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4713,
[final] ).
cnf(c_0_6359,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4714,
[final] ).
cnf(c_0_6360,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4715,
[final] ).
cnf(c_0_6361,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4716,
[final] ).
cnf(c_0_6362,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4717,
[final] ).
cnf(c_0_6363,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4718,
[final] ).
cnf(c_0_6364,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4719,
[final] ).
cnf(c_0_6365,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4720,
[final] ).
cnf(c_0_6366,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4721,
[final] ).
cnf(c_0_6367,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4722,
[final] ).
cnf(c_0_6368,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4723,
[final] ).
cnf(c_0_6369,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
c_0_4724,
[final] ).
cnf(c_0_6370,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,X2,X3)
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4725,
[final] ).
cnf(c_0_6371,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
c_0_4726,
[final] ).
cnf(c_0_6372,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
c_0_4727,
[final] ).
cnf(c_0_6373,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4728,
[final] ).
cnf(c_0_6374,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4729,
[final] ).
cnf(c_0_6375,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X3 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
c_0_4730,
[final] ).
cnf(c_0_6376,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| X1 != X3 ),
c_0_4731,
[final] ).
cnf(c_0_6377,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
c_0_4732,
[final] ).
cnf(c_0_6378,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X2 != X1 ),
c_0_4733,
[final] ).
cnf(c_0_6379,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4734,
[final] ).
cnf(c_0_6380,plain,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4735,
[final] ).
cnf(c_0_6381,plain,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4736,
[final] ).
cnf(c_0_6382,plain,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4737,
[final] ).
cnf(c_0_6383,plain,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4738,
[final] ).
cnf(c_0_6384,plain,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
c_0_4739,
[final] ).
cnf(c_0_6385,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4740,
[final] ).
cnf(c_0_6386,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4741,
[final] ).
cnf(c_0_6387,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
c_0_4742,
[final] ).
cnf(c_0_6388,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
c_0_4743,
[final] ).
cnf(c_0_6389,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4744,
[final] ).
cnf(c_0_6390,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4745,
[final] ).
cnf(c_0_6391,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
c_0_4746,
[final] ).
cnf(c_0_6392,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
c_0_4747,
[final] ).
cnf(c_0_6393,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),
c_0_4748,
[final] ).
cnf(c_0_6394,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
c_0_4749,
[final] ).
cnf(c_0_6395,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
c_0_4750,
[final] ).
cnf(c_0_6396,plain,
( c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Ozero(X1) ),
c_0_4751,
[final] ).
cnf(c_0_6397,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
c_0_4752,
[final] ).
cnf(c_0_6398,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
c_0_4753,
[final] ).
cnf(c_0_6399,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4754,
[final] ).
cnf(c_0_6400,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4755,
[final] ).
cnf(c_0_6401,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4756,
[final] ).
cnf(c_0_6402,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4757,
[final] ).
cnf(c_0_6403,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4758,
[final] ).
cnf(c_0_6404,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
c_0_4759,
[final] ).
cnf(c_0_6405,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_4760,
[final] ).
cnf(c_0_6406,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
c_0_4761,
[final] ).
cnf(c_0_6407,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) ),
c_0_4762,
[final] ).
cnf(c_0_6408,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),
c_0_4763,
[final] ).
cnf(c_0_6409,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),
c_0_4764,
[final] ).
cnf(c_0_6410,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),
c_0_4765,
[final] ).
cnf(c_0_6411,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),
c_0_4766,
[final] ).
cnf(c_0_6412,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),
c_0_4767,
[final] ).
cnf(c_0_6413,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(esk10_2(X2,X1)) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
c_0_4768,
[final] ).
cnf(c_0_6414,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
c_0_4769,
[final] ).
cnf(c_0_6415,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,X3,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_4770,
[final] ).
cnf(c_0_6416,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_4771,
[final] ).
cnf(c_0_6417,plain,
( c_Polynomial_OpCons(X1,X2,X3) = c_Polynomial_OpCons(X1,X4,X5)
| ~ class_Groups_Ozero(X1)
| X3 != X5
| X2 != X4 ),
c_0_4772,
[final] ).
cnf(c_0_6418,plain,
( ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4773,
[final] ).
cnf(c_0_6419,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4774,
[final] ).
cnf(c_0_6420,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| X2 = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1) ),
c_0_4775,
[final] ).
cnf(c_0_6421,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_4776,
[final] ).
cnf(c_0_6422,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
c_0_4777,
[final] ).
cnf(c_0_6423,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
c_0_4778,
[final] ).
cnf(c_0_6424,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_4779,
[final] ).
cnf(c_0_6425,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3)
| X2 != X3 ),
c_0_4780,
[final] ).
cnf(c_0_6426,plain,
( c_Polynomial_Omonom(X1,X2,X3) = c_Polynomial_Omonom(X1,X4,X3)
| ~ class_Groups_Ozero(X1)
| X2 != X4 ),
c_0_4781,
[final] ).
cnf(c_0_6427,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X4,X3)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 != X4 ),
c_0_4782,
[final] ).
cnf(c_0_6428,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X3 != X4 ),
c_0_4783,
[final] ).
cnf(c_0_6429,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4784,
[final] ).
cnf(c_0_6430,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_4785,
[final] ).
cnf(c_0_6431,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4786,
[final] ).
cnf(c_0_6432,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4787,
[final] ).
cnf(c_0_6433,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4788,
[final] ).
cnf(c_0_6434,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_4789,
[final] ).
cnf(c_0_6435,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4790,
[final] ).
cnf(c_0_6436,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,X3)
| hAPP(X3,esk17_1(X3)) != hAPP(X3,esk16_1(X3)) ),
c_0_4791,
[final] ).
cnf(c_0_6437,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
c_0_4792,
[final] ).
cnf(c_0_6438,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
c_0_4793,
[final] ).
cnf(c_0_6439,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4794,
[final] ).
cnf(c_0_6440,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4795,
[final] ).
cnf(c_0_6441,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4796,
[final] ).
cnf(c_0_6442,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4797,
[final] ).
cnf(c_0_6443,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4798,
[final] ).
cnf(c_0_6444,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4799,
[final] ).
cnf(c_0_6445,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_4800,
[final] ).
cnf(c_0_6446,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
c_0_4801,
[final] ).
cnf(c_0_6447,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4802,
[final] ).
cnf(c_0_6448,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1)
| X2 != X3 ),
c_0_4803,
[final] ).
cnf(c_0_6449,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4804,
[final] ).
cnf(c_0_6450,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4805,
[final] ).
cnf(c_0_6451,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4806,
[final] ).
cnf(c_0_6452,plain,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4,X5,X1) ),
c_0_4807,
[final] ).
cnf(c_0_6453,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_4808,
[final] ).
cnf(c_0_6454,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_4809,
[final] ).
cnf(c_0_6455,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
c_0_4810,
[final] ).
cnf(c_0_6456,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
c_0_4811,
[final] ).
cnf(c_0_6457,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4812,
[final] ).
cnf(c_0_6458,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
c_0_4813,
[final] ).
cnf(c_0_6459,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
c_0_4814,
[final] ).
cnf(c_0_6460,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
c_0_4815,
[final] ).
cnf(c_0_6461,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
c_0_4816,
[final] ).
cnf(c_0_6462,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4817,
[final] ).
cnf(c_0_6463,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) ),
c_0_4818,
[final] ).
cnf(c_0_6464,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) ),
c_0_4819,
[final] ).
cnf(c_0_6465,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
c_0_4820,
[final] ).
cnf(c_0_6466,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4821,
[final] ).
cnf(c_0_6467,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4822,
[final] ).
cnf(c_0_6468,plain,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_4823,
[final] ).
cnf(c_0_6469,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)
| X2 != X3 ),
c_0_4824,
[final] ).
cnf(c_0_6470,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
| X1 != X3 ),
c_0_4825,
[final] ).
cnf(c_0_6471,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X2 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
c_0_4826,
[final] ).
cnf(c_0_6472,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X2 = X1 ),
c_0_4827,
[final] ).
cnf(c_0_6473,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X2 = X1 ),
c_0_4828,
[final] ).
cnf(c_0_6474,plain,
( 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) ),
c_0_4829,
[final] ).
cnf(c_0_6475,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
c_0_4830,
[final] ).
cnf(c_0_6476,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4831,
[final] ).
cnf(c_0_6477,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4832,
[final] ).
cnf(c_0_6478,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4833,
[final] ).
cnf(c_0_6479,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4834,
[final] ).
cnf(c_0_6480,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
c_0_4835,
[final] ).
cnf(c_0_6481,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
c_0_4836,
[final] ).
cnf(c_0_6482,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
c_0_4837,
[final] ).
cnf(c_0_6483,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
c_0_4838,
[final] ).
cnf(c_0_6484,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4839,
[final] ).
cnf(c_0_6485,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1) ),
c_0_4840,
[final] ).
cnf(c_0_6486,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Ono__zero__divisors(X2) ),
c_0_4841,
[final] ).
cnf(c_0_6487,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4842,
[final] ).
cnf(c_0_6488,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
c_0_4843,
[final] ).
cnf(c_0_6489,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
c_0_4844,
[final] ).
cnf(c_0_6490,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4845,
[final] ).
cnf(c_0_6491,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4846,
[final] ).
cnf(c_0_6492,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
c_0_4847,
[final] ).
cnf(c_0_6493,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4848,
[final] ).
cnf(c_0_6494,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4849,
[final] ).
cnf(c_0_6495,plain,
( X2 = X3
| ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4850,
[final] ).
cnf(c_0_6496,plain,
( X2 = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4851,
[final] ).
cnf(c_0_6497,plain,
( X1 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_4852,
[final] ).
cnf(c_0_6498,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
c_0_4853,
[final] ).
cnf(c_0_6499,plain,
( c_Nat_OSuc(esk11_1(X1)) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
c_0_4854,
[final] ).
cnf(c_0_6500,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,X2) != X3 ),
c_0_4855,
[final] ).
cnf(c_0_6501,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)
| X2 != X3 ),
c_0_4856,
[final] ).
cnf(c_0_6502,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)
| X2 != X3 ),
c_0_4857,
[final] ).
cnf(c_0_6503,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
c_0_4858,
[final] ).
cnf(c_0_6504,plain,
( c_Polynomial_OpCons(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4859,
[final] ).
cnf(c_0_6505,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_4860,
[final] ).
cnf(c_0_6506,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4861,
[final] ).
cnf(c_0_6507,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) ),
c_0_4862,
[final] ).
cnf(c_0_6508,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) ),
c_0_4863,
[final] ).
cnf(c_0_6509,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4864,
[final] ).
cnf(c_0_6510,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4865,
[final] ).
cnf(c_0_6511,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) ),
c_0_4866,
[final] ).
cnf(c_0_6512,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
c_0_4867,
[final] ).
cnf(c_0_6513,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
c_0_4868,
[final] ).
cnf(c_0_6514,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
c_0_4869,
[final] ).
cnf(c_0_6515,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
c_0_4870,
[final] ).
cnf(c_0_6516,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
c_0_4871,
[final] ).
cnf(c_0_6517,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
c_0_4872,
[final] ).
cnf(c_0_6518,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
c_0_4873,
[final] ).
cnf(c_0_6519,plain,
( c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4874,
[final] ).
cnf(c_0_6520,plain,
( 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) ),
c_0_4875,
[final] ).
cnf(c_0_6521,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4876,
[final] ).
cnf(c_0_6522,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)
| X1 != X3 ),
c_0_4877,
[final] ).
cnf(c_0_6523,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)
| X2 != X3 ),
c_0_4878,
[final] ).
cnf(c_0_6524,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)
| X2 != X3 ),
c_0_4879,
[final] ).
cnf(c_0_6525,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_4880,
[final] ).
cnf(c_0_6526,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_4881,
[final] ).
cnf(c_0_6527,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) ),
c_0_4882,
[final] ).
cnf(c_0_6528,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
c_0_4883,
[final] ).
cnf(c_0_6529,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
c_0_4884,
[final] ).
cnf(c_0_6530,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
c_0_4885,
[final] ).
cnf(c_0_6531,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_4886,
[final] ).
cnf(c_0_6532,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
c_0_4887,
[final] ).
cnf(c_0_6533,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4888,
[final] ).
cnf(c_0_6534,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4889,
[final] ).
cnf(c_0_6535,plain,
( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4890,
[final] ).
cnf(c_0_6536,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),
c_0_4891,
[final] ).
cnf(c_0_6537,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),
c_0_4892,
[final] ).
cnf(c_0_6538,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
c_0_4893,
[final] ).
cnf(c_0_6539,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4894,
[final] ).
cnf(c_0_6540,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4895,
[final] ).
cnf(c_0_6541,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4896,
[final] ).
cnf(c_0_6542,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4897,
[final] ).
cnf(c_0_6543,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4898,
[final] ).
cnf(c_0_6544,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
c_0_4899,
[final] ).
cnf(c_0_6545,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) ),
c_0_4900,
[final] ).
cnf(c_0_6546,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) ),
c_0_4901,
[final] ).
cnf(c_0_6547,plain,
( 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) ),
c_0_4902,
[final] ).
cnf(c_0_6548,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),esk15_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4903,
[final] ).
cnf(c_0_6549,plain,
( c_Polynomial_Osmult(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_4904,
[final] ).
cnf(c_0_6550,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
c_0_4905,
[final] ).
cnf(c_0_6551,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
c_0_4906,
[final] ).
cnf(c_0_6552,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
c_0_4907,
[final] ).
cnf(c_0_6553,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk34_2(X2,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4908,
[final] ).
cnf(c_0_6554,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_2(X2,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4909,
[final] ).
cnf(c_0_6555,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_4910,
[final] ).
cnf(c_0_6556,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
c_0_4911,
[final] ).
cnf(c_0_6557,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4912,
[final] ).
cnf(c_0_6558,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
c_0_4913,
[final] ).
cnf(c_0_6559,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_4914,
[final] ).
cnf(c_0_6560,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_4915,
[final] ).
cnf(c_0_6561,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_4916,
[final] ).
cnf(c_0_6562,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) ),
c_0_4917,
[final] ).
cnf(c_0_6563,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) ),
c_0_4918,
[final] ).
cnf(c_0_6564,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
c_0_4919,
[final] ).
cnf(c_0_6565,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
c_0_4920,
[final] ).
cnf(c_0_6566,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 != X2 ),
c_0_4921,
[final] ).
cnf(c_0_6567,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4922,
[final] ).
cnf(c_0_6568,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
c_0_4923,
[final] ).
cnf(c_0_6569,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
c_0_4924,
[final] ).
cnf(c_0_6570,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
c_0_4925,
[final] ).
cnf(c_0_6571,plain,
( 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) ),
c_0_4926,
[final] ).
cnf(c_0_6572,plain,
( 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) ),
c_0_4927,
[final] ).
cnf(c_0_6573,plain,
( 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) ),
c_0_4928,
[final] ).
cnf(c_0_6574,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
c_0_4929,
[final] ).
cnf(c_0_6575,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
c_0_4930,
[final] ).
cnf(c_0_6576,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),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4931,
[final] ).
cnf(c_0_6577,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
c_0_4932,
[final] ).
cnf(c_0_6578,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
c_0_4933,
[final] ).
cnf(c_0_6579,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != X2 ),
c_0_4934,
[final] ).
cnf(c_0_6580,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4935,
[final] ).
cnf(c_0_6581,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != X1 ),
c_0_4936,
[final] ).
cnf(c_0_6582,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) ),
c_0_4937,
[final] ).
cnf(c_0_6583,plain,
( X2 = 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) ),
c_0_4938,
[final] ).
cnf(c_0_6584,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) ),
c_0_4939,
[final] ).
cnf(c_0_6585,plain,
( X2 = 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) ),
c_0_4940,
[final] ).
cnf(c_0_6586,plain,
( c_Polynomial_Omonom(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4941,
[final] ).
cnf(c_0_6587,plain,
( c_Polynomial_Osmult(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4942,
[final] ).
cnf(c_0_6588,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4943,
[final] ).
cnf(c_0_6589,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4944,
[final] ).
cnf(c_0_6590,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4945,
[final] ).
cnf(c_0_6591,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4946,
[final] ).
cnf(c_0_6592,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4947,
[final] ).
cnf(c_0_6593,plain,
( c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_4948,
[final] ).
cnf(c_0_6594,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4949,
[final] ).
cnf(c_0_6595,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_4950,
[final] ).
cnf(c_0_6596,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) ),
c_0_4951,
[final] ).
cnf(c_0_6597,plain,
( 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) ),
c_0_4952,
[final] ).
cnf(c_0_6598,plain,
( c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1)) = c_Power_Opower__class_Opower(X1)
| ~ class_Power_Opower(X1) ),
c_0_4953,
[final] ).
cnf(c_0_6599,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_4954,
[final] ).
cnf(c_0_6600,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) ),
c_0_4955,
[final] ).
cnf(c_0_6601,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) ),
c_0_4956,
[final] ).
cnf(c_0_6602,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) ),
c_0_4957,
[final] ).
cnf(c_0_6603,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) ),
c_0_4958,
[final] ).
cnf(c_0_6604,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) ),
c_0_4959,
[final] ).
cnf(c_0_6605,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) ),
c_0_4960,
[final] ).
cnf(c_0_6606,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4961,
[final] ).
cnf(c_0_6607,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4962,
[final] ).
cnf(c_0_6608,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4963,
[final] ).
cnf(c_0_6609,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4964,
[final] ).
cnf(c_0_6610,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
c_0_4965,
[final] ).
cnf(c_0_6611,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4966,
[final] ).
cnf(c_0_6612,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_4967,
[final] ).
cnf(c_0_6613,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) ),
c_0_4968,
[final] ).
cnf(c_0_6614,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) ),
c_0_4969,
[final] ).
cnf(c_0_6615,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
c_0_4970,
[final] ).
cnf(c_0_6616,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4971,
[final] ).
cnf(c_0_6617,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4972,
[final] ).
cnf(c_0_6618,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1)
| X2 != X3 ),
c_0_4973,
[final] ).
cnf(c_0_6619,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4974,
[final] ).
cnf(c_0_6620,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4975,
[final] ).
cnf(c_0_6621,plain,
( c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
c_0_4976,
[final] ).
cnf(c_0_6622,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4977,
[final] ).
cnf(c_0_6623,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) ),
c_0_4978,
[final] ).
cnf(c_0_6624,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) ),
c_0_4979,
[final] ).
cnf(c_0_6625,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) ),
c_0_4980,
[final] ).
cnf(c_0_6626,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) ),
c_0_4981,
[final] ).
cnf(c_0_6627,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4982,
[final] ).
cnf(c_0_6628,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1)
| X2 != X3 ),
c_0_4983,
[final] ).
cnf(c_0_6629,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 != X3 ),
c_0_4984,
[final] ).
cnf(c_0_6630,plain,
( hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_4985,
[final] ).
cnf(c_0_6631,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____),
c_0_4986,
[final] ).
cnf(c_0_6632,plain,
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4987,
[final] ).
cnf(c_0_6633,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4988,
[final] ).
cnf(c_0_6634,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_4989,
[final] ).
cnf(c_0_6635,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4990,
[final] ).
cnf(c_0_6636,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Omonoid__add(X1) ),
c_0_4991,
[final] ).
cnf(c_0_6637,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_4992,
[final] ).
cnf(c_0_6638,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4993,
[final] ).
cnf(c_0_6639,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Omonoid__add(X1) ),
c_0_4994,
[final] ).
cnf(c_0_6640,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4995,
[final] ).
cnf(c_0_6641,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4996,
[final] ).
cnf(c_0_6642,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Nat_OSuc(X2) ),
c_0_4997,
[final] ).
cnf(c_0_6643,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4998,
[final] ).
cnf(c_0_6644,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
c_0_4999,
[final] ).
cnf(c_0_6645,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5000,
[final] ).
cnf(c_0_6646,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_5001,
[final] ).
cnf(c_0_6647,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) ),
c_0_5002,
[final] ).
cnf(c_0_6648,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) ),
c_0_5003,
[final] ).
cnf(c_0_6649,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_5004,
[final] ).
cnf(c_0_6650,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
c_0_5005,
[final] ).
cnf(c_0_6651,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
c_0_5006,
[final] ).
cnf(c_0_6652,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
c_0_5007,
[final] ).
cnf(c_0_6653,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
c_0_5008,
[final] ).
cnf(c_0_6654,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Opreorder(X1) ),
c_0_5009,
[final] ).
cnf(c_0_6655,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
c_0_5010,
[final] ).
cnf(c_0_6656,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5011,
[final] ).
cnf(c_0_6657,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != c_Nat_OSuc(X2) ),
c_0_5012,
[final] ).
cnf(c_0_6658,plain,
( X1 = X2
| X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 = c_Groups_Ozero__class_Ozero(X3)
| c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| ~ class_Rings_Odivision__ring(X3) ),
c_0_5013,
[final] ).
cnf(c_0_6659,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) ),
c_0_5014,
[final] ).
cnf(c_0_6660,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_5015,
[final] ).
cnf(c_0_6661,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
c_0_5016,
[final] ).
cnf(c_0_6662,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
c_0_5017,
[final] ).
cnf(c_0_6663,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X1)),
c_0_5018,
[final] ).
cnf(c_0_6664,plain,
( 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) ),
c_0_5019,
[final] ).
cnf(c_0_6665,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5020,
[final] ).
cnf(c_0_6666,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_5021,
[final] ).
cnf(c_0_6667,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5022,
[final] ).
cnf(c_0_6668,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
c_0_5023,
[final] ).
cnf(c_0_6669,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_5024,
[final] ).
cnf(c_0_6670,plain,
( X2 = X3
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3) ),
c_0_5025,
[final] ).
cnf(c_0_6671,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
c_0_5026,
[final] ).
cnf(c_0_6672,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
c_0_5027,
[final] ).
cnf(c_0_6673,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_OSuc(X1),
c_0_5028,
[final] ).
cnf(c_0_6674,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = c_Nat_OSuc(X1),
c_0_5029,
[final] ).
cnf(c_0_6675,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) ),
c_0_5030,
[final] ).
cnf(c_0_6676,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) ),
c_0_5031,
[final] ).
cnf(c_0_6677,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5032,
[final] ).
cnf(c_0_6678,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
c_0_5033,
[final] ).
cnf(c_0_6679,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
c_0_5034,
[final] ).
cnf(c_0_6680,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)),
c_0_5035,
[final] ).
cnf(c_0_6681,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
c_0_5036,
[final] ).
cnf(c_0_6682,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5037,
[final] ).
cnf(c_0_6683,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),
c_0_5038,
[final] ).
cnf(c_0_6684,plain,
( ~ c_Polynomial_Opos__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5039,
[final] ).
cnf(c_0_6685,plain,
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),
c_0_5040,
[final] ).
cnf(c_0_6686,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = X1,
c_0_5041,
[final] ).
cnf(c_0_6687,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
c_0_5042,
[final] ).
cnf(c_0_6688,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
c_0_5043,
[final] ).
cnf(c_0_6689,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
c_0_5044,
[final] ).
cnf(c_0_6690,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
c_0_5045,
[final] ).
cnf(c_0_6691,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
c_0_5046,
[final] ).
cnf(c_0_6692,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
c_0_5047,
[final] ).
cnf(c_0_6693,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
c_0_5048,
[final] ).
cnf(c_0_6694,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
c_0_5049,
[final] ).
cnf(c_0_6695,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X2 ),
c_0_5050,
[final] ).
cnf(c_0_6696,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
c_0_5051,
[final] ).
cnf(c_0_6697,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
c_0_5052,
[final] ).
cnf(c_0_6698,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
c_0_5053,
[final] ).
cnf(c_0_6699,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
c_0_5054,
[final] ).
cnf(c_0_6700,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
c_0_5055,
[final] ).
cnf(c_0_6701,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_5056,
[final] ).
cnf(c_0_6702,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
c_0_5057,
[final] ).
cnf(c_0_6703,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
c_0_5058,
[final] ).
cnf(c_0_6704,plain,
( 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) ),
c_0_5059,
[final] ).
cnf(c_0_6705,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5060,
[final] ).
cnf(c_0_6706,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_5061,
[final] ).
cnf(c_0_6707,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk24_0),
c_0_5062,
[final] ).
cnf(c_0_6708,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk19_0),
c_0_5063,
[final] ).
cnf(c_0_6709,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),
c_0_5064,
[final] ).
cnf(c_0_6710,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
c_0_5065,
[final] ).
cnf(c_0_6711,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5066,
[final] ).
cnf(c_0_6712,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) ),
c_0_5067,
[final] ).
cnf(c_0_6713,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) ),
c_0_5068,
[final] ).
cnf(c_0_6714,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5069,
[final] ).
cnf(c_0_6715,plain,
( X2 = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
c_0_5070,
[final] ).
cnf(c_0_6716,plain,
( X2 = X3
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Rings_Oinverse__class_Oinverse(X1,X3) ),
c_0_5071,
[final] ).
cnf(c_0_6717,plain,
( X1 = X2
| c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X3) ),
c_0_5072,
[final] ).
cnf(c_0_6718,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_5073,
[final] ).
cnf(c_0_6719,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
c_0_5074,
[final] ).
cnf(c_0_6720,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
c_0_5075,
[final] ).
cnf(c_0_6721,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
c_0_5076,
[final] ).
cnf(c_0_6722,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
c_0_5077,
[final] ).
cnf(c_0_6723,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) = X1,
c_0_5078,
[final] ).
cnf(c_0_6724,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
c_0_5079,
[final] ).
cnf(c_0_6725,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
c_0_5080,
[final] ).
cnf(c_0_6726,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),
c_0_5081,
[final] ).
cnf(c_0_6727,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
c_0_5082,
[final] ).
cnf(c_0_6728,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
c_0_5083,
[final] ).
cnf(c_0_6729,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
c_0_5084,
[final] ).
cnf(c_0_6730,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
c_0_5085,
[final] ).
cnf(c_0_6731,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
c_0_5086,
[final] ).
cnf(c_0_6732,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
c_0_5087,
[final] ).
cnf(c_0_6733,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X3) != X2 ),
c_0_5088,
[final] ).
cnf(c_0_6734,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X3) != X2 ),
c_0_5089,
[final] ).
cnf(c_0_6735,plain,
( c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,X3)
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 != X3 ),
c_0_5090,
[final] ).
cnf(c_0_6736,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5091,
[final] ).
cnf(c_0_6737,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_5092,
[final] ).
cnf(c_0_6738,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5093,
[final] ).
cnf(c_0_6739,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5094,
[final] ).
cnf(c_0_6740,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Oone__class_Oone(X1) ),
c_0_5095,
[final] ).
cnf(c_0_6741,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5096,
[final] ).
cnf(c_0_6742,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_5097,
[final] ).
cnf(c_0_6743,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Oinverse(X2,X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring(X2) ),
c_0_5098,
[final] ).
cnf(c_0_6744,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| X2 != X3 ),
c_0_5099,
[final] ).
cnf(c_0_6745,plain,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Oinverse(X1,X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 != X3 ),
c_0_5100,
[final] ).
cnf(c_0_6746,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_5101,
[final] ).
cnf(c_0_6747,plain,
( class_Orderings_Oord(tc_fun(X1,X2))
| ~ class_Orderings_Oord(X2) ),
c_0_5102,
[final] ).
cnf(c_0_6748,plain,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
c_0_5103,
[final] ).
cnf(c_0_6749,plain,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
c_0_5104,
[final] ).
cnf(c_0_6750,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = X1,
c_0_5105,
[final] ).
cnf(c_0_6751,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X2 ),
c_0_5106,
[final] ).
cnf(c_0_6752,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X2 ),
c_0_5107,
[final] ).
cnf(c_0_6753,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
c_0_5108,
[final] ).
cnf(c_0_6754,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5109,
[final] ).
cnf(c_0_6755,plain,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
c_0_5110,
[final] ).
cnf(c_0_6756,plain,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5111,
[final] ).
cnf(c_0_6757,plain,
( c_RealVector_Onorm__class_Onorm(X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5112,
[final] ).
cnf(c_0_6758,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
c_0_5113,
[final] ).
cnf(c_0_6759,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_5114,
[final] ).
cnf(c_0_6760,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
c_0_5115,
[final] ).
cnf(c_0_6761,plain,
( 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) ),
c_0_5116,
[final] ).
cnf(c_0_6762,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5117,
[final] ).
cnf(c_0_6763,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5118,
[final] ).
cnf(c_0_6764,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
c_0_5119,
[final] ).
cnf(c_0_6765,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_5120,
[final] ).
cnf(c_0_6766,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk32_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
c_0_5121,
[final] ).
cnf(c_0_6767,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk14_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
c_0_5122,
[final] ).
cnf(c_0_6768,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
c_0_5123,
[final] ).
cnf(c_0_6769,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii),
c_0_5124,
[final] ).
cnf(c_0_6770,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Oone(X1)
| c_Groups_Oone__class_Oone(X1) != X2 ),
c_0_5125,
[final] ).
cnf(c_0_6771,plain,
( c_Groups_Oone__class_Oone(X1) = X2
| ~ class_Groups_Oone(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
c_0_5126,
[final] ).
cnf(c_0_6772,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
c_0_5127,
[final] ).
cnf(c_0_6773,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| ~ class_Groups_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5128,
[final] ).
cnf(c_0_6774,plain,
( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1) ),
c_0_5129,
[final] ).
cnf(c_0_6775,plain,
( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1) ),
c_0_5130,
[final] ).
cnf(c_0_6776,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_5131,
[final] ).
cnf(c_0_6777,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_5132,
[final] ).
cnf(c_0_6778,plain,
( class_Rings_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5133,
[final] ).
cnf(c_0_6779,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5134,
[final] ).
cnf(c_0_6780,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
c_0_5135,
[final] ).
cnf(c_0_6781,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
c_0_5136,
[final] ).
cnf(c_0_6782,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
c_0_5137,
[final] ).
cnf(c_0_6783,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5138,
[final] ).
cnf(c_0_6784,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
c_0_5139,
[final] ).
cnf(c_0_6785,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5140,
[final] ).
cnf(c_0_6786,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5141,
[final] ).
cnf(c_0_6787,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5142,
[final] ).
cnf(c_0_6788,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5143,
[final] ).
cnf(c_0_6789,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
c_0_5144,
[final] ).
cnf(c_0_6790,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5145,
[final] ).
cnf(c_0_6791,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_5146,
[final] ).
cnf(c_0_6792,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5147,
[final] ).
cnf(c_0_6793,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_5148,
[final] ).
cnf(c_0_6794,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
c_0_5149,
[final] ).
cnf(c_0_6795,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5150,
[final] ).
cnf(c_0_6796,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5151,
[final] ).
cnf(c_0_6797,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5152,
[final] ).
cnf(c_0_6798,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5153,
[final] ).
cnf(c_0_6799,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5154,
[final] ).
cnf(c_0_6800,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_5155,
[final] ).
cnf(c_0_6801,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5156,
[final] ).
cnf(c_0_6802,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
c_0_5157,
[final] ).
cnf(c_0_6803,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5158,
[final] ).
cnf(c_0_6804,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5159,
[final] ).
cnf(c_0_6805,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5160,
[final] ).
cnf(c_0_6806,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5161,
[final] ).
cnf(c_0_6807,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_5162,
[final] ).
cnf(c_0_6808,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
c_0_5163,
[final] ).
cnf(c_0_6809,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5164,
[final] ).
cnf(c_0_6810,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_5165,
[final] ).
cnf(c_0_6811,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5166,
[final] ).
cnf(c_0_6812,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5167,
[final] ).
cnf(c_0_6813,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5168,
[final] ).
cnf(c_0_6814,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5169,
[final] ).
cnf(c_0_6815,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
c_0_5170,
[final] ).
cnf(c_0_6816,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5171,
[final] ).
cnf(c_0_6817,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5172,
[final] ).
cnf(c_0_6818,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5173,
[final] ).
cnf(c_0_6819,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
c_0_5174,
[final] ).
cnf(c_0_6820,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5175,
[final] ).
cnf(c_0_6821,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5176,
[final] ).
cnf(c_0_6822,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
c_0_5177,
[final] ).
cnf(c_0_6823,plain,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
c_0_5178,
[final] ).
cnf(c_0_6824,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5179,
[final] ).
cnf(c_0_6825,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5180,
[final] ).
cnf(c_0_6826,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5181,
[final] ).
cnf(c_0_6827,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5182,
[final] ).
cnf(c_0_6828,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5183,
[final] ).
cnf(c_0_6829,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5184,
[final] ).
cnf(c_0_6830,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5185,
[final] ).
cnf(c_0_6831,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5186,
[final] ).
cnf(c_0_6832,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
c_0_5187,
[final] ).
cnf(c_0_6833,plain,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
c_0_5188,
[final] ).
cnf(c_0_6834,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
c_0_5189,
[final] ).
cnf(c_0_6835,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
c_0_5190,
[final] ).
cnf(c_0_6836,plain,
( c_Nat_OSuc(X1) = c_Nat_OSuc(X2)
| X1 != X2 ),
c_0_5191,
[final] ).
cnf(c_0_6837,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5192,
[final] ).
cnf(c_0_6838,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5193,
[final] ).
cnf(c_0_6839,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5194,
[final] ).
cnf(c_0_6840,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5195,
[final] ).
cnf(c_0_6841,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5196,
[final] ).
cnf(c_0_6842,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5197,
[final] ).
cnf(c_0_6843,plain,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
c_0_5198,
[final] ).
cnf(c_0_6844,plain,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_5199,
[final] ).
cnf(c_0_6845,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_5200,
[final] ).
cnf(c_0_6846,plain,
c_Nat_OSuc(X1) != X1,
c_0_5201,
[final] ).
cnf(c_0_6847,plain,
c_Nat_OSuc(X1) != X1,
c_0_5202,
[final] ).
cnf(c_0_6848,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_5203,
[final] ).
cnf(c_0_6849,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != esk26_0,
c_0_5204,
[final] ).
cnf(c_0_6850,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != esk25_0,
c_0_5205,
[final] ).
cnf(c_0_6851,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
c_0_5206,
[final] ).
cnf(c_0_6852,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
c_0_5207,
[final] ).
cnf(c_0_6853,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_w____,
c_0_5208,
[final] ).
cnf(c_0_6854,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_a____,
c_0_5209,
[final] ).
cnf(c_0_6855,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != v_k____,
c_0_5210,
[final] ).
cnf(c_0_6856,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
c_0_5211,
[final] ).
cnf(c_0_6857,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
c_0_5212,
[final] ).
cnf(c_0_6858,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
c_0_5213,
[final] ).
cnf(c_0_6859,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
c_0_5214,
[final] ).
cnf(c_0_6860,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
c_0_5215,
[final] ).
cnf(c_0_6861,plain,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_5216,
[final] ).
cnf(c_0_6862,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
c_0_5217,
[final] ).
cnf(c_0_6863,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
c_0_5218,
[final] ).
cnf(c_0_6864,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
c_0_5219,
[final] ).
cnf(c_0_6865,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
c_0_5220,
[final] ).
cnf(c_0_6866,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
c_0_5221,
[final] ).
cnf(c_0_6867,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
c_0_5222,
[final] ).
cnf(c_0_6868,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
c_0_5223,
[final] ).
cnf(c_0_6869,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
c_0_5224,
[final] ).
cnf(c_0_6870,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
c_0_5225,
[final] ).
cnf(c_0_6871,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_5226,
[final] ).
cnf(c_0_6872,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
c_0_5227,
[final] ).
cnf(c_0_6873,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_5228,
[final] ).
cnf(c_0_6874,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
c_0_5229,
[final] ).
cnf(c_0_6875,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_5230,
[final] ).
cnf(c_0_6876,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
c_0_5231,
[final] ).
cnf(c_0_6877,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_5232,
[final] ).
cnf(c_0_6878,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_5233,
[final] ).
cnf(c_0_6879,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_5234,
[final] ).
cnf(c_0_6880,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_5235,
[final] ).
cnf(c_0_6881,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_5236,
[final] ).
cnf(c_0_6882,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_5237,
[final] ).
cnf(c_0_6883,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_5238,
[final] ).
cnf(c_0_6884,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
c_0_5239,
[final] ).
cnf(c_0_6885,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_5240,
[final] ).
cnf(c_0_6886,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_5241,
[final] ).
cnf(c_0_6887,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
c_0_5242,
[final] ).
cnf(c_0_6888,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_5243,
[final] ).
cnf(c_0_6889,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_5244,
[final] ).
cnf(c_0_6890,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_5245,
[final] ).
cnf(c_0_6891,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
c_0_5246,
[final] ).
cnf(c_0_6892,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
c_0_5247,
[final] ).
cnf(c_0_6893,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
c_0_5248,
[final] ).
cnf(c_0_6894,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
c_0_5249,
[final] ).
cnf(c_0_6895,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
c_0_5250,
[final] ).
cnf(c_0_6896,plain,
class_Groups_Oone(tc_RealDef_Oreal),
c_0_5251,
[final] ).
cnf(c_0_6897,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
c_0_5252,
[final] ).
cnf(c_0_6898,plain,
class_Rings_Oring(tc_RealDef_Oreal),
c_0_5253,
[final] ).
cnf(c_0_6899,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
c_0_5254,
[final] ).
cnf(c_0_6900,plain,
class_Power_Opower(tc_RealDef_Oreal),
c_0_5255,
[final] ).
cnf(c_0_6901,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
c_0_5256,
[final] ).
cnf(c_0_6902,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
c_0_5257,
[final] ).
cnf(c_0_6903,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
c_0_5258,
[final] ).
cnf(c_0_6904,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
c_0_5259,
[final] ).
cnf(c_0_6905,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
c_0_5260,
[final] ).
cnf(c_0_6906,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
c_0_5261,
[final] ).
cnf(c_0_6907,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
c_0_5262,
[final] ).
cnf(c_0_6908,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
c_0_5263,
[final] ).
cnf(c_0_6909,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
c_0_5264,
[final] ).
cnf(c_0_6910,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
c_0_5265,
[final] ).
cnf(c_0_6911,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
c_0_5266,
[final] ).
cnf(c_0_6912,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
c_0_5267,
[final] ).
cnf(c_0_6913,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
c_0_5268,
[final] ).
cnf(c_0_6914,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
c_0_5269,
[final] ).
cnf(c_0_6915,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
c_0_5270,
[final] ).
cnf(c_0_6916,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
c_0_5271,
[final] ).
cnf(c_0_6917,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
c_0_5272,
[final] ).
cnf(c_0_6918,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
c_0_5273,
[final] ).
cnf(c_0_6919,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
c_0_5274,
[final] ).
cnf(c_0_6920,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
c_0_5275,
[final] ).
cnf(c_0_6921,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
c_0_5276,
[final] ).
cnf(c_0_6922,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
c_0_5277,
[final] ).
cnf(c_0_6923,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
c_0_5278,
[final] ).
cnf(c_0_6924,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
c_0_5279,
[final] ).
cnf(c_0_6925,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
c_0_5280,
[final] ).
cnf(c_0_6926,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
c_0_5281,
[final] ).
cnf(c_0_6927,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
c_0_5282,
[final] ).
cnf(c_0_6928,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
c_0_5283,
[final] ).
cnf(c_0_6929,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
c_0_5284,
[final] ).
cnf(c_0_6930,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
c_0_5285,
[final] ).
cnf(c_0_6931,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
c_0_5286,
[final] ).
cnf(c_0_6932,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
c_0_5287,
[final] ).
cnf(c_0_6933,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
c_0_5288,
[final] ).
cnf(c_0_6934,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
c_0_5289,
[final] ).
cnf(c_0_6935,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
c_0_5290,
[final] ).
cnf(c_0_6936,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
c_0_5291,
[final] ).
cnf(c_0_6937,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
c_0_5292,
[final] ).
cnf(c_0_6938,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
c_0_5293,
[final] ).
cnf(c_0_6939,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
c_0_5294,
[final] ).
cnf(c_0_6940,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
c_0_5295,
[final] ).
cnf(c_0_6941,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
c_0_5296,
[final] ).
cnf(c_0_6942,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
c_0_5297,
[final] ).
cnf(c_0_6943,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
c_0_5298,
[final] ).
cnf(c_0_6944,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_5299,
[final] ).
cnf(c_0_6945,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
c_0_5300,
[final] ).
cnf(c_0_6946,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
c_0_5301,
[final] ).
cnf(c_0_6947,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
c_0_5302,
[final] ).
cnf(c_0_6948,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
c_0_5303,
[final] ).
cnf(c_0_6949,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
c_0_5304,
[final] ).
cnf(c_0_6950,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
c_0_5305,
[final] ).
cnf(c_0_6951,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
c_0_5306,
[final] ).
cnf(c_0_6952,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
c_0_5307,
[final] ).
cnf(c_0_6953,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
c_0_5308,
[final] ).
cnf(c_0_6954,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
c_0_5309,
[final] ).
cnf(c_0_6955,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
c_0_5310,
[final] ).
cnf(c_0_6956,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
c_0_5311,
[final] ).
cnf(c_0_6957,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_5312,
[final] ).
cnf(c_0_6958,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
c_0_5313,
[final] ).
cnf(c_0_6959,plain,
class_Orderings_Oord(tc_HOL_Obool),
c_0_5314,
[final] ).
cnf(c_0_6960,plain,
class_Orderings_Oorder(tc_HOL_Obool),
c_0_5315,
[final] ).
cnf(c_0_6961,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
c_0_5316,
[final] ).
cnf(c_0_6962,plain,
class_Rings_Odvd(tc_Nat_Onat),
c_0_5317,
[final] ).
cnf(c_0_6963,plain,
class_Groups_Oone(tc_Nat_Onat),
c_0_5318,
[final] ).
cnf(c_0_6964,plain,
class_Groups_Ozero(tc_Nat_Onat),
c_0_5319,
[final] ).
cnf(c_0_6965,plain,
class_Power_Opower(tc_Nat_Onat),
c_0_5320,
[final] ).
cnf(c_0_6966,plain,
class_Orderings_Oord(tc_Nat_Onat),
c_0_5321,
[final] ).
cnf(c_0_6967,plain,
class_Rings_Osemiring(tc_Nat_Onat),
c_0_5322,
[final] ).
cnf(c_0_6968,plain,
class_Orderings_Oorder(tc_Nat_Onat),
c_0_5323,
[final] ).
cnf(c_0_6969,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
c_0_5324,
[final] ).
cnf(c_0_6970,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
c_0_5325,
[final] ).
cnf(c_0_6971,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
c_0_5326,
[final] ).
cnf(c_0_6972,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
c_0_5327,
[final] ).
cnf(c_0_6973,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
c_0_5328,
[final] ).
cnf(c_0_6974,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
c_0_5329,
[final] ).
cnf(c_0_6975,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
c_0_5330,
[final] ).
cnf(c_0_6976,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
c_0_5331,
[final] ).
cnf(c_0_6977,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
c_0_5332,
[final] ).
cnf(c_0_6978,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
c_0_5333,
[final] ).
cnf(c_0_6979,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
c_0_5334,
[final] ).
cnf(c_0_6980,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
c_0_5335,
[final] ).
cnf(c_0_6981,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
c_0_5336,
[final] ).
cnf(c_0_6982,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
c_0_5337,
[final] ).
cnf(c_0_6983,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
c_0_5338,
[final] ).
cnf(c_0_6984,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
c_0_5339,
[final] ).
cnf(c_0_6985,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
c_0_5340,
[final] ).
cnf(c_0_6986,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
c_0_5341,
[final] ).
cnf(c_0_6987,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
c_0_5342,
[final] ).
cnf(c_0_6988,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
c_0_5343,
[final] ).
cnf(c_0_6989,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
c_0_5344,
[final] ).
cnf(c_0_6990,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
c_0_5345,
[final] ).
cnf(c_0_6991,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
c_0_5346,
[final] ).
cnf(c_0_6992,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
c_0_5347,
[final] ).
cnf(c_0_6993,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
c_0_5348,
[final] ).
cnf(c_0_6994,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
c_0_5349,
[final] ).
cnf(c_0_6995,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
c_0_5350,
[final] ).
cnf(c_0_6996,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
c_0_5351,
[final] ).
cnf(c_0_6997,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
c_0_5352,
[final] ).
cnf(c_0_6998,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
c_0_5353,
[final] ).
cnf(c_0_6999,plain,
class_Rings_Odvd(tc_Int_Oint),
c_0_5354,
[final] ).
cnf(c_0_7000,plain,
class_Groups_Oone(tc_Int_Oint),
c_0_5355,
[final] ).
cnf(c_0_7001,plain,
class_Rings_Oidom(tc_Int_Oint),
c_0_5356,
[final] ).
cnf(c_0_7002,plain,
class_Rings_Oring(tc_Int_Oint),
c_0_5357,
[final] ).
cnf(c_0_7003,plain,
class_Groups_Ozero(tc_Int_Oint),
c_0_5358,
[final] ).
cnf(c_0_7004,plain,
class_Power_Opower(tc_Int_Oint),
c_0_5359,
[final] ).
cnf(c_0_7005,plain,
class_Rings_Oring__1(tc_Int_Oint),
c_0_5360,
[final] ).
cnf(c_0_7006,plain,
class_Orderings_Oord(tc_Int_Oint),
c_0_5361,
[final] ).
cnf(c_0_7007,plain,
class_Rings_Osemiring(tc_Int_Oint),
c_0_5362,
[final] ).
cnf(c_0_7008,plain,
class_Int_Oring__char__0(tc_Int_Oint),
c_0_5363,
[final] ).
cnf(c_0_7009,plain,
class_Orderings_Oorder(tc_Int_Oint),
c_0_5364,
[final] ).
cnf(c_0_7010,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
c_0_5365,
[final] ).
cnf(c_0_7011,plain,
class_Rings_Omult__zero(tc_Int_Oint),
c_0_5366,
[final] ).
cnf(c_0_7012,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
c_0_5367,
[final] ).
cnf(c_0_7013,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
c_0_5368,
[final] ).
cnf(c_0_7014,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
c_0_5369,
[final] ).
cnf(c_0_7015,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
c_0_5370,
[final] ).
cnf(c_0_7016,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
c_0_5371,
[final] ).
cnf(c_0_7017,plain,
class_Orderings_Olinorder(tc_Int_Oint),
c_0_5372,
[final] ).
cnf(c_0_7018,plain,
class_Orderings_Opreorder(tc_Int_Oint),
c_0_5373,
[final] ).
cnf(c_0_7019,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
c_0_5374,
[final] ).
cnf(c_0_7020,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
c_0_5375,
[final] ).
cnf(c_0_7021,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
c_0_5376,
[final] ).
cnf(c_0_7022,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
c_0_5377,
[final] ).
cnf(c_0_7023,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
c_0_5378,
[final] ).
cnf(c_0_7024,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
c_0_5379,
[final] ).
cnf(c_0_7025,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
c_0_5380,
[final] ).
cnf(c_0_7026,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
c_0_5381,
[final] ).
cnf(c_0_7027,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
c_0_5382,
[final] ).
cnf(c_0_7028,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
c_0_5383,
[final] ).
cnf(c_0_7029,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
c_0_5384,
[final] ).
cnf(c_0_7030,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
c_0_5385,
[final] ).
cnf(c_0_7031,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
c_0_5386,
[final] ).
cnf(c_0_7032,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
c_0_5387,
[final] ).
cnf(c_0_7033,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
c_0_5388,
[final] ).
cnf(c_0_7034,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
c_0_5389,
[final] ).
cnf(c_0_7035,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
c_0_5390,
[final] ).
cnf(c_0_7036,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
c_0_5391,
[final] ).
cnf(c_0_7037,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
c_0_5392,
[final] ).
cnf(c_0_7038,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
c_0_5393,
[final] ).
cnf(c_0_7039,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
c_0_5394,
[final] ).
cnf(c_0_7040,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
c_0_5395,
[final] ).
cnf(c_0_7041,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
c_0_5396,
[final] ).
cnf(c_0_7042,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
c_0_5397,
[final] ).
cnf(c_0_7043,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
c_0_5398,
[final] ).
cnf(c_0_7044,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
c_0_5399,
[final] ).
cnf(c_0_7045,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
c_0_5400,
[final] ).
cnf(c_0_7046,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
c_0_5401,
[final] ).
cnf(c_0_7047,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
c_0_5402,
[final] ).
cnf(c_0_7048,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
c_0_5403,
[final] ).
cnf(c_0_7049,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
c_0_5404,
[final] ).
cnf(c_0_7050,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
c_0_5405,
[final] ).
cnf(c_0_7051,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
c_0_5406,
[final] ).
cnf(c_0_7052,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
c_0_5407,
[final] ).
cnf(c_0_7053,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
c_0_5408,
[final] ).
cnf(c_0_7054,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
c_0_5409,
[final] ).
cnf(c_0_7055,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
c_0_5410,
[final] ).
cnf(c_0_7056,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
c_0_5411,
[final] ).
cnf(c_0_7057,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_5412,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_5413_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| ~ class_Orderings_Oord(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,hAPP(X3,X5),hAPP(X3,sk1_esk31_4(X3,X5,X1,X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5413_1,axiom,
( ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,hAPP(X3,X5),hAPP(X3,sk1_esk31_4(X3,X5,X1,X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5413_2,axiom,
( ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,hAPP(X3,X5),hAPP(X3,sk1_esk31_4(X3,X5,X1,X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5413_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,hAPP(X3,X5),hAPP(X3,sk1_esk31_4(X3,X5,X1,X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5413_4,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,hAPP(X3,X5),hAPP(X3,sk1_esk31_4(X3,X5,X1,X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5414_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5414_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5415_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
inference(literals_permutation,[status(thm)],[c_0_5415]) ).
cnf(c_0_5415_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5415]) ).
cnf(c_0_5418_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X2,X3))),X3)
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X2,X3))),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_2,axiom,
( ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X2,X3))),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5419_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X3,X2))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5419_1,axiom,
( ~ class_Rings_Oidom(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X3,X2))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5419_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X3,X2))),X2)
| ~ class_Rings_Oidom(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5420_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),sk1_esk18_0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) ),
inference(literals_permutation,[status(thm)],[c_0_5420]) ).
cnf(c_0_5420_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),sk1_esk18_0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5420]) ).
cnf(c_0_5423_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,sk1_esk28_4(X4,X3,X2,X1)),hAPP(X4,sk1_esk28_4(X4,X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5423_1,axiom,
( ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,sk1_esk28_4(X4,X3,X2,X1)),hAPP(X4,sk1_esk28_4(X4,X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5423_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,sk1_esk28_4(X4,X3,X2,X1)),hAPP(X4,sk1_esk28_4(X4,X3,X2,X1)))
| ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5425_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),c_Groups_Ominus__class_Ominus(X1,X3,X5))) = 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))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5425]) ).
cnf(c_0_5425_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),c_Groups_Ominus__class_Ominus(X1,X3,X5))) = 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5425]) ).
cnf(c_0_5427_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),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)),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(literals_permutation,[status(thm)],[c_0_5427]) ).
cnf(c_0_5427_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),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)),c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X3),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5427]) ).
cnf(c_0_5428_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5428]) ).
cnf(c_0_5428_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5428]) ).
cnf(c_0_5428_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5428]) ).
cnf(c_0_5429_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5429_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5429_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5430_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5431_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5432_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5433_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5434_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5435_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5437_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Oorder(X1,X3,X2)),X2)
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Oorder(X1,X3,X2)),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_2,axiom,
( ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Oorder(X1,X3,X2)),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5438_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),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(literals_permutation,[status(thm)],[c_0_5438]) ).
cnf(c_0_5438_1,axiom,
( ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),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) ),
inference(literals_permutation,[status(thm)],[c_0_5438]) ).
cnf(c_0_5439_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5440_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5441_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5441_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5441_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5442_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5443_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5444_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5444_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5444_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5445_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5446_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5447_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sk1_esk4_2(X2,X1)),X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5447]) ).
cnf(c_0_5447_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sk1_esk4_2(X2,X1)),X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5447]) ).
cnf(c_0_5447_2,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sk1_esk4_2(X2,X1)),X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5447]) ).
cnf(c_0_5448_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5448]) ).
cnf(c_0_5448_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5448]) ).
cnf(c_0_5449_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3))) = c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5449_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3))) = c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5449_2,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3))) = c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5449_3,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3))) = c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5450_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5450]) ).
cnf(c_0_5450_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5450]) ).
cnf(c_0_5451_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5451]) ).
cnf(c_0_5451_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5451]) ).
cnf(c_0_5452_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5452]) ).
cnf(c_0_5452_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5452]) ).
cnf(c_0_5454_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5454]) ).
cnf(c_0_5454_1,axiom,
( ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5454]) ).
cnf(c_0_5454_2,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5454]) ).
cnf(c_0_5454_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5454]) ).
cnf(c_0_5454_4,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5454]) ).
cnf(c_0_5455_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5455]) ).
cnf(c_0_5455_1,axiom,
( ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5455]) ).
cnf(c_0_5455_2,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5455]) ).
cnf(c_0_5455_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5455]) ).
cnf(c_0_5455_4,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X3)),X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5455]) ).
cnf(c_0_5457_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_4,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_5,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_6,axiom,
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X6))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5458_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_4,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_5,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_6,axiom,
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5459_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2)),X4))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5460_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),sk1_esk35_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),sk1_esk35_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5461_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_2,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_3,axiom,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5462_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_4,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5463_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_4,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5464_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4) != X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5465_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X4 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)
| X4 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_2,axiom,
( X4 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5466_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| ~ class_Rings_Oring(X1)
| X4 != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5466]) ).
cnf(c_0_5466_1,axiom,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| X4 != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5466]) ).
cnf(c_0_5466_2,axiom,
( X4 != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5466]) ).
cnf(c_0_5467_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4) != X6 ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5467_1,axiom,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4) != X6 ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5467_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4) != X6
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5468_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_1,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_2,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_3,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_4,axiom,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5469_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)) = 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))
| ~ class_Rings_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5469_1,axiom,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)) = 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5470_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5470_1,axiom,
( ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5470_2,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5470_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5470_4,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5471_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5471_1,axiom,
( ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ class_Rings_Ocomm__ring(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5471_2,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5471_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5471_4,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5472_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4) = X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4) = X5
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5473_0,axiom,
( X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5473_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5473_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5474_0,axiom,
( X2 = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6)
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5474]) ).
cnf(c_0_5474_1,axiom,
( ~ class_Rings_Oring(X1)
| X2 = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5474]) ).
cnf(c_0_5474_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6)
| ~ class_Rings_Oring(X1)
| X2 = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5474]) ).
cnf(c_0_5475_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5) = X6
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5475]) ).
cnf(c_0_5475_1,axiom,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5) = X6
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5475]) ).
cnf(c_0_5475_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)
| ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5) = X6 ),
inference(literals_permutation,[status(thm)],[c_0_5475]) ).
cnf(c_0_5476_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3),X5)
| ~ class_Rings_Osemiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5476]) ).
cnf(c_0_5476_1,axiom,
( ~ class_Rings_Osemiring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5476]) ).
cnf(c_0_5477_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X5))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X5))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X5))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5479_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| c_Orderings_Oord__class_Oless__eq(X1,X5,sk1_esk31_4(X3,X5,X1,X2))
| ~ class_Orderings_Oord(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5479_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X5,sk1_esk31_4(X3,X5,X1,X2))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| ~ class_Orderings_Oord(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5479_2,axiom,
( ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X5,sk1_esk31_4(X3,X5,X1,X2))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5479_3,axiom,
( ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X5,sk1_esk31_4(X3,X5,X1,X2))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5))))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5479_4,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X4)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X5,sk1_esk31_4(X3,X5,X1,X2))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5480_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X3,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X3,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_2,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X3,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_3,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X3,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5481_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Oplus__class_Oplus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Oplus__class_Oplus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_2,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Oplus__class_Oplus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_3,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Oplus__class_Oplus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5482_0,axiom,
( c_Orderings_Oord__class_Oless(X1,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)),X6)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_1,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless(X1,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)),X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless(X1,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)),X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless(X1,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)),X6)
| ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_4,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless(X1,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)),X6)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_5,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
| ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless(X1,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)),X6)
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_6,axiom,
( ~ class_Rings_Olinordered__semiring__1__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
| ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless(X1,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)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5483_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,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)),X6)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_1,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless__eq(X1,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)),X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless__eq(X1,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)),X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless__eq(X1,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)),X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_4,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless__eq(X1,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)),X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_5,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless__eq(X1,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)),X6)
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_6,axiom,
( ~ class_Rings_Olinordered__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
| c_Orderings_Oord__class_Oless__eq(X1,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)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5484_0,axiom,
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),sk1_esk30_3(X3,X2,X1))))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_1,axiom,
( ~ class_Rings_Osemiring__0(X1)
| hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),sk1_esk30_3(X3,X2,X1))))
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_2,axiom,
( ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1)
| hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),sk1_esk30_3(X3,X2,X1))))
| ~ hBOOL(hAPP(X2,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_3,axiom,
( ~ hBOOL(hAPP(X2,X4))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1)
| hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),sk1_esk30_3(X3,X2,X1))))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_4,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(X2,X4))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1)
| hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),sk1_esk30_3(X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5486_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3)),X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3)),X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3)),X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_3,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5487_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X4))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_2,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5488_0,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5489_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5489_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5490_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,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(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,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(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5491_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,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(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,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(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5492_0,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,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))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_1,axiom,
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,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(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5494_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5494_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5495_0,axiom,
( hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_1,axiom,
( ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2)
| ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5496_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_3,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5497_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_2,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5498_0,axiom,
( hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X3,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_1,axiom,
( ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X3,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X3,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2)
| ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5499_0,axiom,
( X2 = X3
| X4 = X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)) != 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_1,axiom,
( X4 = X5
| X2 = X3
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)) != 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_2,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X4 = X5
| X2 = X3
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)) != 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_3,axiom,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)) != 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))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X4 = X5
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5500_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) != 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_1,axiom,
( X2 = X4
| X3 = X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) != 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_2,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X4
| X3 = X5
| 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)) != 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_3,axiom,
( 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)) != 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)
| X2 = X4
| X3 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5503_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(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)),X2),c_Polynomial_OpCons(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(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)),X2),c_Polynomial_OpCons(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5504_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_Rings_Oring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_1,axiom,
( ~ class_Rings_Oring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5505_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,sk1_esk29_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_1,axiom,
( ~ class_Rings_Osemiring__0(X1)
| c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,sk1_esk29_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_2,axiom,
( ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1)
| c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,sk1_esk29_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_3,axiom,
( ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1)
| c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,sk1_esk29_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5506_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_3,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5507_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5508_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5509_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),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))) = c_Polynomial_Opcompose(X1,c_Polynomial_OpCons(X1,X2,X3),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5509_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),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))) = c_Polynomial_Opcompose(X1,c_Polynomial_OpCons(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5510_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5510_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5511_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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))) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5514_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5514_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5515_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,sk1_esk6_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,sk1_esk6_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk6_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5516_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,sk1_esk5_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5516_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,sk1_esk5_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5516_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk5_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5517_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk6_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5517]) ).
cnf(c_0_5517_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,sk1_esk6_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5517]) ).
cnf(c_0_5517_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk6_3(X3,X2,X1)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5517]) ).
cnf(c_0_5518_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk5_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5518_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,sk1_esk5_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5518_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk5_3(X3,X2,X1)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5519_0,axiom,
( 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X5))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5519]) ).
cnf(c_0_5519_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5519]) ).
cnf(c_0_5520_0,axiom,
( 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))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5520]) ).
cnf(c_0_5520_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| 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))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5520]) ).
cnf(c_0_5520_2,axiom,
( ~ 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))
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5520]) ).
cnf(c_0_5520_3,axiom,
( ~ 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))
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5520]) ).
cnf(c_0_5521_0,axiom,
( 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_Oplus__class_Oplus(tc_Int_Oint,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(literals_permutation,[status(thm)],[c_0_5521]) ).
cnf(c_0_5521_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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(literals_permutation,[status(thm)],[c_0_5521]) ).
cnf(c_0_5522_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X5))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5522_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X5))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5522_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X5))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5522_3,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5525_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5525_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5526_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5526]) ).
cnf(c_0_5526_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5526]) ).
cnf(c_0_5527_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5527_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5527_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5527_3,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5528_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5528_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5528_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5528_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5529_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(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,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_4,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_5,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5530_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5530_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5530_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5530_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(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_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5530_4,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(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_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5530_5,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(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_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5531_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_4,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_5,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5532_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_4,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_5,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5533_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_4,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_5,axiom,
( ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5534_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_4,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_5,axiom,
( ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5535_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X5))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X5))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X5))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_3,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),X5)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5536_0,axiom,
( hBOOL(hAPP(X2,sk1_esk29_3(X3,X2,X1)))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5536_1,axiom,
( ~ class_Rings_Osemiring__0(X1)
| hBOOL(hAPP(X2,sk1_esk29_3(X3,X2,X1)))
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5536_2,axiom,
( ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1)
| hBOOL(hAPP(X2,sk1_esk29_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5536_3,axiom,
( ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1)
| hBOOL(hAPP(X2,sk1_esk29_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5537_0,axiom,
( c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3),c_Polynomial_Osynthetic__div(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,c_Polynomial_Osynthetic__div(X1,X2,X3)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5537_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3),c_Polynomial_Osynthetic__div(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,c_Polynomial_Osynthetic__div(X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5538_0,axiom,
( 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)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5538]) ).
cnf(c_0_5538_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5538]) ).
cnf(c_0_5539_0,axiom,
( 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)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5539]) ).
cnf(c_0_5539_1,axiom,
( ~ class_Groups_Ocomm__monoid__mult(X1)
| 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)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5539]) ).
cnf(c_0_5540_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3)
| ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X3),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_1,axiom,
( ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3)
| hAPP(c_Polynomial_Opoly(X1,X3),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_2,axiom,
( hAPP(c_Polynomial_Opoly(X1,X3),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5541_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(X4)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(X4)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(X4)))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(X4)))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5542_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5542_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,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))
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5542_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,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))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5542_3,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,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(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5543_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3)
| ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5543]) ).
cnf(c_0_5543_1,axiom,
( ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3)
| hAPP(c_Polynomial_Opoly(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5543]) ).
cnf(c_0_5543_2,axiom,
( hAPP(c_Polynomial_Opoly(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5543]) ).
cnf(c_0_5544_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5544_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5544_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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))) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5545_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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)))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5545_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5545_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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))) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5546_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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)))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_1,axiom,
( ~ class_Rings_Olinordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),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))) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5547_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5547]) ).
cnf(c_0_5547_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5547]) ).
cnf(c_0_5548_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1))) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5548_1,axiom,
( ~ class_Rings_Oring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1))) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5549_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_OpCons(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_OpCons(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5550_0,axiom,
( 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)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_1,axiom,
( ~ 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_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_2,axiom,
( ~ 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_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5551_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5552_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(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) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(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) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(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,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5553_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(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) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(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) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5554_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5554_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5554_2,axiom,
( ~ 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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5554_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ 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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5555_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5555_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ 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(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5555_2,axiom,
( ~ 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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Rings_Olinordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5555_3,axiom,
( ~ class_Rings_Olinordered__semiring(X1)
| ~ 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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5556_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_2,axiom,
( ~ 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))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ 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))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5557_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ 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(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5557_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ 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(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5557_2,axiom,
( ~ 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))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Rings_Olinordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5557_3,axiom,
( ~ class_Rings_Olinordered__semiring(X1)
| ~ 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))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5558_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5558_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5558_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5558_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5559_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5559_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5559_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5559_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5560_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5560_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5560_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5560_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5561_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ 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),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_3,axiom,
( ~ 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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5562_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(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(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X1,X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_3,axiom,
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5563_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5564_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ 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(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5565_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ 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(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ 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)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_3,axiom,
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5566_0,axiom,
( c_Polynomial_OpCons(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X5)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Polynomial_OpCons(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X5)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5567_0,axiom,
( c_Polynomial_OpCons(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X5)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5))
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Polynomial_OpCons(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X5)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5568_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5568_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5569_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5))
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5569_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5570_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5570_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5571_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5571_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5571_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X4,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5571_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5571_4,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5572_0,axiom,
( 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,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5572_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| 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_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5572_2,axiom,
( ~ 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))
| 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(tc_Nat_Onat,X4,X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5572_3,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
| ~ 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))
| 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))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5572_4,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
| ~ 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))
| 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(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5573_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_4,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5574_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5574]) ).
cnf(c_0_5574_1,axiom,
( 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)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5574]) ).
cnf(c_0_5574_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(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),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),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5574]) ).
cnf(c_0_5574_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(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),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5574]) ).
cnf(c_0_5575_0,axiom,
( 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))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5575_1,axiom,
( 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)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5575_2,axiom,
( ~ 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,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)) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5575_3,axiom,
( ~ 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)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5576_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sk1_esk34_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5576]) ).
cnf(c_0_5576_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sk1_esk34_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5576]) ).
cnf(c_0_5577_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),sk1_esk33_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5577]) ).
cnf(c_0_5577_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),sk1_esk33_2(X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5577]) ).
cnf(c_0_5578_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5578]) ).
cnf(c_0_5578_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5578]) ).
cnf(c_0_5579_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5579_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5580_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5580]) ).
cnf(c_0_5580_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5580]) ).
cnf(c_0_5581_0,axiom,
( 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),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5581_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5582_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5582]) ).
cnf(c_0_5582_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5582]) ).
cnf(c_0_5583_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5583_1,axiom,
( ~ class_Rings_Ocomm__semiring(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5584_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5584]) ).
cnf(c_0_5584_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5584]) ).
cnf(c_0_5585_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5585_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5586_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5586]) ).
cnf(c_0_5586_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X4,X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5586]) ).
cnf(c_0_5586_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5586]) ).
cnf(c_0_5586_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5586]) ).
cnf(c_0_5587_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5587_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5587_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,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),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5587_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5588_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5588_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5588_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5588_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5589_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5589_1,axiom,
( 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)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5589_2,axiom,
( ~ 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,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)) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5589_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5590_0,axiom,
( 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)) = 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)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_5590]) ).
cnf(c_0_5590_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) = 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))
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_5590]) ).
cnf(c_0_5590_2,axiom,
( X2 != X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) = 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5590]) ).
cnf(c_0_5591_0,axiom,
( 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)) = 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)
| X3 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5591]) ).
cnf(c_0_5591_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) = 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))
| X3 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5591]) ).
cnf(c_0_5591_2,axiom,
( X3 != X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) = 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5591]) ).
cnf(c_0_5592_0,axiom,
( 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)) = 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)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_5592]) ).
cnf(c_0_5592_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) = 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))
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_5592]) ).
cnf(c_0_5592_2,axiom,
( X2 != X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) = 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5592]) ).
cnf(c_0_5593_0,axiom,
( 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)) = 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)
| X3 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5593]) ).
cnf(c_0_5593_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) = 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))
| X3 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5593]) ).
cnf(c_0_5593_2,axiom,
( X3 != X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| 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)) = 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5593]) ).
cnf(c_0_5594_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5594]) ).
cnf(c_0_5594_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X4,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5594]) ).
cnf(c_0_5594_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X2)
| c_Orderings_Oord__class_Oless(X1,X2,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),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5594]) ).
cnf(c_0_5594_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5594]) ).
cnf(c_0_5595_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5596_0,axiom,
( 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5596]) ).
cnf(c_0_5596_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5596]) ).
cnf(c_0_5597_0,axiom,
( 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5597]) ).
cnf(c_0_5597_1,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5597]) ).
cnf(c_0_5598_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5598_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5599_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5599]) ).
cnf(c_0_5599_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5599]) ).
cnf(c_0_5600_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5600]) ).
cnf(c_0_5600_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5600]) ).
cnf(c_0_5601_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5601_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5601_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5601_3,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5602_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5602]) ).
cnf(c_0_5602_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5602]) ).
cnf(c_0_5602_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5602]) ).
cnf(c_0_5602_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5602]) ).
cnf(c_0_5603_0,axiom,
( X4 = X6
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != c_Groups_Oplus__class_Oplus(X1,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X6))
| X2 != X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5603]) ).
cnf(c_0_5603_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| X4 = X6
| c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != c_Groups_Oplus__class_Oplus(X1,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X6))
| X2 != X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5603]) ).
cnf(c_0_5603_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != c_Groups_Oplus__class_Oplus(X1,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X6))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X4 = X6
| X2 != X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5603]) ).
cnf(c_0_5603_3,axiom,
( X2 != X5
| c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != c_Groups_Oplus__class_Oplus(X1,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X6))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X4 = X6
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5603]) ).
cnf(c_0_5603_4,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 != X5
| c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != c_Groups_Oplus__class_Oplus(X1,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X6))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X4 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_5603]) ).
cnf(c_0_5604_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5604_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5604_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5605_0,axiom,
( 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)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5605]) ).
cnf(c_0_5605_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5605]) ).
cnf(c_0_5605_2,axiom,
( ~ 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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5605]) ).
cnf(c_0_5606_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ 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(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5606_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ 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(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5606_2,axiom,
( ~ 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)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5607_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5607_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5607_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5608_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5608_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5608_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5609_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5609]) ).
cnf(c_0_5609_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5609]) ).
cnf(c_0_5609_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5609]) ).
cnf(c_0_5610_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5610]) ).
cnf(c_0_5610_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5610]) ).
cnf(c_0_5610_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5610]) ).
cnf(c_0_5611_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(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(literals_permutation,[status(thm)],[c_0_5611]) ).
cnf(c_0_5611_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5611]) ).
cnf(c_0_5611_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5611]) ).
cnf(c_0_5612_0,axiom,
( 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_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5612]) ).
cnf(c_0_5612_1,axiom,
( ~ 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)
| ~ 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(literals_permutation,[status(thm)],[c_0_5612]) ).
cnf(c_0_5612_2,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_5612]) ).
cnf(c_0_5613_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5613]) ).
cnf(c_0_5613_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5613]) ).
cnf(c_0_5613_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5613]) ).
cnf(c_0_5614_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5614]) ).
cnf(c_0_5614_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(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(literals_permutation,[status(thm)],[c_0_5614]) ).
cnf(c_0_5614_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5614]) ).
cnf(c_0_5615_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5615]) ).
cnf(c_0_5615_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5615]) ).
cnf(c_0_5616_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5616]) ).
cnf(c_0_5616_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5616]) ).
cnf(c_0_5617_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5617]) ).
cnf(c_0_5617_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5617]) ).
cnf(c_0_5618_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5618_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5619_0,axiom,
( c_Polynomial_Osmult(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5619]) ).
cnf(c_0_5619_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5619]) ).
cnf(c_0_5620_0,axiom,
( 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),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5621_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5621_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5622_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5622]) ).
cnf(c_0_5622_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5622]) ).
cnf(c_0_5623_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)),X4)
| ~ class_Rings_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5623]) ).
cnf(c_0_5623_1,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| c_Groups_Ominus__class_Ominus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5623]) ).
cnf(c_0_5624_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X5),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5624]) ).
cnf(c_0_5624_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X4)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X5),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5624]) ).
cnf(c_0_5624_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X5),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5624]) ).
cnf(c_0_5624_3,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X5),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5624]) ).
cnf(c_0_5625_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5625_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,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),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5625_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5626_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5627_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5627_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5627_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5628_0,axiom,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5628_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,X4))
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5628_2,axiom,
( X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5629_0,axiom,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5629_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,X4))
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5629_2,axiom,
( X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5630_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5630_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5630_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5631_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5631_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5631_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5637_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5637]) ).
cnf(c_0_5637_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5637]) ).
cnf(c_0_5638_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5638]) ).
cnf(c_0_5638_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5638]) ).
cnf(c_0_5638_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5638]) ).
cnf(c_0_5639_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5639]) ).
cnf(c_0_5639_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5639]) ).
cnf(c_0_5639_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5639]) ).
cnf(c_0_5640_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5640]) ).
cnf(c_0_5640_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5640]) ).
cnf(c_0_5640_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5640]) ).
cnf(c_0_5641_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5641]) ).
cnf(c_0_5641_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5641]) ).
cnf(c_0_5641_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5641]) ).
cnf(c_0_5642_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5642]) ).
cnf(c_0_5642_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),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(literals_permutation,[status(thm)],[c_0_5642]) ).
cnf(c_0_5642_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5642]) ).
cnf(c_0_5643_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5643]) ).
cnf(c_0_5643_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),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(literals_permutation,[status(thm)],[c_0_5643]) ).
cnf(c_0_5643_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5643]) ).
cnf(c_0_5644_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5644]) ).
cnf(c_0_5644_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5644]) ).
cnf(c_0_5644_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5644]) ).
cnf(c_0_5645_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5645]) ).
cnf(c_0_5645_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5645]) ).
cnf(c_0_5645_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5645]) ).
cnf(c_0_5646_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5646_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5646_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5647_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_1,axiom,
( X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Oidom(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_2,axiom,
( ~ class_Rings_Oidom(X1)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_3,axiom,
( ~ 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))
| ~ class_Rings_Oidom(X1)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5648_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_1,axiom,
( X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Oidom(X1)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_2,axiom,
( ~ class_Rings_Oidom(X1)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_3,axiom,
( ~ 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))
| ~ class_Rings_Oidom(X1)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5649_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5650_0,axiom,
( 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)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5650_1,axiom,
( ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5650_2,axiom,
( ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5653_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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(literals_permutation,[status(thm)],[c_0_5653]) ).
cnf(c_0_5653_1,axiom,
( ~ 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_Oplus__class_Oplus(tc_Int_Oint,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(literals_permutation,[status(thm)],[c_0_5653]) ).
cnf(c_0_5654_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5654]) ).
cnf(c_0_5654_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5654]) ).
cnf(c_0_5654_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5654]) ).
cnf(c_0_5654_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5654]) ).
cnf(c_0_5655_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5655]) ).
cnf(c_0_5655_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5655]) ).
cnf(c_0_5655_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5655]) ).
cnf(c_0_5655_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5655]) ).
cnf(c_0_5657_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_OpCons(X2,X4,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5657_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_OpCons(X2,X4,X1)) != 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(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5657_2,axiom,
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_OpCons(X2,X4,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5658_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5658]) ).
cnf(c_0_5658_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5658]) ).
cnf(c_0_5659_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5659]) ).
cnf(c_0_5659_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5659]) ).
cnf(c_0_5660_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5660_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5660_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5660_3,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5662_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk6_3(X3,X2,X1)) = X2
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5662]) ).
cnf(c_0_5662_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk6_3(X3,X2,X1)) = X2
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5662]) ).
cnf(c_0_5662_2,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk6_3(X3,X2,X1)) = X2
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5662]) ).
cnf(c_0_5663_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk5_3(X3,X2,X1)) = X2
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5663]) ).
cnf(c_0_5663_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk5_3(X3,X2,X1)) = X2
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5663]) ).
cnf(c_0_5663_2,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk5_3(X3,X2,X1)) = X2
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5663]) ).
cnf(c_0_5664_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5664]) ).
cnf(c_0_5664_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5664]) ).
cnf(c_0_5664_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5664]) ).
cnf(c_0_5664_3,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5664]) ).
cnf(c_0_5665_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5665]) ).
cnf(c_0_5665_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5665]) ).
cnf(c_0_5666_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5666]) ).
cnf(c_0_5666_1,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5666]) ).
cnf(c_0_5667_0,axiom,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X3)
| ~ class_Rings_Olinordered__semidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5667_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X3)
| ~ class_Rings_Olinordered__semidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5667_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X3)
| ~ class_Rings_Olinordered__semidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5667_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| X1 = X2
| hAPP(hAPP(c_Power_Opower__class_Opower(X4),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X3)
| ~ class_Rings_Olinordered__semidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5667_4,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X4),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| X1 = X2
| ~ class_Rings_Olinordered__semidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5667_5,axiom,
( ~ class_Rings_Olinordered__semidom(X4)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5668_0,axiom,
( 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),c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5668_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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),c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5669_0,axiom,
( 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),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5669_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5670_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk6_3(X3,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk6_3(X3,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk6_3(X3,X2,X1)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5671_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk5_3(X3,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk5_3(X3,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk5_3(X3,X2,X1)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5672_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_4,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5673_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5673_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5673_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5673_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5673_4,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5674_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_RealVector_Onorm__class_Onorm(X2,X4)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5674_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_RealVector_Onorm__class_Onorm(X2,X4)))
| X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5674_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_RealVector_Onorm__class_Onorm(X2,X4)))
| X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5674_3,axiom,
( ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_RealVector_Onorm__class_Onorm(X2,X4)))
| X1 = c_Groups_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5675_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5675_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5675_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(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__eq(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5675_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5676_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5676_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(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__eq(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5676_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(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__eq(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5676_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5677_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5677]) ).
cnf(c_0_5677_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5677]) ).
cnf(c_0_5677_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5677]) ).
cnf(c_0_5677_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5677]) ).
cnf(c_0_5678_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5678_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(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__eq(X1,X4,X3)
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5678_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5678_3,axiom,
( ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5679_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5679]) ).
cnf(c_0_5679_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5679]) ).
cnf(c_0_5679_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5679]) ).
cnf(c_0_5679_3,axiom,
( ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5679]) ).
cnf(c_0_5680_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Oordered__comm__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5680]) ).
cnf(c_0_5680_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(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__eq(X1,X3,X4)
| ~ class_Rings_Oordered__comm__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5680]) ).
cnf(c_0_5680_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Oordered__comm__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5680]) ).
cnf(c_0_5680_3,axiom,
( ~ class_Rings_Oordered__comm__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5680]) ).
cnf(c_0_5681_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(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__eq(X1,X3,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_3,axiom,
( ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5682_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_3,axiom,
( ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5683_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5684_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5685_0,axiom,
( 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)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| 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,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_3,axiom,
( ~ 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)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5686_0,axiom,
( 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)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| 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,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5687_0,axiom,
( 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)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5687]) ).
cnf(c_0_5687_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5687]) ).
cnf(c_0_5687_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5687]) ).
cnf(c_0_5687_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5687]) ).
cnf(c_0_5688_0,axiom,
( 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)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5688_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| 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))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5688_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5688_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5689_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5689_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5689_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5689_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5690_0,axiom,
( 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__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_1,axiom,
( ~ 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))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ 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__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5691_0,axiom,
( 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__comm__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_1,axiom,
( ~ 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))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__comm__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ 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__comm__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_3,axiom,
( ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5692_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5692_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5692_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5692_3,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5693_0,axiom,
( 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))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_1,axiom,
( ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_2,axiom,
( ~ c_Orderings_Oord__class_Oless(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_3,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5694_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5694_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5695_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_3,axiom,
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5696_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_3,axiom,
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5697_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5697_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5697_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5697_3,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5698_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_3,axiom,
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5699_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5700_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5701_0,axiom,
( 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))
| ~ 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,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5701_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| 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)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5701_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| 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(tc_Nat_Onat,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5701_3,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| 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(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5702_0,axiom,
( 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)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5702_1,axiom,
( ~ 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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5702_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ 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))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5702_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ 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(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5703_0,axiom,
( 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,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5703_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| 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,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5704_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5704_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5705_0,axiom,
( 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,c_Groups_Ominus__class_Ominus(X1,X2,X4),X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5705]) ).
cnf(c_0_5705_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| 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,c_Groups_Ominus__class_Ominus(X1,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5705]) ).
cnf(c_0_5706_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
| ~ class_Rings_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5706]) ).
cnf(c_0_5706_1,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5706]) ).
cnf(c_0_5707_0,axiom,
( 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),X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5707]) ).
cnf(c_0_5707_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
| 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),X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5707]) ).
cnf(c_0_5707_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
| 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),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5707]) ).
cnf(c_0_5707_3,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
| 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),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5707]) ).
cnf(c_0_5708_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_2,axiom,
( ~ class_Power_Opower(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5709_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5709_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X5))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5709_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5709_3,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5710_0,axiom,
( c_Polynomial_OpCons(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Polynomial_OpCons(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5710_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_OpCons(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Polynomial_OpCons(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5711_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5711_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5711_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5712_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5712_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5712_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5713_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5713_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5713_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5714_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5714]) ).
cnf(c_0_5714_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5714]) ).
cnf(c_0_5714_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5714]) ).
cnf(c_0_5715_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5715]) ).
cnf(c_0_5715_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5715]) ).
cnf(c_0_5715_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5715]) ).
cnf(c_0_5716_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5716_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| 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(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5716_2,axiom,
( 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)
| ~ class_Rings_Olinordered__ring__strict(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5717_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5717_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| 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(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5717_2,axiom,
( 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)
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5718_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5718]) ).
cnf(c_0_5718_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5718]) ).
cnf(c_0_5719_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5719]) ).
cnf(c_0_5719_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5719]) ).
cnf(c_0_5720_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5720]) ).
cnf(c_0_5720_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5720]) ).
cnf(c_0_5721_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5721_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5722_0,axiom,
( 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5722]) ).
cnf(c_0_5722_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5722]) ).
cnf(c_0_5723_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5723]) ).
cnf(c_0_5723_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5723]) ).
cnf(c_0_5723_2,axiom,
( ~ 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)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5723]) ).
cnf(c_0_5724_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5724]) ).
cnf(c_0_5724_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5724]) ).
cnf(c_0_5724_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X1))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5724]) ).
cnf(c_0_5725_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5725]) ).
cnf(c_0_5725_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5725]) ).
cnf(c_0_5725_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5725]) ).
cnf(c_0_5726_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5726]) ).
cnf(c_0_5726_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5726]) ).
cnf(c_0_5726_2,axiom,
( ~ 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)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5726]) ).
cnf(c_0_5727_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5727]) ).
cnf(c_0_5727_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5727]) ).
cnf(c_0_5727_2,axiom,
( ~ 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))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5727]) ).
cnf(c_0_5728_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5728]) ).
cnf(c_0_5728_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5728]) ).
cnf(c_0_5728_2,axiom,
( ~ 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)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5728]) ).
cnf(c_0_5729_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| ~ 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(literals_permutation,[status(thm)],[c_0_5729]) ).
cnf(c_0_5729_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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(literals_permutation,[status(thm)],[c_0_5729]) ).
cnf(c_0_5729_2,axiom,
( ~ 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))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_5729]) ).
cnf(c_0_5730_0,axiom,
( 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,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(literals_permutation,[status(thm)],[c_0_5730]) ).
cnf(c_0_5730_1,axiom,
( ~ 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),X3),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5730]) ).
cnf(c_0_5731_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5731]) ).
cnf(c_0_5731_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_5731]) ).
cnf(c_0_5732_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5732]) ).
cnf(c_0_5732_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5732]) ).
cnf(c_0_5733_0,axiom,
( 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,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5733]) ).
cnf(c_0_5733_1,axiom,
( ~ 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,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5733]) ).
cnf(c_0_5733_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ 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)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5733]) ).
cnf(c_0_5733_3,axiom,
( ~ 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),X3),X2))
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_5733]) ).
cnf(c_0_5734_0,axiom,
( 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,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5734]) ).
cnf(c_0_5734_1,axiom,
( ~ 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,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5734]) ).
cnf(c_0_5734_2,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5734]) ).
cnf(c_0_5734_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5734]) ).
cnf(c_0_5735_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,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),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5735]) ).
cnf(c_0_5735_1,axiom,
( ~ 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),X3),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5735]) ).
cnf(c_0_5736_0,axiom,
( 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5736]) ).
cnf(c_0_5736_1,axiom,
( ~ 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,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5736]) ).
cnf(c_0_5737_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5737]) ).
cnf(c_0_5737_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5737]) ).
cnf(c_0_5738_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5738]) ).
cnf(c_0_5738_1,axiom,
( ~ class_Groups_Oab__semigroup__mult(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5738]) ).
cnf(c_0_5739_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5739]) ).
cnf(c_0_5739_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5739]) ).
cnf(c_0_5740_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5740]) ).
cnf(c_0_5740_1,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5740]) ).
cnf(c_0_5741_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5741]) ).
cnf(c_0_5741_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5741]) ).
cnf(c_0_5742_0,axiom,
( X4 = c_Polynomial_Osynthetic__div(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) != c_Polynomial_OpCons(X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5742]) ).
cnf(c_0_5742_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| X4 = c_Polynomial_Osynthetic__div(X1,X2,X3)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) != c_Polynomial_OpCons(X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5742]) ).
cnf(c_0_5742_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) != c_Polynomial_OpCons(X1,X5,X4)
| ~ class_Rings_Ocomm__semiring__0(X1)
| X4 = c_Polynomial_Osynthetic__div(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5742]) ).
cnf(c_0_5743_0,axiom,
( c_Polynomial_Osynthetic__div(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = 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(literals_permutation,[status(thm)],[c_0_5743]) ).
cnf(c_0_5743_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osynthetic__div(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X3),X4),c_Polynomial_Osynthetic__div(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5743]) ).
cnf(c_0_5744_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5744]) ).
cnf(c_0_5744_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5744]) ).
cnf(c_0_5745_0,axiom,
( 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_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5745]) ).
cnf(c_0_5745_1,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5745]) ).
cnf(c_0_5746_0,axiom,
( 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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5746_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| 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_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5746_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| 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(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5747_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5747_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5747_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5748_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5748]) ).
cnf(c_0_5748_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5748]) ).
cnf(c_0_5748_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5748]) ).
cnf(c_0_5749_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5749]) ).
cnf(c_0_5749_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5749]) ).
cnf(c_0_5749_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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__eq(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(literals_permutation,[status(thm)],[c_0_5749]) ).
cnf(c_0_5750_0,axiom,
( c_Orderings_Oord__class_Oless(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))
| ~ 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,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5750_1,axiom,
( ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5750_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| ~ 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,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(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5751_0,axiom,
( 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),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5751_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,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),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5751_2,axiom,
( ~ 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,X1,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),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5752_0,axiom,
( 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,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5752_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5752_2,axiom,
( ~ 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)
| 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(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5753_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5753]) ).
cnf(c_0_5753_1,axiom,
( ~ 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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5753]) ).
cnf(c_0_5753_2,axiom,
( ~ 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_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5753]) ).
cnf(c_0_5754_0,axiom,
( 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),X3),X2))
| ~ 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,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5754_1,axiom,
( ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5754_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ 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,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(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5755_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5755_1,axiom,
( ~ 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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5755_2,axiom,
( ~ 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_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5756_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5756_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5756_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5757_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5757_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5757_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5758_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5758_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5759_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5759_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5760_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5760_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5761_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5761]) ).
cnf(c_0_5761_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5761]) ).
cnf(c_0_5762_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5762]) ).
cnf(c_0_5762_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5762]) ).
cnf(c_0_5763_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5763_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
| c_Orderings_Oord__class_Oless__eq(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),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5763_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
| c_Orderings_Oord__class_Oless__eq(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),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5764_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5764]) ).
cnf(c_0_5764_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5764]) ).
cnf(c_0_5765_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5765_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5766_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5766]) ).
cnf(c_0_5766_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5766]) ).
cnf(c_0_5767_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5767_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5768_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5768]) ).
cnf(c_0_5768_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5768]) ).
cnf(c_0_5769_0,axiom,
( X5 = hAPP(c_Polynomial_Opoly(X1,X2),X3)
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) != c_Polynomial_OpCons(X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5769_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| X5 = hAPP(c_Polynomial_Opoly(X1,X2),X3)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) != c_Polynomial_OpCons(X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5769_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) != c_Polynomial_OpCons(X1,X5,X4)
| ~ class_Rings_Ocomm__semiring__0(X1)
| X5 = hAPP(c_Polynomial_Opoly(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5770_0,axiom,
( c_Polynomial_Osmult(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5770_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Osmult(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5771_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5771_1,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5771_2,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5771_3,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5772_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5772_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5772_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5772_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5773_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Osmult(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5773]) ).
cnf(c_0_5773_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Osmult(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5773]) ).
cnf(c_0_5774_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5774_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5774_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5774_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5775_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5775_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5775_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5775_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5776_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5777_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5778_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5779_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5780_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5781_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5782_0,axiom,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),c_Nat_OSuc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X4))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),c_Nat_OSuc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X4))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| X1 = X2
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),c_Nat_OSuc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X4))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_3,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),c_Nat_OSuc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X4))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| X1 = X2
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_4,axiom,
( ~ class_Rings_Olinordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),c_Nat_OSuc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X4))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5783_0,axiom,
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5783_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5784_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5784_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5784_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5789_0,axiom,
( hAPP(c_Polynomial_Opoly(X1,X2),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Opcompose(X1,X2,X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5789_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(c_Polynomial_Opoly(X1,X2),hAPP(c_Polynomial_Opoly(X1,X3),X4)) = hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Opcompose(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5790_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),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(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5790_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5791_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_3,axiom,
( ~ class_RealVector_Oreal__normed__div__algebra(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5792_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_2,axiom,
( ~ 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))
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_3,axiom,
( ~ 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))
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5793_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5793_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5794_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5794_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5796_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5797_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(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_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5798_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5798]) ).
cnf(c_0_5798_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5798]) ).
cnf(c_0_5798_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5798]) ).
cnf(c_0_5798_3,axiom,
( ~ 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__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5798]) ).
cnf(c_0_5799_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5799_1,axiom,
( ~ 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),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5799_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(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,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5799_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(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,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5800_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5800]) ).
cnf(c_0_5800_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5800]) ).
cnf(c_0_5800_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5800]) ).
cnf(c_0_5800_3,axiom,
( ~ 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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5800]) ).
cnf(c_0_5801_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5801]) ).
cnf(c_0_5801_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5801]) ).
cnf(c_0_5801_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5801]) ).
cnf(c_0_5801_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5801]) ).
cnf(c_0_5802_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5802]) ).
cnf(c_0_5802_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5802]) ).
cnf(c_0_5802_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5802]) ).
cnf(c_0_5802_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5802]) ).
cnf(c_0_5803_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ 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)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5803]) ).
cnf(c_0_5803_1,axiom,
( ~ 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),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5803]) ).
cnf(c_0_5803_2,axiom,
( ~ 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,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5803]) ).
cnf(c_0_5803_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5803]) ).
cnf(c_0_5804_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),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,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5804_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5804_2,axiom,
( ~ 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_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5804_3,axiom,
( ~ 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))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5805_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5805_1,axiom,
( ~ 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),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5806_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5806_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5807_0,axiom,
( 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_1,axiom,
( 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)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5812_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5812_1,axiom,
( ~ class_Rings_Oordered__cancel__semiring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5812_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5812_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5813_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5813]) ).
cnf(c_0_5813_1,axiom,
( ~ class_Rings_Oordered__cancel__semiring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5813]) ).
cnf(c_0_5813_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__cancel__semiring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5813]) ).
cnf(c_0_5813_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__cancel__semiring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5813]) ).
cnf(c_0_5814_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5814]) ).
cnf(c_0_5814_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5814]) ).
cnf(c_0_5814_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5814]) ).
cnf(c_0_5814_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5814]) ).
cnf(c_0_5815_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5815_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5815_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5815_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5816_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5816_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5816_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5816_3,axiom,
( ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5817_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5817_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5817_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5817_3,axiom,
( ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5818_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5818_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5818_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5818_3,axiom,
( ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5819_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5819_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5819_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5819_3,axiom,
( ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5820_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5820_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5820_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5820_3,axiom,
( ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5821_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5821_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5821_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5821_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5822_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5822]) ).
cnf(c_0_5822_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5822]) ).
cnf(c_0_5822_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5822]) ).
cnf(c_0_5822_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5822]) ).
cnf(c_0_5823_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5823]) ).
cnf(c_0_5823_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5823]) ).
cnf(c_0_5823_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5823]) ).
cnf(c_0_5823_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5823]) ).
cnf(c_0_5824_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5824_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5824_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5824_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5825_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5825]) ).
cnf(c_0_5825_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5825]) ).
cnf(c_0_5825_2,axiom,
( ~ 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)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5825]) ).
cnf(c_0_5825_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5825]) ).
cnf(c_0_5826_0,axiom,
( 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)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5826]) ).
cnf(c_0_5826_1,axiom,
( ~ 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_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5826]) ).
cnf(c_0_5826_2,axiom,
( ~ 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,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5826]) ).
cnf(c_0_5826_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5826]) ).
cnf(c_0_5827_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),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)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5827]) ).
cnf(c_0_5827_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5827]) ).
cnf(c_0_5827_2,axiom,
( ~ 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))
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5827]) ).
cnf(c_0_5827_3,axiom,
( ~ 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))
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5827]) ).
cnf(c_0_5828_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5828_1,axiom,
( ~ 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),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5828_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5828_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5829_0,axiom,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),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,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_2,axiom,
( ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5830_0,axiom,
( 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,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5830_1,axiom,
( ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5830_2,axiom,
( ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5830_3,axiom,
( ~ 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))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5831_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5831_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5831_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5832_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5832_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5832_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5833_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5833_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5833_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5834_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5834_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5834_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5835_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_2,axiom,
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5836_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5836_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5836_2,axiom,
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5837_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5837_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5837_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5838_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5838_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5838_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5839_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5839_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5839_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5840_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5840]) ).
cnf(c_0_5840_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5840]) ).
cnf(c_0_5840_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5840]) ).
cnf(c_0_5841_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5841_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5841_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5841_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5841_4,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5842_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sk1_esk24_0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(literals_permutation,[status(thm)],[c_0_5842]) ).
cnf(c_0_5842_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sk1_esk24_0) ),
inference(literals_permutation,[status(thm)],[c_0_5842]) ).
cnf(c_0_5843_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sk1_esk19_0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(literals_permutation,[status(thm)],[c_0_5843]) ).
cnf(c_0_5843_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),sk1_esk19_0) ),
inference(literals_permutation,[status(thm)],[c_0_5843]) ).
cnf(c_0_5844_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(literals_permutation,[status(thm)],[c_0_5844]) ).
cnf(c_0_5844_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1)),v_m____) ),
inference(literals_permutation,[status(thm)],[c_0_5844]) ).
cnf(c_0_5845_0,axiom,
( X3 = sk1_esk8_2(X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X1) != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5845_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X3 = sk1_esk8_2(X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X1) != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5845_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X3 = sk1_esk8_2(X2,X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X1) != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5845_3,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X1) != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X3 = sk1_esk8_2(X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5845_4,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X1) != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X3 = sk1_esk8_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5847_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5847_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5847_2,axiom,
( ~ 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)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5847_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5848_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5848_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5848_2,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5849_0,axiom,
( 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)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5849]) ).
cnf(c_0_5849_1,axiom,
( ~ class_Rings_Oidom(X1)
| 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))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5849]) ).
cnf(c_0_5849_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Oidom(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5849]) ).
cnf(c_0_5850_0,axiom,
( 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)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5850]) ).
cnf(c_0_5850_1,axiom,
( ~ class_Rings_Oidom(X1)
| 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))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5850]) ).
cnf(c_0_5850_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Rings_Oidom(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5850]) ).
cnf(c_0_5851_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5851]) ).
cnf(c_0_5851_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5851]) ).
cnf(c_0_5851_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5851]) ).
cnf(c_0_5851_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5851]) ).
cnf(c_0_5852_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5852_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5852_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5852_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5853_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5853]) ).
cnf(c_0_5853_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5853]) ).
cnf(c_0_5853_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5853]) ).
cnf(c_0_5853_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5853]) ).
cnf(c_0_5854_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5854]) ).
cnf(c_0_5854_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5854]) ).
cnf(c_0_5854_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5854]) ).
cnf(c_0_5854_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5854]) ).
cnf(c_0_5855_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5855]) ).
cnf(c_0_5855_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5855]) ).
cnf(c_0_5855_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5855]) ).
cnf(c_0_5855_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5855]) ).
cnf(c_0_5856_0,axiom,
( c_Rings_Odvd__class_Odvd(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__eq(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5856]) ).
cnf(c_0_5856_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5856]) ).
cnf(c_0_5856_2,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5856]) ).
cnf(c_0_5857_0,axiom,
( 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,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5857_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| 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,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5857_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5858_0,axiom,
( 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,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5858_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| 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,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5858_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5859_0,axiom,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5859_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5859_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5859_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5859_4,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5861_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5861_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5862_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5862]) ).
cnf(c_0_5862_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5862]) ).
cnf(c_0_5863_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5863]) ).
cnf(c_0_5863_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5863]) ).
cnf(c_0_5864_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5864]) ).
cnf(c_0_5864_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5864]) ).
cnf(c_0_5865_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5865]) ).
cnf(c_0_5865_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5865]) ).
cnf(c_0_5866_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5866]) ).
cnf(c_0_5866_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5866]) ).
cnf(c_0_5867_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5867]) ).
cnf(c_0_5867_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5867]) ).
cnf(c_0_5868_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5868]) ).
cnf(c_0_5868_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5868]) ).
cnf(c_0_5869_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5869]) ).
cnf(c_0_5869_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5869]) ).
cnf(c_0_5870_0,axiom,
( X3 = X2
| hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5870_1,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5870_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5870_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(X1,X2),X3))
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5871_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5871_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5871_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5871_3,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5872_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5872_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5872_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5872_3,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5873_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5873]) ).
cnf(c_0_5873_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5873]) ).
cnf(c_0_5873_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5873]) ).
cnf(c_0_5874_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5874_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5874_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5875_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5875_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5875_2,axiom,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5875_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5876_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5876_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5876_2,axiom,
( ~ class_Fields_Ofield(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5876_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Fields_Ofield(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5877_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5877_1,axiom,
( X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5877_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5877_3,axiom,
( ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5878_0,axiom,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5878_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5878_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = X3
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5878_3,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5879_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5879]) ).
cnf(c_0_5879_1,axiom,
( ~ 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_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5879]) ).
cnf(c_0_5879_2,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5879]) ).
cnf(c_0_5880_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5880]) ).
cnf(c_0_5880_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5880]) ).
cnf(c_0_5880_2,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5880]) ).
cnf(c_0_5881_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5881]) ).
cnf(c_0_5881_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5881]) ).
cnf(c_0_5881_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5881]) ).
cnf(c_0_5882_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5882]) ).
cnf(c_0_5882_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5882]) ).
cnf(c_0_5882_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5882]) ).
cnf(c_0_5883_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5883]) ).
cnf(c_0_5883_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5883]) ).
cnf(c_0_5883_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5883]) ).
cnf(c_0_5884_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5884]) ).
cnf(c_0_5884_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5884]) ).
cnf(c_0_5884_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5884]) ).
cnf(c_0_5885_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5885]) ).
cnf(c_0_5885_1,axiom,
( ~ class_Groups_Olinordered__ab__group__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),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5885]) ).
cnf(c_0_5885_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5885]) ).
cnf(c_0_5887_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5887]) ).
cnf(c_0_5887_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5887]) ).
cnf(c_0_5888_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5888]) ).
cnf(c_0_5888_1,axiom,
( ~ class_Groups_Oab__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5888]) ).
cnf(c_0_5889_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5889]) ).
cnf(c_0_5889_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5889]) ).
cnf(c_0_5890_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5890]) ).
cnf(c_0_5890_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5890]) ).
cnf(c_0_5891_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5891]) ).
cnf(c_0_5891_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5891]) ).
cnf(c_0_5892_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5892_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5892_2,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5892_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5892_4,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5893_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5893]) ).
cnf(c_0_5893_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5893]) ).
cnf(c_0_5894_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5894]) ).
cnf(c_0_5894_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5894]) ).
cnf(c_0_5895_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5895]) ).
cnf(c_0_5895_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5895]) ).
cnf(c_0_5896_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5896]) ).
cnf(c_0_5896_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5896]) ).
cnf(c_0_5897_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = c_Divides_Odiv__class_Odiv(X1,X2,X4)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5897]) ).
cnf(c_0_5897_1,axiom,
( X3 = 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),X4),X3)) = c_Divides_Odiv__class_Odiv(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5897]) ).
cnf(c_0_5897_2,axiom,
( ~ class_Divides_Osemiring__div(X1)
| X3 = 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),X4),X3)) = c_Divides_Odiv__class_Odiv(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5897]) ).
cnf(c_0_5898_0,axiom,
( 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)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5898]) ).
cnf(c_0_5898_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5898]) ).
cnf(c_0_5898_2,axiom,
( ~ class_Divides_Osemiring__div(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5898]) ).
cnf(c_0_5899_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5899_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5899_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5899_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5900_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5900_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5900_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5900_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5901_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5901_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5901_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5902_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5902]) ).
cnf(c_0_5902_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5902]) ).
cnf(c_0_5902_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5902]) ).
cnf(c_0_5903_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5903]) ).
cnf(c_0_5903_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5903]) ).
cnf(c_0_5903_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5903]) ).
cnf(c_0_5903_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5903]) ).
cnf(c_0_5904_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5904]) ).
cnf(c_0_5904_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5904]) ).
cnf(c_0_5904_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5904]) ).
cnf(c_0_5904_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5904]) ).
cnf(c_0_5905_0,axiom,
( c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Polynomial_Osmult(X1,X2,c_Polynomial_Omonom(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5905]) ).
cnf(c_0_5905_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Polynomial_Osmult(X1,X2,c_Polynomial_Omonom(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5905]) ).
cnf(c_0_5906_0,axiom,
( c_Polynomial_Osmult(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Polynomial_Osmult(X1,X2,c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5906]) ).
cnf(c_0_5906_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Polynomial_Osmult(X1,X2,c_Polynomial_Osmult(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5906]) ).
cnf(c_0_5907_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5907]) ).
cnf(c_0_5907_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5907]) ).
cnf(c_0_5907_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5907]) ).
cnf(c_0_5908_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5908]) ).
cnf(c_0_5908_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5908]) ).
cnf(c_0_5908_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5908]) ).
cnf(c_0_5909_0,axiom,
( 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),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5909]) ).
cnf(c_0_5909_1,axiom,
( ~ 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_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) ),
inference(literals_permutation,[status(thm)],[c_0_5909]) ).
cnf(c_0_5909_2,axiom,
( ~ 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_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5909]) ).
cnf(c_0_5910_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5910]) ).
cnf(c_0_5910_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5910]) ).
cnf(c_0_5910_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5910]) ).
cnf(c_0_5912_0,axiom,
( 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),c_Nat_OSuc(X3))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5912]) ).
cnf(c_0_5912_1,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| 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),c_Nat_OSuc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5912]) ).
cnf(c_0_5913_0,axiom,
( 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),c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5913]) ).
cnf(c_0_5913_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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),c_Nat_OSuc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5913]) ).
cnf(c_0_5914_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5914]) ).
cnf(c_0_5914_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5914]) ).
cnf(c_0_5914_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5914]) ).
cnf(c_0_5915_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5916_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| 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))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5916_1,axiom,
( 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))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5916_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| 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))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5917_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5917]) ).
cnf(c_0_5917_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5917]) ).
cnf(c_0_5917_2,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5917]) ).
cnf(c_0_5917_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5917]) ).
cnf(c_0_5918_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5918]) ).
cnf(c_0_5918_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5918]) ).
cnf(c_0_5918_2,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5918]) ).
cnf(c_0_5918_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5918]) ).
cnf(c_0_5919_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5919_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X5)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5919_2,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5919_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5920_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5920_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5920_2,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5920_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5921_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5921_1,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5921_2,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5921_3,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5922_0,axiom,
( X2 = 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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5922]) ).
cnf(c_0_5922_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5922]) ).
cnf(c_0_5922_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5922]) ).
cnf(c_0_5923_0,axiom,
( X2 = 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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5923_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5923_2,axiom,
( ~ 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)
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5924_0,axiom,
( 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_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5924]) ).
cnf(c_0_5924_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| 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(literals_permutation,[status(thm)],[c_0_5924]) ).
cnf(c_0_5925_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5925]) ).
cnf(c_0_5925_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5925]) ).
cnf(c_0_5926_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5926]) ).
cnf(c_0_5926_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5926]) ).
cnf(c_0_5927_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5927]) ).
cnf(c_0_5927_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5927]) ).
cnf(c_0_5928_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5928]) ).
cnf(c_0_5928_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5928]) ).
cnf(c_0_5929_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5929_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5938_0,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5938_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5938_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,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)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5939_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5939]) ).
cnf(c_0_5939_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5939]) ).
cnf(c_0_5940_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5940_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5941_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5941]) ).
cnf(c_0_5941_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5941]) ).
cnf(c_0_5942_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5942]) ).
cnf(c_0_5942_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5942]) ).
cnf(c_0_5943_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5943]) ).
cnf(c_0_5943_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5943]) ).
cnf(c_0_5944_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5944]) ).
cnf(c_0_5944_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5944]) ).
cnf(c_0_5944_2,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5944]) ).
cnf(c_0_5945_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5945]) ).
cnf(c_0_5945_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),X3)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5945]) ).
cnf(c_0_5945_2,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),X3)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5945]) ).
cnf(c_0_5946_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5946]) ).
cnf(c_0_5946_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5946]) ).
cnf(c_0_5946_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5946]) ).
cnf(c_0_5946_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5946]) ).
cnf(c_0_5947_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5947]) ).
cnf(c_0_5947_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5947]) ).
cnf(c_0_5947_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5947]) ).
cnf(c_0_5947_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5947]) ).
cnf(c_0_5948_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5948]) ).
cnf(c_0_5948_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5948]) ).
cnf(c_0_5949_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(literals_permutation,[status(thm)],[c_0_5949]) ).
cnf(c_0_5949_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,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(literals_permutation,[status(thm)],[c_0_5949]) ).
cnf(c_0_5950_0,axiom,
( 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5950]) ).
cnf(c_0_5950_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5950]) ).
cnf(c_0_5951_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5951]) ).
cnf(c_0_5951_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5951]) ).
cnf(c_0_5951_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5951]) ).
cnf(c_0_5952_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5952]) ).
cnf(c_0_5952_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5952]) ).
cnf(c_0_5953_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5953]) ).
cnf(c_0_5953_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5953]) ).
cnf(c_0_5954_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5954]) ).
cnf(c_0_5954_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5954]) ).
cnf(c_0_5955_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5955]) ).
cnf(c_0_5955_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5955]) ).
cnf(c_0_5956_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5956]) ).
cnf(c_0_5956_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5956]) ).
cnf(c_0_5957_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5957]) ).
cnf(c_0_5957_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5957]) ).
cnf(c_0_5958_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5958_1,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5958_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5958_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5958_4,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5959_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5959_1,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5959_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5959_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5959_4,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5960_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5960_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5960_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5960_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5961_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5961_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5961_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5961_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5962_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5962_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5962_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5962_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5963_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5963]) ).
cnf(c_0_5963_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5963]) ).
cnf(c_0_5963_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5963]) ).
cnf(c_0_5963_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5963]) ).
cnf(c_0_5964_0,axiom,
( c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5964]) ).
cnf(c_0_5964_1,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3)
| c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5964]) ).
cnf(c_0_5964_2,axiom,
( ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3)
| c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5964]) ).
cnf(c_0_5964_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3)
| c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5964]) ).
cnf(c_0_5965_0,axiom,
( X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5965_1,axiom,
( ~ class_Fields_Ofield(X1)
| X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5965_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5965_3,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5966_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5966]) ).
cnf(c_0_5966_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5966]) ).
cnf(c_0_5966_2,axiom,
( ~ 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))
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_5966]) ).
cnf(c_0_5967_0,axiom,
( 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),X2)
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5967]) ).
cnf(c_0_5967_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5967]) ).
cnf(c_0_5967_2,axiom,
( ~ 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))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5967]) ).
cnf(c_0_5968_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5968]) ).
cnf(c_0_5968_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5968]) ).
cnf(c_0_5969_0,axiom,
( c_Orderings_Oord__class_Oless__eq(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))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5969]) ).
cnf(c_0_5969_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(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(literals_permutation,[status(thm)],[c_0_5969]) ).
cnf(c_0_5970_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5970]) ).
cnf(c_0_5970_1,axiom,
( ~ class_Fields_Ofield(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5970]) ).
cnf(c_0_5970_2,axiom,
( X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5970]) ).
cnf(c_0_5970_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5970]) ).
cnf(c_0_5971_0,axiom,
( 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)
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5971]) ).
cnf(c_0_5971_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| 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)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5971]) ).
cnf(c_0_5971_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5971]) ).
cnf(c_0_5971_3,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| 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(literals_permutation,[status(thm)],[c_0_5971]) ).
cnf(c_0_5972_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5972]) ).
cnf(c_0_5972_1,axiom,
( ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_5972]) ).
cnf(c_0_5973_0,axiom,
( 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_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5973]) ).
cnf(c_0_5973_1,axiom,
( ~ 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),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5973]) ).
cnf(c_0_5974_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5974_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5974_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5974_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5975_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5975_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5975_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5975_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5976_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5976_1,axiom,
( ~ 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),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5976_2,axiom,
( ~ 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))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5976_3,axiom,
( ~ 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))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5977_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5977_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5977_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5977_3,axiom,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5978_0,axiom,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| X2 = X3
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5978_1,axiom,
( X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5978_2,axiom,
( ~ class_Rings_Oidom(X1)
| X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5978_3,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X1)
| X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5979_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5979]) ).
cnf(c_0_5979_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5979]) ).
cnf(c_0_5980_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5980]) ).
cnf(c_0_5980_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5980]) ).
cnf(c_0_5981_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5981]) ).
cnf(c_0_5981_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_5981]) ).
cnf(c_0_5982_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5982_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5983_0,axiom,
( 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_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5983]) ).
cnf(c_0_5983_1,axiom,
( ~ class_Divides_Osemiring__div(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_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5983]) ).
cnf(c_0_5983_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(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_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5983]) ).
cnf(c_0_5984_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5984_1,axiom,
( ~ 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),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5984_2,axiom,
( ~ 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),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5985_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5985]) ).
cnf(c_0_5985_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5985]) ).
cnf(c_0_5985_2,axiom,
( ~ c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2))
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5985]) ).
cnf(c_0_5986_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_5986]) ).
cnf(c_0_5986_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_5986]) ).
cnf(c_0_5986_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_5986]) ).
cnf(c_0_5986_3,axiom,
( X2 != X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5986]) ).
cnf(c_0_5987_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sk1_esk8_2(X2,X1)),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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5987]) ).
cnf(c_0_5987_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sk1_esk8_2(X2,X1)),X1) = X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5987]) ).
cnf(c_0_5987_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sk1_esk8_2(X2,X1)),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5987]) ).
cnf(c_0_5988_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sk1_esk7_2(X2,X1)),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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5988]) ).
cnf(c_0_5988_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sk1_esk7_2(X2,X1)),X1) = X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5988]) ).
cnf(c_0_5988_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sk1_esk7_2(X2,X1)),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5988]) ).
cnf(c_0_5989_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5989]) ).
cnf(c_0_5989_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5989]) ).
cnf(c_0_5989_2,axiom,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5989]) ).
cnf(c_0_5989_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5989]) ).
cnf(c_0_5990_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5990]) ).
cnf(c_0_5990_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5990]) ).
cnf(c_0_5990_2,axiom,
( ~ class_Fields_Ofield(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5990]) ).
cnf(c_0_5990_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,c_Polynomial_Osmult(X1,X2,X4))
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5990]) ).
cnf(c_0_5991_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_3,axiom,
( ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5992_0,axiom,
( 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)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_1,axiom,
( ~ class_Rings_Oidom(X1)
| 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))
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5993_0,axiom,
( 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)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5993_1,axiom,
( ~ class_Rings_Oidom(X1)
| 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))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5993_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5994_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5994_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5994_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5994_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5995_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5995]) ).
cnf(c_0_5995_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5995]) ).
cnf(c_0_5995_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5995]) ).
cnf(c_0_5995_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5995]) ).
cnf(c_0_5996_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5996_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5996_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5996_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5997_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5997_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5997_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5997_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5998_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5998_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5998_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5998_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5999_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5999]) ).
cnf(c_0_5999_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5999]) ).
cnf(c_0_5999_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5999]) ).
cnf(c_0_5999_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5999]) ).
cnf(c_0_6000_0,axiom,
( 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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6000_1,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6000_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6000_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6000_4,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6000_5,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6001_0,axiom,
( c_Polynomial_Opos__poly(X1,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_1,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Polynomial_Opos__poly(X1,X3)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_2,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_3,axiom,
( ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Polynomial_Opos__poly(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6002_0,axiom,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sk1_esk20_1(X1)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X1),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)) ),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6002_1,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X1))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sk1_esk20_1(X1)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X1),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)) ),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6002_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X1),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X1))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sk1_esk20_1(X1)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6003_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6003_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X4)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6003_2,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X4)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6004_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6004]) ).
cnf(c_0_6004_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6004]) ).
cnf(c_0_6004_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6004]) ).
cnf(c_0_6005_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6005_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6005_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6006_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6006_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,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)) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6006_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6007_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6007_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,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)) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6007_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6008_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6008_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6008_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6009_0,axiom,
( X3 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6009_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| X3 = X4
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6009_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| X3 = X4
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6009_3,axiom,
( 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)
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6010_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6010_1,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6010_2,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6010_3,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6011_0,axiom,
( X3 = X2
| hBOOL(hAPP(hAPP(X1,X2),X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6011_1,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| X3 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6011_2,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(hAPP(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6011_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(hAPP(X1,X2),X3))
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6014_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6014_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6014_2,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6015_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6015]) ).
cnf(c_0_6015_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6015]) ).
cnf(c_0_6015_2,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6015]) ).
cnf(c_0_6016_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6016]) ).
cnf(c_0_6016_1,axiom,
( ~ 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_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6016]) ).
cnf(c_0_6016_2,axiom,
( ~ class_Rings_Olinordered__semidom(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_Power_Opower__class_Opower(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6016]) ).
cnf(c_0_6017_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6017_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6017_2,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6017_3,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6018_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_2,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6019_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6019_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6019_2,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6019_3,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6020_0,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6020_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6021_0,axiom,
( ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6021_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6021_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6022_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6022]) ).
cnf(c_0_6022_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6022]) ).
cnf(c_0_6022_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6022]) ).
cnf(c_0_6023_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6023]) ).
cnf(c_0_6023_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6023]) ).
cnf(c_0_6023_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6023]) ).
cnf(c_0_6025_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6025]) ).
cnf(c_0_6025_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6025]) ).
cnf(c_0_6025_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6025]) ).
cnf(c_0_6026_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk8_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6026_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk8_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6026_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk8_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6027_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk7_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6027]) ).
cnf(c_0_6027_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk7_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6027]) ).
cnf(c_0_6027_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk7_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6027]) ).
cnf(c_0_6028_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(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__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6028]) ).
cnf(c_0_6028_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6028]) ).
cnf(c_0_6029_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6029]) ).
cnf(c_0_6029_1,axiom,
( ~ 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_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6029]) ).
cnf(c_0_6031_0,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ 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),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6031]) ).
cnf(c_0_6031_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ 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),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6031]) ).
cnf(c_0_6031_2,axiom,
( ~ 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,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6031]) ).
cnf(c_0_6032_0,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6032_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6032_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6033_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6033_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6034_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6034]) ).
cnf(c_0_6034_1,axiom,
( ~ class_Fields_Ofield__inverse__zero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6034]) ).
cnf(c_0_6035_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6035]) ).
cnf(c_0_6035_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6035]) ).
cnf(c_0_6035_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6035]) ).
cnf(c_0_6036_0,axiom,
( c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6036]) ).
cnf(c_0_6036_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6036]) ).
cnf(c_0_6037_0,axiom,
( c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6037_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6038_0,axiom,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6038_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6039_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6039]) ).
cnf(c_0_6039_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6039]) ).
cnf(c_0_6039_2,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6039]) ).
cnf(c_0_6040_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6040_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6040_2,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6041_0,axiom,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6041]) ).
cnf(c_0_6041_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6041]) ).
cnf(c_0_6042_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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(literals_permutation,[status(thm)],[c_0_6042]) ).
cnf(c_0_6042_1,axiom,
( ~ 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6042]) ).
cnf(c_0_6043_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6043]) ).
cnf(c_0_6043_1,axiom,
( ~ 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6043]) ).
cnf(c_0_6044_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6044]) ).
cnf(c_0_6044_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6044]) ).
cnf(c_0_6044_2,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6044]) ).
cnf(c_0_6045_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)) = c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6045]) ).
cnf(c_0_6045_1,axiom,
( ~ class_RealVector_Oreal__normed__div__algebra(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)) = c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6045]) ).
cnf(c_0_6046_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6046]) ).
cnf(c_0_6046_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6046]) ).
cnf(c_0_6047_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,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(literals_permutation,[status(thm)],[c_0_6047]) ).
cnf(c_0_6047_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6047]) ).
cnf(c_0_6048_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6048_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6049_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6049_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6050_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6050]) ).
cnf(c_0_6050_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6050]) ).
cnf(c_0_6053_0,axiom,
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sk1_esk12_2(X1,X2))) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6053]) ).
cnf(c_0_6053_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sk1_esk12_2(X1,X2))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6053]) ).
cnf(c_0_6054_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6054]) ).
cnf(c_0_6054_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_6054]) ).
cnf(c_0_6055_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,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(literals_permutation,[status(thm)],[c_0_6055]) ).
cnf(c_0_6055_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(literals_permutation,[status(thm)],[c_0_6055]) ).
cnf(c_0_6056_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6056]) ).
cnf(c_0_6056_1,axiom,
( ~ 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6056]) ).
cnf(c_0_6057_0,axiom,
( c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6057]) ).
cnf(c_0_6057_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6057]) ).
cnf(c_0_6057_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1)
| c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6057]) ).
cnf(c_0_6057_3,axiom,
( X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1)
| c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6057]) ).
cnf(c_0_6058_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6058]) ).
cnf(c_0_6058_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6058]) ).
cnf(c_0_6059_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6059]) ).
cnf(c_0_6059_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6059]) ).
cnf(c_0_6060_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6060]) ).
cnf(c_0_6060_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6060]) ).
cnf(c_0_6061_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6061_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6062_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6062]) ).
cnf(c_0_6062_1,axiom,
( ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6062]) ).
cnf(c_0_6062_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6062]) ).
cnf(c_0_6063_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6063]) ).
cnf(c_0_6063_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6063]) ).
cnf(c_0_6063_2,axiom,
( ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6063]) ).
cnf(c_0_6064_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6064]) ).
cnf(c_0_6064_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6064]) ).
cnf(c_0_6064_2,axiom,
( ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6064]) ).
cnf(c_0_6065_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6065]) ).
cnf(c_0_6065_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6065]) ).
cnf(c_0_6066_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6066]) ).
cnf(c_0_6066_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6066]) ).
cnf(c_0_6067_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6067]) ).
cnf(c_0_6067_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6067]) ).
cnf(c_0_6068_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6068]) ).
cnf(c_0_6068_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6068]) ).
cnf(c_0_6069_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6069]) ).
cnf(c_0_6069_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6069]) ).
cnf(c_0_6070_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6070]) ).
cnf(c_0_6070_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6070]) ).
cnf(c_0_6071_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6071]) ).
cnf(c_0_6071_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6071]) ).
cnf(c_0_6072_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6072]) ).
cnf(c_0_6072_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6072]) ).
cnf(c_0_6073_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6073]) ).
cnf(c_0_6073_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6073]) ).
cnf(c_0_6074_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6074]) ).
cnf(c_0_6074_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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(literals_permutation,[status(thm)],[c_0_6074]) ).
cnf(c_0_6075_0,axiom,
( c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6075]) ).
cnf(c_0_6075_1,axiom,
( X3 = X2
| c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6075]) ).
cnf(c_0_6075_2,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| X3 = X2
| c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6075]) ).
cnf(c_0_6075_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X3,X2)
| ~ class_Rings_Olinordered__idom(X1)
| X3 = X2
| c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6075]) ).
cnf(c_0_6076_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6076]) ).
cnf(c_0_6076_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6076]) ).
cnf(c_0_6076_2,axiom,
( X2 != 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)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6076]) ).
cnf(c_0_6077_0,axiom,
( 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)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6077]) ).
cnf(c_0_6077_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6077]) ).
cnf(c_0_6077_2,axiom,
( X2 != 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)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6077]) ).
cnf(c_0_6078_0,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6078_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6079_0,axiom,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| 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(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6079_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| 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(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6079_2,axiom,
( 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)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6080_0,axiom,
( c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),c_Polynomial_Omonom(X1,X2,X3)) = c_Polynomial_Omonom(X1,X2,c_Nat_OSuc(X3))
| ~ class_Groups_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6080]) ).
cnf(c_0_6080_1,axiom,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),c_Polynomial_Omonom(X1,X2,X3)) = c_Polynomial_Omonom(X1,X2,c_Nat_OSuc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6080]) ).
cnf(c_0_6081_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6081]) ).
cnf(c_0_6081_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6081]) ).
cnf(c_0_6082_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6082]) ).
cnf(c_0_6082_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_6082]) ).
cnf(c_0_6083_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6083]) ).
cnf(c_0_6083_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_6083]) ).
cnf(c_0_6084_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6084_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6084_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6084_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6085_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6085]) ).
cnf(c_0_6085_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6085]) ).
cnf(c_0_6085_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6085]) ).
cnf(c_0_6085_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6085]) ).
cnf(c_0_6086_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6086]) ).
cnf(c_0_6086_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6086]) ).
cnf(c_0_6086_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6086]) ).
cnf(c_0_6086_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6086]) ).
cnf(c_0_6087_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6087]) ).
cnf(c_0_6087_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6087]) ).
cnf(c_0_6087_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6087]) ).
cnf(c_0_6087_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6087]) ).
cnf(c_0_6088_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6088]) ).
cnf(c_0_6088_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6088]) ).
cnf(c_0_6088_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6088]) ).
cnf(c_0_6088_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6088]) ).
cnf(c_0_6089_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6089]) ).
cnf(c_0_6089_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6089]) ).
cnf(c_0_6089_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6089]) ).
cnf(c_0_6089_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6089]) ).
cnf(c_0_6090_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6090]) ).
cnf(c_0_6090_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6090]) ).
cnf(c_0_6090_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6090]) ).
cnf(c_0_6090_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6090]) ).
cnf(c_0_6091_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6091]) ).
cnf(c_0_6091_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6091]) ).
cnf(c_0_6091_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6091]) ).
cnf(c_0_6091_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6091]) ).
cnf(c_0_6092_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6092]) ).
cnf(c_0_6092_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6092]) ).
cnf(c_0_6092_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6092]) ).
cnf(c_0_6092_3,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6092]) ).
cnf(c_0_6093_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6093]) ).
cnf(c_0_6093_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6093]) ).
cnf(c_0_6094_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6094]) ).
cnf(c_0_6094_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6094]) ).
cnf(c_0_6095_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6095]) ).
cnf(c_0_6095_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6095]) ).
cnf(c_0_6096_0,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6096]) ).
cnf(c_0_6096_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6096]) ).
cnf(c_0_6096_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6096]) ).
cnf(c_0_6097_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6097]) ).
cnf(c_0_6097_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6097]) ).
cnf(c_0_6097_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6097]) ).
cnf(c_0_6098_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6098]) ).
cnf(c_0_6098_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6098]) ).
cnf(c_0_6098_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6098]) ).
cnf(c_0_6099_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ 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),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6099]) ).
cnf(c_0_6099_1,axiom,
( ~ 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),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6099]) ).
cnf(c_0_6099_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ 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),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6099]) ).
cnf(c_0_6100_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_Rings_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6100]) ).
cnf(c_0_6100_1,axiom,
( ~ class_Rings_Oring(X1)
| c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6100]) ).
cnf(c_0_6101_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6101]) ).
cnf(c_0_6101_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6101]) ).
cnf(c_0_6102_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6102]) ).
cnf(c_0_6102_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6102]) ).
cnf(c_0_6103_0,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6103_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6104_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6104]) ).
cnf(c_0_6104_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6104]) ).
cnf(c_0_6104_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6104]) ).
cnf(c_0_6105_0,axiom,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6105]) ).
cnf(c_0_6105_1,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| c_Polynomial_Osmult(X1,X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6105]) ).
cnf(c_0_6106_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6106_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6106_2,axiom,
( ~ 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),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6107_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6107_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6107_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6108_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X3
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6108_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X3
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6108_2,axiom,
( X1 != X3
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6108_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| X1 != X3
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6109_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6109]) ).
cnf(c_0_6109_1,axiom,
( X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6109]) ).
cnf(c_0_6109_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6109]) ).
cnf(c_0_6109_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6109]) ).
cnf(c_0_6110_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6110]) ).
cnf(c_0_6110_1,axiom,
( X2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6110]) ).
cnf(c_0_6111_0,axiom,
( c_Polynomial_Opos__poly(X1,X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6111_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opos__poly(X1,X3)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6111_2,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6111_3,axiom,
( ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opos__poly(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6112_0,axiom,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6112]) ).
cnf(c_0_6112_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6112]) ).
cnf(c_0_6112_2,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6112]) ).
cnf(c_0_6113_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6113_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6113_2,axiom,
( X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6114_0,axiom,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,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(literals_permutation,[status(thm)],[c_0_6114]) ).
cnf(c_0_6114_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6114]) ).
cnf(c_0_6117_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6117_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6118_0,axiom,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6118]) ).
cnf(c_0_6118_1,axiom,
( ~ class_RealVector_Oreal__normed__div__algebra(X1)
| c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6118]) ).
cnf(c_0_6119_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6119]) ).
cnf(c_0_6119_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6119]) ).
cnf(c_0_6119_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6119]) ).
cnf(c_0_6120_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6120]) ).
cnf(c_0_6120_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6120]) ).
cnf(c_0_6120_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6120]) ).
cnf(c_0_6121_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6121]) ).
cnf(c_0_6121_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6121]) ).
cnf(c_0_6121_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6121]) ).
cnf(c_0_6122_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6122]) ).
cnf(c_0_6122_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6122]) ).
cnf(c_0_6122_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6122]) ).
cnf(c_0_6123_0,axiom,
( 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),c_Nat_OSuc(X3))
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6123]) ).
cnf(c_0_6123_1,axiom,
( ~ class_Power_Opower(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),c_Nat_OSuc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6123]) ).
cnf(c_0_6124_0,axiom,
( 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),c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6124]) ).
cnf(c_0_6124_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(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),c_Nat_OSuc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6124]) ).
cnf(c_0_6125_0,axiom,
( 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),c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6125]) ).
cnf(c_0_6125_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(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),c_Nat_OSuc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6125]) ).
cnf(c_0_6126_0,axiom,
( c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6126]) ).
cnf(c_0_6126_1,axiom,
( ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6126]) ).
cnf(c_0_6126_2,axiom,
( ~ c_Polynomial_Opos__poly(X1,X2)
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6126]) ).
cnf(c_0_6126_3,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6126]) ).
cnf(c_0_6127_0,axiom,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6127]) ).
cnf(c_0_6127_1,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| hAPP(c_Polynomial_Opoly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6127]) ).
cnf(c_0_6128_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6128]) ).
cnf(c_0_6128_1,axiom,
( ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6128]) ).
cnf(c_0_6128_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3,X4)
| ~ class_Orderings_Oord(X1)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6128]) ).
cnf(c_0_6129_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6129_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6129_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6130_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6130]) ).
cnf(c_0_6130_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6130]) ).
cnf(c_0_6130_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6130]) ).
cnf(c_0_6131_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6131]) ).
cnf(c_0_6131_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6131]) ).
cnf(c_0_6131_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6131]) ).
cnf(c_0_6132_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6132]) ).
cnf(c_0_6132_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6132]) ).
cnf(c_0_6132_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6132]) ).
cnf(c_0_6134_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6134_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6134_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6135_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6135]) ).
cnf(c_0_6135_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6135]) ).
cnf(c_0_6135_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6135]) ).
cnf(c_0_6136_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6136]) ).
cnf(c_0_6136_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6136]) ).
cnf(c_0_6136_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6136]) ).
cnf(c_0_6137_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6137]) ).
cnf(c_0_6137_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6137]) ).
cnf(c_0_6137_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6137]) ).
cnf(c_0_6138_0,axiom,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Omonom(X1,X2,X3)) = c_Polynomial_Omonom(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6138]) ).
cnf(c_0_6138_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Omonom(X1,X2,X3)) = c_Polynomial_Omonom(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6138]) ).
cnf(c_0_6139_0,axiom,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3)) = c_Polynomial_Osmult(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6139]) ).
cnf(c_0_6139_1,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3)) = c_Polynomial_Osmult(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6139]) ).
cnf(c_0_6140_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6140]) ).
cnf(c_0_6140_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6140]) ).
cnf(c_0_6141_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6141]) ).
cnf(c_0_6141_1,axiom,
( ~ class_Rings_Olinordered__semidom(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)
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6141]) ).
cnf(c_0_6141_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6141]) ).
cnf(c_0_6141_3,axiom,
( X3 != X4
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6141]) ).
cnf(c_0_6142_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6142]) ).
cnf(c_0_6142_1,axiom,
( 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),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6142]) ).
cnf(c_0_6142_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_6142]) ).
cnf(c_0_6142_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6142]) ).
cnf(c_0_6143_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6143]) ).
cnf(c_0_6143_1,axiom,
( X2 = 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_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6143]) ).
cnf(c_0_6143_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(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(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6143]) ).
cnf(c_0_6143_3,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6143]) ).
cnf(c_0_6144_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6144]) ).
cnf(c_0_6144_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6144]) ).
cnf(c_0_6144_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6144]) ).
cnf(c_0_6145_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6145]) ).
cnf(c_0_6145_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6145]) ).
cnf(c_0_6145_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6145]) ).
cnf(c_0_6146_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6146_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6146_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6147_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6147]) ).
cnf(c_0_6147_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6147]) ).
cnf(c_0_6147_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6147]) ).
cnf(c_0_6148_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6148]) ).
cnf(c_0_6148_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6148]) ).
cnf(c_0_6148_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6148]) ).
cnf(c_0_6149_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6149_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6149_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6150_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6150_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(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),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6150_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6151_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6151]) ).
cnf(c_0_6151_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6151]) ).
cnf(c_0_6151_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6151]) ).
cnf(c_0_6152_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6152]) ).
cnf(c_0_6152_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(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),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6152]) ).
cnf(c_0_6152_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6152]) ).
cnf(c_0_6153_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6153]) ).
cnf(c_0_6153_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6153]) ).
cnf(c_0_6153_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6153]) ).
cnf(c_0_6154_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6154]) ).
cnf(c_0_6154_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| 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),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6154]) ).
cnf(c_0_6154_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6154]) ).
cnf(c_0_6155_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6155]) ).
cnf(c_0_6155_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| 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),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6155]) ).
cnf(c_0_6155_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6155]) ).
cnf(c_0_6156_0,axiom,
( c_Nat_OSuc(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(literals_permutation,[status(thm)],[c_0_6156]) ).
cnf(c_0_6156_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6156]) ).
cnf(c_0_6157_0,axiom,
( c_Nat_OSuc(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(literals_permutation,[status(thm)],[c_0_6157]) ).
cnf(c_0_6157_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6157]) ).
cnf(c_0_6158_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6158]) ).
cnf(c_0_6158_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6158]) ).
cnf(c_0_6158_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6158]) ).
cnf(c_0_6158_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6158]) ).
cnf(c_0_6159_0,axiom,
( 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),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6159]) ).
cnf(c_0_6159_1,axiom,
( ~ class_Rings_Oring(X1)
| 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),c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6159]) ).
cnf(c_0_6160_0,axiom,
( 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),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6160]) ).
cnf(c_0_6160_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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),c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6160]) ).
cnf(c_0_6161_0,axiom,
( 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),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6161]) ).
cnf(c_0_6161_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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),c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6161]) ).
cnf(c_0_6162_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6162]) ).
cnf(c_0_6162_1,axiom,
( ~ class_Fields_Ofield(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6162]) ).
cnf(c_0_6162_2,axiom,
( X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6162]) ).
cnf(c_0_6162_3,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6162]) ).
cnf(c_0_6164_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6164]) ).
cnf(c_0_6164_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6164]) ).
cnf(c_0_6164_2,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6164]) ).
cnf(c_0_6165_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6165]) ).
cnf(c_0_6165_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6165]) ).
cnf(c_0_6165_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6165]) ).
cnf(c_0_6166_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6166]) ).
cnf(c_0_6166_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6166]) ).
cnf(c_0_6166_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6166]) ).
cnf(c_0_6167_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6167]) ).
cnf(c_0_6167_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6167]) ).
cnf(c_0_6168_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6168]) ).
cnf(c_0_6168_1,axiom,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6168]) ).
cnf(c_0_6168_2,axiom,
( X2 != c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(literals_permutation,[status(thm)],[c_0_6168]) ).
cnf(c_0_6169_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oplus__class_Oplus(X1,X2,X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6169_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oplus__class_Oplus(X1,X2,X3)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6171_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6171_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6171_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6172_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6172]) ).
cnf(c_0_6172_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6172]) ).
cnf(c_0_6172_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6172]) ).
cnf(c_0_6173_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6173]) ).
cnf(c_0_6173_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6173]) ).
cnf(c_0_6173_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6173]) ).
cnf(c_0_6174_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6174]) ).
cnf(c_0_6174_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6174]) ).
cnf(c_0_6174_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6174]) ).
cnf(c_0_6176_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6176_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6176_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6176_3,axiom,
( X1 != X3
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6177_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6177_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6177_2,axiom,
( X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6177_3,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6178_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6178]) ).
cnf(c_0_6178_1,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6178]) ).
cnf(c_0_6178_2,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6178]) ).
cnf(c_0_6178_3,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(hAPP(X3,X2),X1))
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6178]) ).
cnf(c_0_6179_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6179]) ).
cnf(c_0_6179_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6179]) ).
cnf(c_0_6179_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6179]) ).
cnf(c_0_6180_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6180_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6180_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6181_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6181]) ).
cnf(c_0_6181_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6181]) ).
cnf(c_0_6181_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6181]) ).
cnf(c_0_6182_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X2,X3,X1) != c_Polynomial_OpCons(X2,X4,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6182]) ).
cnf(c_0_6182_1,axiom,
( c_Polynomial_Osmult(X2,X3,X1) != c_Polynomial_OpCons(X2,X4,X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6182]) ).
cnf(c_0_6182_2,axiom,
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Polynomial_Osmult(X2,X3,X1) != c_Polynomial_OpCons(X2,X4,X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6182]) ).
cnf(c_0_6183_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6183]) ).
cnf(c_0_6183_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6183]) ).
cnf(c_0_6183_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6183]) ).
cnf(c_0_6184_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6184]) ).
cnf(c_0_6184_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6184]) ).
cnf(c_0_6184_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6184]) ).
cnf(c_0_6185_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6185]) ).
cnf(c_0_6185_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6185]) ).
cnf(c_0_6185_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6185]) ).
cnf(c_0_6186_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6186]) ).
cnf(c_0_6186_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6186]) ).
cnf(c_0_6186_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6186]) ).
cnf(c_0_6187_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6187]) ).
cnf(c_0_6187_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6187]) ).
cnf(c_0_6187_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6187]) ).
cnf(c_0_6188_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6188_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6188_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6189_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6189_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6189_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6190_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6190]) ).
cnf(c_0_6190_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6190]) ).
cnf(c_0_6190_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6190]) ).
cnf(c_0_6191_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6191]) ).
cnf(c_0_6191_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6191]) ).
cnf(c_0_6191_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6191]) ).
cnf(c_0_6192_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6192_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,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) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6192_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6193_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6193_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6193_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6194_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6194]) ).
cnf(c_0_6194_1,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,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)) ),
inference(literals_permutation,[status(thm)],[c_0_6194]) ).
cnf(c_0_6194_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6194]) ).
cnf(c_0_6195_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6195]) ).
cnf(c_0_6195_1,axiom,
( ~ 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),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6195]) ).
cnf(c_0_6195_2,axiom,
( ~ 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),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6195]) ).
cnf(c_0_6196_0,axiom,
( c_Orderings_Oord__class_Oless(X1,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(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6196_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6196_2,axiom,
( ~ 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_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6197_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6197_1,axiom,
( ~ class_Rings_Oring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6198_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Rings_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6198_1,axiom,
( ~ class_Rings_Oring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6199_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6199]) ).
cnf(c_0_6199_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6199]) ).
cnf(c_0_6199_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6199]) ).
cnf(c_0_6200_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6200]) ).
cnf(c_0_6200_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6200]) ).
cnf(c_0_6200_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6200]) ).
cnf(c_0_6201_0,axiom,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| X2 = X3
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6201_1,axiom,
( X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6201_2,axiom,
( ~ class_Rings_Oidom(X1)
| X2 = X3
| X2 = 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) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6201_3,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1)
| X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6202_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6202]) ).
cnf(c_0_6202_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| ~ class_Fields_Ofield(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6202]) ).
cnf(c_0_6202_2,axiom,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6202]) ).
cnf(c_0_6202_3,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6202]) ).
cnf(c_0_6203_0,axiom,
( c_Polynomial_Opos__poly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6203]) ).
cnf(c_0_6203_1,axiom,
( ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6203]) ).
cnf(c_0_6203_2,axiom,
( ~ c_Polynomial_Opos__poly(X1,X2)
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6203]) ).
cnf(c_0_6203_3,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6203]) ).
cnf(c_0_6204_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6204]) ).
cnf(c_0_6204_1,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6204]) ).
cnf(c_0_6205_0,axiom,
( 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)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6205]) ).
cnf(c_0_6205_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6205]) ).
cnf(c_0_6205_2,axiom,
( X2 != X3
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| 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(literals_permutation,[status(thm)],[c_0_6205]) ).
cnf(c_0_6206_0,axiom,
( X4 = X5
| ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6206]) ).
cnf(c_0_6206_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| X4 = X5
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6206]) ).
cnf(c_0_6206_2,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oab__group__add(X1)
| X4 = X5
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6206]) ).
cnf(c_0_6206_3,axiom,
( X2 != X3
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oab__group__add(X1)
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_6206]) ).
cnf(c_0_6207_0,axiom,
( X2 = X3
| ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| X4 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_6207]) ).
cnf(c_0_6207_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| X2 = X3
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| X4 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_6207]) ).
cnf(c_0_6207_2,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oab__group__add(X1)
| X2 = X3
| X4 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_6207]) ).
cnf(c_0_6207_3,axiom,
( X4 != X5
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oab__group__add(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6207]) ).
cnf(c_0_6208_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6208]) ).
cnf(c_0_6208_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6208]) ).
cnf(c_0_6208_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6208]) ).
cnf(c_0_6209_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6209]) ).
cnf(c_0_6209_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6209]) ).
cnf(c_0_6209_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6209]) ).
cnf(c_0_6210_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6210]) ).
cnf(c_0_6210_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6210]) ).
cnf(c_0_6210_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6210]) ).
cnf(c_0_6211_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6211]) ).
cnf(c_0_6211_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6211]) ).
cnf(c_0_6211_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6211]) ).
cnf(c_0_6212_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6212]) ).
cnf(c_0_6212_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6212]) ).
cnf(c_0_6212_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6212]) ).
cnf(c_0_6212_3,axiom,
( X2 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6212]) ).
cnf(c_0_6213_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,X3,X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6213]) ).
cnf(c_0_6213_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6213]) ).
cnf(c_0_6214_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6214]) ).
cnf(c_0_6214_1,axiom,
( ~ class_Orderings_Oorder(X1)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6214]) ).
cnf(c_0_6214_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6214]) ).
cnf(c_0_6214_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6214]) ).
cnf(c_0_6215_0,axiom,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6215]) ).
cnf(c_0_6215_1,axiom,
( ~ class_Orderings_Oorder(X1)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6215]) ).
cnf(c_0_6215_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6215]) ).
cnf(c_0_6215_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6215]) ).
cnf(c_0_6216_0,axiom,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6216]) ).
cnf(c_0_6216_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6216]) ).
cnf(c_0_6216_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6216]) ).
cnf(c_0_6216_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6216]) ).
cnf(c_0_6217_0,axiom,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6217]) ).
cnf(c_0_6217_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6217]) ).
cnf(c_0_6217_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6217]) ).
cnf(c_0_6217_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6217]) ).
cnf(c_0_6218_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6218]) ).
cnf(c_0_6218_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6218]) ).
cnf(c_0_6219_0,axiom,
( X2 = X3
| ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X4) != c_Polynomial_Omonom(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6219_1,axiom,
( ~ class_Groups_Ozero(X1)
| X2 = X3
| c_Polynomial_Omonom(X1,X2,X4) != c_Polynomial_Omonom(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6219_2,axiom,
( c_Polynomial_Omonom(X1,X2,X4) != c_Polynomial_Omonom(X1,X3,X4)
| ~ class_Groups_Ozero(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6220_0,axiom,
( X2 = X4
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_6220]) ).
cnf(c_0_6220_1,axiom,
( ~ class_Groups_Ozero(X1)
| X2 = X4
| c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_6220]) ).
cnf(c_0_6220_2,axiom,
( c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5)
| ~ class_Groups_Ozero(X1)
| X2 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_6220]) ).
cnf(c_0_6221_0,axiom,
( X3 = X5
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_6221]) ).
cnf(c_0_6221_1,axiom,
( ~ class_Groups_Ozero(X1)
| X3 = X5
| c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_6221]) ).
cnf(c_0_6221_2,axiom,
( c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5)
| ~ class_Groups_Ozero(X1)
| X3 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_6221]) ).
cnf(c_0_6222_0,axiom,
( X1 = X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) != c_Groups_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6222]) ).
cnf(c_0_6222_1,axiom,
( c_Groups_Oplus__class_Oplus(X3,X1,X4) != c_Groups_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6222]) ).
cnf(c_0_6222_2,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X1,X4) != c_Groups_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6222]) ).
cnf(c_0_6223_0,axiom,
( X1 = X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6223_1,axiom,
( c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
| X1 = X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6223_2,axiom,
( ~ class_Groups_Ocancel__ab__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6224_0,axiom,
( X1 = X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6224_1,axiom,
( c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
| X1 = X2
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6224_2,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6225_0,axiom,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6225]) ).
cnf(c_0_6225_1,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X3
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6225]) ).
cnf(c_0_6225_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6225]) ).
cnf(c_0_6226_0,axiom,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X4,X2) != c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6226]) ).
cnf(c_0_6226_1,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X3
| c_Groups_Oplus__class_Oplus(X1,X4,X2) != c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6226]) ).
cnf(c_0_6226_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,X4,X2) != c_Groups_Oplus__class_Oplus(X1,X4,X3)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6226]) ).
cnf(c_0_6228_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6228]) ).
cnf(c_0_6228_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6228]) ).
cnf(c_0_6228_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6228]) ).
cnf(c_0_6229_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6229]) ).
cnf(c_0_6229_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6229]) ).
cnf(c_0_6229_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6229]) ).
cnf(c_0_6230_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6230]) ).
cnf(c_0_6230_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6230]) ).
cnf(c_0_6230_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6230]) ).
cnf(c_0_6231_0,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6231_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6231_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6232_0,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6232]) ).
cnf(c_0_6232_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6232]) ).
cnf(c_0_6232_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6232]) ).
cnf(c_0_6233_0,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6233]) ).
cnf(c_0_6233_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6233]) ).
cnf(c_0_6233_2,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6233]) ).
cnf(c_0_6234_0,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6234]) ).
cnf(c_0_6234_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6234]) ).
cnf(c_0_6234_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6234]) ).
cnf(c_0_6235_0,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6235]) ).
cnf(c_0_6235_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6235]) ).
cnf(c_0_6235_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6235]) ).
cnf(c_0_6236_0,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6236_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6236_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6237_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6237_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6237_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6238_0,axiom,
( X2 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6238]) ).
cnf(c_0_6238_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6238]) ).
cnf(c_0_6238_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6238]) ).
cnf(c_0_6239_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_6239]) ).
cnf(c_0_6239_1,axiom,
( ~ class_Rings_Oidom(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_6239]) ).
cnf(c_0_6239_2,axiom,
( c_Polynomial_Oorder(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| hAPP(c_Polynomial_Opoly(X1,X3),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6239]) ).
cnf(c_0_6239_3,axiom,
( hAPP(c_Polynomial_Opoly(X1,X3),X2) != c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Oorder(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6239]) ).
cnf(c_0_6240_0,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6240]) ).
cnf(c_0_6240_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6240]) ).
cnf(c_0_6241_0,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6241]) ).
cnf(c_0_6241_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6241]) ).
cnf(c_0_6242_0,axiom,
( X1 = X2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6242]) ).
cnf(c_0_6242_1,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = X2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6242]) ).
cnf(c_0_6242_2,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6242]) ).
cnf(c_0_6243_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk10_2(X2,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6243]) ).
cnf(c_0_6243_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk10_2(X2,X1),X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6243]) ).
cnf(c_0_6243_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk10_2(X2,X1),X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6243]) ).
cnf(c_0_6244_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6244]) ).
cnf(c_0_6244_1,axiom,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6244]) ).
cnf(c_0_6244_2,axiom,
( X2 != X3
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(literals_permutation,[status(thm)],[c_0_6244]) ).
cnf(c_0_6245_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6245]) ).
cnf(c_0_6245_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6245]) ).
cnf(c_0_6245_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6245]) ).
cnf(c_0_6246_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6246]) ).
cnf(c_0_6246_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6246]) ).
cnf(c_0_6246_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6246]) ).
cnf(c_0_6247_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6247]) ).
cnf(c_0_6247_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6247]) ).
cnf(c_0_6248_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6248]) ).
cnf(c_0_6248_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6248]) ).
cnf(c_0_6249_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6249]) ).
cnf(c_0_6249_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6249]) ).
cnf(c_0_6249_2,axiom,
( X2 != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6249]) ).
cnf(c_0_6251_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6251]) ).
cnf(c_0_6251_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6251]) ).
cnf(c_0_6251_2,axiom,
( ~ class_Divides_Osemiring__div(X1)
| 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 ),
inference(literals_permutation,[status(thm)],[c_0_6251]) ).
cnf(c_0_6252_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = X2
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6252]) ).
cnf(c_0_6252_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6252]) ).
cnf(c_0_6252_2,axiom,
( ~ class_Divides_Osemiring__div(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6252]) ).
cnf(c_0_6253_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6253]) ).
cnf(c_0_6253_1,axiom,
( ~ class_Rings_Olinordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6253]) ).
cnf(c_0_6254_0,axiom,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6254]) ).
cnf(c_0_6254_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6254]) ).
cnf(c_0_6254_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6254]) ).
cnf(c_0_6255_0,axiom,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6255]) ).
cnf(c_0_6255_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6255]) ).
cnf(c_0_6255_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6255]) ).
cnf(c_0_6256_0,axiom,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6256]) ).
cnf(c_0_6256_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6256]) ).
cnf(c_0_6256_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6256]) ).
cnf(c_0_6257_0,axiom,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6257]) ).
cnf(c_0_6257_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6257]) ).
cnf(c_0_6257_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6257]) ).
cnf(c_0_6258_0,axiom,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6258]) ).
cnf(c_0_6258_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6258]) ).
cnf(c_0_6258_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6258]) ).
cnf(c_0_6259_0,axiom,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6259]) ).
cnf(c_0_6259_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6259]) ).
cnf(c_0_6259_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6259]) ).
cnf(c_0_6260_0,axiom,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6260]) ).
cnf(c_0_6260_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6260]) ).
cnf(c_0_6260_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6260]) ).
cnf(c_0_6261_0,axiom,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6261]) ).
cnf(c_0_6261_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6261]) ).
cnf(c_0_6261_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6261]) ).
cnf(c_0_6262_0,axiom,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6262]) ).
cnf(c_0_6262_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6262]) ).
cnf(c_0_6262_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6262]) ).
cnf(c_0_6263_0,axiom,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6263]) ).
cnf(c_0_6263_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6263]) ).
cnf(c_0_6263_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6263]) ).
cnf(c_0_6264_0,axiom,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6264]) ).
cnf(c_0_6264_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6264]) ).
cnf(c_0_6264_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6264]) ).
cnf(c_0_6265_0,axiom,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6265]) ).
cnf(c_0_6265_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6265]) ).
cnf(c_0_6265_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6265]) ).
cnf(c_0_6266_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6266]) ).
cnf(c_0_6266_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6266]) ).
cnf(c_0_6267_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6267]) ).
cnf(c_0_6267_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6267]) ).
cnf(c_0_6268_0,axiom,
( 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),X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6268]) ).
cnf(c_0_6268_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_6268]) ).
cnf(c_0_6268_2,axiom,
( 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)
| X1 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6268]) ).
cnf(c_0_6269_0,axiom,
( 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)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6269]) ).
cnf(c_0_6269_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X2 = 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) ),
inference(literals_permutation,[status(thm)],[c_0_6269]) ).
cnf(c_0_6269_2,axiom,
( 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)
| X2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6269]) ).
cnf(c_0_6270_0,axiom,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6270]) ).
cnf(c_0_6270_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6270]) ).
cnf(c_0_6271_0,axiom,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6271]) ).
cnf(c_0_6271_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6271]) ).
cnf(c_0_6277_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6277]) ).
cnf(c_0_6277_1,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6277]) ).
cnf(c_0_6278_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6278]) ).
cnf(c_0_6278_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6278]) ).
cnf(c_0_6279_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6279]) ).
cnf(c_0_6279_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6279]) ).
cnf(c_0_6280_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sk1_esk23_2(X1,X2)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6280]) ).
cnf(c_0_6280_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sk1_esk23_2(X1,X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6280]) ).
cnf(c_0_6281_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sk1_esk9_2(X1,X2)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6281]) ).
cnf(c_0_6281_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sk1_esk9_2(X1,X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6281]) ).
cnf(c_0_6283_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6283_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6284_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6284]) ).
cnf(c_0_6284_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6284]) ).
cnf(c_0_6291_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6291]) ).
cnf(c_0_6291_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6291]) ).
cnf(c_0_6292_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6292]) ).
cnf(c_0_6292_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6292]) ).
cnf(c_0_6293_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6293]) ).
cnf(c_0_6293_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6293]) ).
cnf(c_0_6294_0,axiom,
( 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))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6294]) ).
cnf(c_0_6294_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6294]) ).
cnf(c_0_6295_0,axiom,
( 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))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6295]) ).
cnf(c_0_6295_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6295]) ).
cnf(c_0_6296_0,axiom,
( X1 = c_Nat_OSuc(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6296]) ).
cnf(c_0_6296_1,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = c_Nat_OSuc(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6296]) ).
cnf(c_0_6296_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6296]) ).
cnf(c_0_6297_0,axiom,
( X1 = c_Nat_OSuc(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6297]) ).
cnf(c_0_6297_1,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = c_Nat_OSuc(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6297]) ).
cnf(c_0_6297_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6297]) ).
cnf(c_0_6298_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X4 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6298]) ).
cnf(c_0_6298_1,axiom,
( X4 != X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6298]) ).
cnf(c_0_6298_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| X4 != X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6298]) ).
cnf(c_0_6298_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| X4 != X2
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6298]) ).
cnf(c_0_6299_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X4 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6299_1,axiom,
( X4 != X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6299_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| X4 != X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6299_3,axiom,
( ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| X4 != X3
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6300_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6300]) ).
cnf(c_0_6300_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6300]) ).
cnf(c_0_6300_2,axiom,
( X3 != X4
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6300]) ).
cnf(c_0_6300_3,axiom,
( ~ class_Orderings_Oorder(X1)
| X3 != X4
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6300]) ).
cnf(c_0_6301_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6301]) ).
cnf(c_0_6301_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6301]) ).
cnf(c_0_6301_2,axiom,
( X2 != X4
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6301]) ).
cnf(c_0_6301_3,axiom,
( ~ class_Orderings_Oord(X1)
| X2 != X4
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6301]) ).
cnf(c_0_6302_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6302]) ).
cnf(c_0_6302_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6302]) ).
cnf(c_0_6302_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6302]) ).
cnf(c_0_6302_3,axiom,
( X3 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6302]) ).
cnf(c_0_6303_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6303]) ).
cnf(c_0_6303_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6303]) ).
cnf(c_0_6303_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6303]) ).
cnf(c_0_6303_3,axiom,
( X3 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6303]) ).
cnf(c_0_6304_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6304]) ).
cnf(c_0_6304_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6304]) ).
cnf(c_0_6304_2,axiom,
( X2 != X4
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6304]) ).
cnf(c_0_6304_3,axiom,
( ~ class_Orderings_Oord(X1)
| X2 != X4
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6304]) ).
cnf(c_0_6305_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6305]) ).
cnf(c_0_6305_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6305]) ).
cnf(c_0_6305_2,axiom,
( X3 != X4
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6305]) ).
cnf(c_0_6305_3,axiom,
( ~ class_Orderings_Oorder(X1)
| X3 != X4
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6305]) ).
cnf(c_0_6306_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X4 != X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6306]) ).
cnf(c_0_6306_1,axiom,
( X4 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6306]) ).
cnf(c_0_6306_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| X4 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6306]) ).
cnf(c_0_6306_3,axiom,
( ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| X4 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6306]) ).
cnf(c_0_6307_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X4 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6307]) ).
cnf(c_0_6307_1,axiom,
( X4 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6307]) ).
cnf(c_0_6307_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| X4 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6307]) ).
cnf(c_0_6307_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| X4 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6307]) ).
cnf(c_0_6308_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| X1 != c_Nat_OSuc(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6308]) ).
cnf(c_0_6308_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Nat_OSuc(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6308]) ).
cnf(c_0_6308_2,axiom,
( X1 != c_Nat_OSuc(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6308]) ).
cnf(c_0_6309_0,axiom,
( c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6309]) ).
cnf(c_0_6309_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ c_Polynomial_Opos__poly(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6309]) ).
cnf(c_0_6309_2,axiom,
( ~ c_Polynomial_Opos__poly(X1,X3)
| ~ class_Rings_Olinordered__idom(X1)
| c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6309]) ).
cnf(c_0_6310_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk2_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6310]) ).
cnf(c_0_6310_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk2_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6310]) ).
cnf(c_0_6311_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6311]) ).
cnf(c_0_6311_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_6311]) ).
cnf(c_0_6312_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X3
| 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(literals_permutation,[status(thm)],[c_0_6312]) ).
cnf(c_0_6312_1,axiom,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(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(literals_permutation,[status(thm)],[c_0_6312]) ).
cnf(c_0_6312_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)
| X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6312]) ).
cnf(c_0_6313_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6313]) ).
cnf(c_0_6313_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6313]) ).
cnf(c_0_6313_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6313]) ).
cnf(c_0_6314_0,axiom,
( X1 = X2
| X3 = c_Groups_Ozero__class_Ozero(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(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6314_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = X2
| 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(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6314_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6315_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6315_1,axiom,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6315_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)
| X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6316_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6316_1,axiom,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6316_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)
| X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6317_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Nat__Transfer_Otsub(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6317_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Nat__Transfer_Otsub(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6318_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Nat__Transfer_Otsub(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6318]) ).
cnf(c_0_6318_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Nat__Transfer_Otsub(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6318]) ).
cnf(c_0_6319_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6319]) ).
cnf(c_0_6319_1,axiom,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6319]) ).
cnf(c_0_6319_2,axiom,
( ~ class_Orderings_Oorder(X1)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6319]) ).
cnf(c_0_6319_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6319]) ).
cnf(c_0_6320_0,axiom,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6320]) ).
cnf(c_0_6320_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6320]) ).
cnf(c_0_6320_2,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6320]) ).
cnf(c_0_6320_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6320]) ).
cnf(c_0_6321_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6321]) ).
cnf(c_0_6321_1,axiom,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6321]) ).
cnf(c_0_6321_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6321]) ).
cnf(c_0_6321_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6321]) ).
cnf(c_0_6322_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6322_1,axiom,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6322_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6322_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6323_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6323_1,axiom,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6323_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6323_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6324_0,axiom,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6324_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6324_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6324_3,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6325_0,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6325_1,axiom,
( c_Orderings_Oord__class_Oless(X3,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6325_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6325_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6326_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6326]) ).
cnf(c_0_6326_1,axiom,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6326]) ).
cnf(c_0_6326_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6326]) ).
cnf(c_0_6326_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6326]) ).
cnf(c_0_6327_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6327]) ).
cnf(c_0_6327_1,axiom,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6327]) ).
cnf(c_0_6327_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6327]) ).
cnf(c_0_6327_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6327]) ).
cnf(c_0_6328_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6328]) ).
cnf(c_0_6328_1,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6328]) ).
cnf(c_0_6329_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6329]) ).
cnf(c_0_6329_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6329]) ).
cnf(c_0_6330_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6330]) ).
cnf(c_0_6330_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6330]) ).
cnf(c_0_6331_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6331]) ).
cnf(c_0_6331_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6331]) ).
cnf(c_0_6332_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6332]) ).
cnf(c_0_6332_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6332]) ).
cnf(c_0_6333_0,axiom,
( 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)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6333]) ).
cnf(c_0_6333_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6333]) ).
cnf(c_0_6333_2,axiom,
( 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)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_6333]) ).
cnf(c_0_6333_3,axiom,
( 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)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6333]) ).
cnf(c_0_6334_0,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6334_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6334_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6335_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6335_1,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6335_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6336_0,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6336]) ).
cnf(c_0_6336_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6336]) ).
cnf(c_0_6336_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6336]) ).
cnf(c_0_6337_0,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6337]) ).
cnf(c_0_6337_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6337]) ).
cnf(c_0_6337_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6337]) ).
cnf(c_0_6338_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Nat_OSuc(X1) = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6338]) ).
cnf(c_0_6338_1,axiom,
( c_Nat_OSuc(X1) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6338]) ).
cnf(c_0_6338_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Nat_OSuc(X1) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6338]) ).
cnf(c_0_6339_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6339]) ).
cnf(c_0_6339_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6339]) ).
cnf(c_0_6339_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6339]) ).
cnf(c_0_6340_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6340]) ).
cnf(c_0_6340_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6340]) ).
cnf(c_0_6340_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6340]) ).
cnf(c_0_6341_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6341]) ).
cnf(c_0_6341_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6341]) ).
cnf(c_0_6341_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6341]) ).
cnf(c_0_6342_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6342]) ).
cnf(c_0_6342_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6342]) ).
cnf(c_0_6342_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6342]) ).
cnf(c_0_6343_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6343]) ).
cnf(c_0_6343_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6343]) ).
cnf(c_0_6344_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6344]) ).
cnf(c_0_6344_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6344]) ).
cnf(c_0_6344_2,axiom,
( X2 != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6344]) ).
cnf(c_0_6345_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6345]) ).
cnf(c_0_6345_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6345]) ).
cnf(c_0_6346_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6346]) ).
cnf(c_0_6346_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6346]) ).
cnf(c_0_6347_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6347]) ).
cnf(c_0_6347_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6347]) ).
cnf(c_0_6348_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6348]) ).
cnf(c_0_6348_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6348]) ).
cnf(c_0_6349_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6349]) ).
cnf(c_0_6349_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6349]) ).
cnf(c_0_6350_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6350]) ).
cnf(c_0_6350_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6350]) ).
cnf(c_0_6351_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)
| ~ class_Rings_Odvd(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6351_1,axiom,
( X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)
| c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Odvd(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6351_2,axiom,
( ~ class_Rings_Odvd(X1)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6352_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6352]) ).
cnf(c_0_6352_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6352]) ).
cnf(c_0_6353_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6353]) ).
cnf(c_0_6353_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6353]) ).
cnf(c_0_6354_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6354]) ).
cnf(c_0_6354_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6354]) ).
cnf(c_0_6354_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6354]) ).
cnf(c_0_6356_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(literals_permutation,[status(thm)],[c_0_6356]) ).
cnf(c_0_6356_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(literals_permutation,[status(thm)],[c_0_6356]) ).
cnf(c_0_6356_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6356]) ).
cnf(c_0_6358_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6358]) ).
cnf(c_0_6358_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6358]) ).
cnf(c_0_6359_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6359]) ).
cnf(c_0_6359_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6359]) ).
cnf(c_0_6360_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6360]) ).
cnf(c_0_6360_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6360]) ).
cnf(c_0_6361_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6361]) ).
cnf(c_0_6361_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6361]) ).
cnf(c_0_6362_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6362]) ).
cnf(c_0_6362_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6362]) ).
cnf(c_0_6363_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6363]) ).
cnf(c_0_6363_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6363]) ).
cnf(c_0_6364_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6364]) ).
cnf(c_0_6364_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6364]) ).
cnf(c_0_6365_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6365]) ).
cnf(c_0_6365_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6365]) ).
cnf(c_0_6366_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6366]) ).
cnf(c_0_6366_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6366]) ).
cnf(c_0_6367_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6367]) ).
cnf(c_0_6367_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6367]) ).
cnf(c_0_6368_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6368]) ).
cnf(c_0_6368_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6368]) ).
cnf(c_0_6369_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6369]) ).
cnf(c_0_6369_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6369]) ).
cnf(c_0_6370_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,X2,X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6370]) ).
cnf(c_0_6370_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6370]) ).
cnf(c_0_6371_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_6371]) ).
cnf(c_0_6371_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_6371]) ).
cnf(c_0_6371_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6371]) ).
cnf(c_0_6372_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6372]) ).
cnf(c_0_6372_1,axiom,
( X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6372]) ).
cnf(c_0_6372_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6372]) ).
cnf(c_0_6373_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6373]) ).
cnf(c_0_6373_1,axiom,
( X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6373]) ).
cnf(c_0_6373_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6373]) ).
cnf(c_0_6374_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6374]) ).
cnf(c_0_6374_1,axiom,
( X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6374]) ).
cnf(c_0_6374_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6374]) ).
cnf(c_0_6375_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X3 != X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6375]) ).
cnf(c_0_6375_1,axiom,
( X3 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6375]) ).
cnf(c_0_6375_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| X3 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6375]) ).
cnf(c_0_6376_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6376]) ).
cnf(c_0_6376_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6376]) ).
cnf(c_0_6376_2,axiom,
( X1 != X3
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6376]) ).
cnf(c_0_6377_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6377]) ).
cnf(c_0_6377_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6377]) ).
cnf(c_0_6377_2,axiom,
( X2 != X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6377]) ).
cnf(c_0_6378_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6378]) ).
cnf(c_0_6378_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6378]) ).
cnf(c_0_6378_2,axiom,
( X2 != X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6378]) ).
cnf(c_0_6379_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6379]) ).
cnf(c_0_6379_1,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6379]) ).
cnf(c_0_6380_0,axiom,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6380]) ).
cnf(c_0_6380_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6380]) ).
cnf(c_0_6380_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6380]) ).
cnf(c_0_6381_0,axiom,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6381]) ).
cnf(c_0_6381_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6381]) ).
cnf(c_0_6381_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6381]) ).
cnf(c_0_6382_0,axiom,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6382]) ).
cnf(c_0_6382_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6382]) ).
cnf(c_0_6382_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6382]) ).
cnf(c_0_6383_0,axiom,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6383]) ).
cnf(c_0_6383_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6383]) ).
cnf(c_0_6383_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6383]) ).
cnf(c_0_6384_0,axiom,
( X1 = X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6384]) ).
cnf(c_0_6384_1,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6384]) ).
cnf(c_0_6384_2,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6384]) ).
cnf(c_0_6385_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6385]) ).
cnf(c_0_6385_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6385]) ).
cnf(c_0_6386_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6386]) ).
cnf(c_0_6386_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6386]) ).
cnf(c_0_6387_0,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6387]) ).
cnf(c_0_6387_1,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6387]) ).
cnf(c_0_6387_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6387]) ).
cnf(c_0_6388_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6388]) ).
cnf(c_0_6388_1,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6388]) ).
cnf(c_0_6388_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6388]) ).
cnf(c_0_6389_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6389]) ).
cnf(c_0_6389_1,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6389]) ).
cnf(c_0_6389_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6389]) ).
cnf(c_0_6390_0,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6390]) ).
cnf(c_0_6390_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6390]) ).
cnf(c_0_6390_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6390]) ).
cnf(c_0_6391_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6391]) ).
cnf(c_0_6391_1,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6391]) ).
cnf(c_0_6391_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6391]) ).
cnf(c_0_6392_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6392]) ).
cnf(c_0_6392_1,axiom,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6392]) ).
cnf(c_0_6392_2,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6392]) ).
cnf(c_0_6394_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6394]) ).
cnf(c_0_6394_1,axiom,
( X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6394]) ).
cnf(c_0_6395_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6395]) ).
cnf(c_0_6395_1,axiom,
( X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6395]) ).
cnf(c_0_6396_0,axiom,
( c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6396_1,axiom,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6397_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6397]) ).
cnf(c_0_6397_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6397]) ).
cnf(c_0_6398_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6398]) ).
cnf(c_0_6398_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6398]) ).
cnf(c_0_6399_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6399]) ).
cnf(c_0_6399_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6399]) ).
cnf(c_0_6400_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6400]) ).
cnf(c_0_6400_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6400]) ).
cnf(c_0_6401_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6401]) ).
cnf(c_0_6401_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6401]) ).
cnf(c_0_6402_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6402_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6403_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6403]) ).
cnf(c_0_6403_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6403]) ).
cnf(c_0_6404_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6404]) ).
cnf(c_0_6404_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6404]) ).
cnf(c_0_6405_0,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6405]) ).
cnf(c_0_6405_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_6405]) ).
cnf(c_0_6406_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6406]) ).
cnf(c_0_6406_1,axiom,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6406]) ).
cnf(c_0_6406_2,axiom,
( X2 != c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6406]) ).
cnf(c_0_6407_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6407]) ).
cnf(c_0_6407_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_6407]) ).
cnf(c_0_6413_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(sk1_esk10_2(X2,X1)) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6413]) ).
cnf(c_0_6413_1,axiom,
( c_Nat_OSuc(sk1_esk10_2(X2,X1)) = X1
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6413]) ).
cnf(c_0_6413_2,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Nat_OSuc(sk1_esk10_2(X2,X1)) = X1
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6413]) ).
cnf(c_0_6414_0,axiom,
( X1 = X2
| hAPP(X1,sk1_esk1_2(X2,X1)) != hAPP(X2,sk1_esk1_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6414]) ).
cnf(c_0_6414_1,axiom,
( hAPP(X1,sk1_esk1_2(X2,X1)) != hAPP(X2,sk1_esk1_2(X2,X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6414]) ).
cnf(c_0_6415_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,X3,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6415_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,X3,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6415_2,axiom,
( ~ class_Rings_Oidom(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Osmult(X1,X3,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6415_3,axiom,
( c_Polynomial_Osmult(X1,X3,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6416_0,axiom,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6416_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6417_0,axiom,
( c_Polynomial_OpCons(X1,X2,X3) = c_Polynomial_OpCons(X1,X4,X5)
| ~ class_Groups_Ozero(X1)
| X3 != X5
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6417_1,axiom,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) = c_Polynomial_OpCons(X1,X4,X5)
| X3 != X5
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6417_2,axiom,
( X3 != X5
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) = c_Polynomial_OpCons(X1,X4,X5)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6417_3,axiom,
( X2 != X4
| X3 != X5
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) = c_Polynomial_OpCons(X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6418_0,axiom,
( ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6418_1,axiom,
( ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6418_2,axiom,
( ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6418_3,axiom,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6418_4,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6418_5,axiom,
( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6419_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6419_1,axiom,
( ~ class_Rings_Ozero__neq__one(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6419_2,axiom,
( ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6419_3,axiom,
( ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6419_4,axiom,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6419_5,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6420_0,axiom,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| X2 = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6420_1,axiom,
( X2 = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6420_2,axiom,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| X2 = c_Groups_Oone__class_Oone(X1)
| X2 = 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) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6420_3,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| X2 = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6421_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6421]) ).
cnf(c_0_6421_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6421]) ).
cnf(c_0_6421_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6421]) ).
cnf(c_0_6422_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6422]) ).
cnf(c_0_6422_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6422]) ).
cnf(c_0_6422_2,axiom,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6422]) ).
cnf(c_0_6423_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6423]) ).
cnf(c_0_6423_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6423]) ).
cnf(c_0_6423_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6423]) ).
cnf(c_0_6423_3,axiom,
( X2 != X3
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6423]) ).
cnf(c_0_6424_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6424]) ).
cnf(c_0_6424_1,axiom,
( ~ class_Groups_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6424]) ).
cnf(c_0_6424_2,axiom,
( c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6424]) ).
cnf(c_0_6425_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6425]) ).
cnf(c_0_6425_1,axiom,
( X2 != X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6425]) ).
cnf(c_0_6426_0,axiom,
( c_Polynomial_Omonom(X1,X2,X3) = c_Polynomial_Omonom(X1,X4,X3)
| ~ class_Groups_Ozero(X1)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6426]) ).
cnf(c_0_6426_1,axiom,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) = c_Polynomial_Omonom(X1,X4,X3)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6426]) ).
cnf(c_0_6426_2,axiom,
( X2 != X4
| ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) = c_Polynomial_Omonom(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6426]) ).
cnf(c_0_6427_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X4,X3)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6427]) ).
cnf(c_0_6427_1,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X4,X3)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6427]) ).
cnf(c_0_6427_2,axiom,
( X2 != X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6427]) ).
cnf(c_0_6428_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6428]) ).
cnf(c_0_6428_1,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,X4)
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6428]) ).
cnf(c_0_6428_2,axiom,
( X3 != X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6428]) ).
cnf(c_0_6429_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6429]) ).
cnf(c_0_6429_1,axiom,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6429]) ).
cnf(c_0_6429_2,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6429]) ).
cnf(c_0_6429_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6429]) ).
cnf(c_0_6430_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6430]) ).
cnf(c_0_6430_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6430]) ).
cnf(c_0_6430_2,axiom,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6430]) ).
cnf(c_0_6430_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6430]) ).
cnf(c_0_6431_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6431]) ).
cnf(c_0_6431_1,axiom,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6431]) ).
cnf(c_0_6431_2,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6431]) ).
cnf(c_0_6431_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6431]) ).
cnf(c_0_6432_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6432]) ).
cnf(c_0_6432_1,axiom,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6432]) ).
cnf(c_0_6432_2,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6432]) ).
cnf(c_0_6432_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6432]) ).
cnf(c_0_6433_0,axiom,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6433]) ).
cnf(c_0_6433_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6433]) ).
cnf(c_0_6433_2,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6433]) ).
cnf(c_0_6433_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6433]) ).
cnf(c_0_6434_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6434]) ).
cnf(c_0_6434_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6434]) ).
cnf(c_0_6434_2,axiom,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6434]) ).
cnf(c_0_6434_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6434]) ).
cnf(c_0_6435_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6435_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6435_2,axiom,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6435_3,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| X3 = X2
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6436_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,X3)
| hAPP(X3,sk1_esk17_1(X3)) != hAPP(X3,sk1_esk16_1(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6436]) ).
cnf(c_0_6436_1,axiom,
( hAPP(X3,sk1_esk17_1(X3)) != hAPP(X3,sk1_esk16_1(X3))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6436]) ).
cnf(c_0_6439_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6439]) ).
cnf(c_0_6439_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6439]) ).
cnf(c_0_6439_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6439]) ).
cnf(c_0_6440_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6440]) ).
cnf(c_0_6440_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6440]) ).
cnf(c_0_6440_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6440]) ).
cnf(c_0_6441_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6441]) ).
cnf(c_0_6441_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6441]) ).
cnf(c_0_6441_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6441]) ).
cnf(c_0_6442_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6442]) ).
cnf(c_0_6442_1,axiom,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6442]) ).
cnf(c_0_6442_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6442]) ).
cnf(c_0_6443_0,axiom,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6443]) ).
cnf(c_0_6443_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6443]) ).
cnf(c_0_6443_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6443]) ).
cnf(c_0_6444_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6444]) ).
cnf(c_0_6444_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6444]) ).
cnf(c_0_6444_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6444]) ).
cnf(c_0_6445_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6445]) ).
cnf(c_0_6445_1,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6445]) ).
cnf(c_0_6445_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6445]) ).
cnf(c_0_6446_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6446]) ).
cnf(c_0_6446_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6446]) ).
cnf(c_0_6446_2,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6446]) ).
cnf(c_0_6447_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6447]) ).
cnf(c_0_6447_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6447]) ).
cnf(c_0_6448_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6448]) ).
cnf(c_0_6448_1,axiom,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6448]) ).
cnf(c_0_6448_2,axiom,
( X2 != X3
| ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6448]) ).
cnf(c_0_6449_0,axiom,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6449]) ).
cnf(c_0_6449_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6449]) ).
cnf(c_0_6449_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6449]) ).
cnf(c_0_6450_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6450]) ).
cnf(c_0_6450_1,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6450]) ).
cnf(c_0_6450_2,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6450]) ).
cnf(c_0_6451_0,axiom,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6451]) ).
cnf(c_0_6451_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| c_Groups_Oplus__class_Oplus(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6451]) ).
cnf(c_0_6451_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6451]) ).
cnf(c_0_6452_0,axiom,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4,X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6452]) ).
cnf(c_0_6452_1,axiom,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4,X5,X1)
| hAPP(X1,X2) = hAPP(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6452]) ).
cnf(c_0_6453_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6453]) ).
cnf(c_0_6453_1,axiom,
( ~ class_Groups_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6453]) ).
cnf(c_0_6453_2,axiom,
( c_Polynomial_Omonom(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6453]) ).
cnf(c_0_6454_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6454]) ).
cnf(c_0_6454_1,axiom,
( ~ class_Groups_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6454]) ).
cnf(c_0_6454_2,axiom,
( c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6454]) ).
cnf(c_0_6455_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6455]) ).
cnf(c_0_6455_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6455]) ).
cnf(c_0_6456_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6456]) ).
cnf(c_0_6456_1,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6456]) ).
cnf(c_0_6457_0,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6457]) ).
cnf(c_0_6457_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6457]) ).
cnf(c_0_6462_0,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6462]) ).
cnf(c_0_6462_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6462]) ).
cnf(c_0_6463_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6463]) ).
cnf(c_0_6463_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_6463]) ).
cnf(c_0_6464_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6464]) ).
cnf(c_0_6464_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6464]) ).
cnf(c_0_6465_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6465]) ).
cnf(c_0_6465_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6465]) ).
cnf(c_0_6466_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6466]) ).
cnf(c_0_6466_1,axiom,
( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6466]) ).
cnf(c_0_6466_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6466]) ).
cnf(c_0_6467_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6467]) ).
cnf(c_0_6467_1,axiom,
( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6467]) ).
cnf(c_0_6467_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6467]) ).
cnf(c_0_6468_0,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6468]) ).
cnf(c_0_6468_1,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Oone__class_Oone(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = X3
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6468]) ).
cnf(c_0_6468_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Oone__class_Oone(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6468]) ).
cnf(c_0_6469_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6469]) ).
cnf(c_0_6469_1,axiom,
( X2 != X3
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6469]) ).
cnf(c_0_6470_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6470]) ).
cnf(c_0_6470_1,axiom,
( X1 != X3
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6470]) ).
cnf(c_0_6471_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X2 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6471]) ).
cnf(c_0_6471_1,axiom,
( X2 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6471]) ).
cnf(c_0_6471_2,axiom,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X2 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6471]) ).
cnf(c_0_6472_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6472]) ).
cnf(c_0_6472_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6472]) ).
cnf(c_0_6472_2,axiom,
( X2 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6472]) ).
cnf(c_0_6473_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6473]) ).
cnf(c_0_6473_1,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6473]) ).
cnf(c_0_6473_2,axiom,
( X2 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6473]) ).
cnf(c_0_6474_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6474]) ).
cnf(c_0_6474_1,axiom,
( c_Polynomial_Oorder(X1,X3,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6474]) ).
cnf(c_0_6474_2,axiom,
( ~ class_Rings_Oidom(X1)
| c_Polynomial_Oorder(X1,X3,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6474]) ).
cnf(c_0_6475_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6475]) ).
cnf(c_0_6475_1,axiom,
( ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6475]) ).
cnf(c_0_6475_2,axiom,
( ~ class_Rings_Ocomm__semiring__1(X2)
| ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| X1 = c_Groups_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6475]) ).
cnf(c_0_6476_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6476]) ).
cnf(c_0_6476_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6476]) ).
cnf(c_0_6476_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6476]) ).
cnf(c_0_6477_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6477]) ).
cnf(c_0_6477_1,axiom,
( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6477]) ).
cnf(c_0_6477_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6477]) ).
cnf(c_0_6478_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6478]) ).
cnf(c_0_6478_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6478]) ).
cnf(c_0_6478_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6478]) ).
cnf(c_0_6479_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6479]) ).
cnf(c_0_6479_1,axiom,
( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6479]) ).
cnf(c_0_6479_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6479]) ).
cnf(c_0_6480_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6480]) ).
cnf(c_0_6480_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6480]) ).
cnf(c_0_6481_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6481]) ).
cnf(c_0_6481_1,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6481]) ).
cnf(c_0_6482_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6482]) ).
cnf(c_0_6482_1,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6482]) ).
cnf(c_0_6483_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6483]) ).
cnf(c_0_6483_1,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6483]) ).
cnf(c_0_6484_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6484]) ).
cnf(c_0_6484_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6484]) ).
cnf(c_0_6484_2,axiom,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6484]) ).
cnf(c_0_6484_3,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6484]) ).
cnf(c_0_6485_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6485]) ).
cnf(c_0_6485_1,axiom,
( 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_Ono__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6485]) ).
cnf(c_0_6485_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6485]) ).
cnf(c_0_6485_3,axiom,
( ~ class_Rings_Ono__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6485]) ).
cnf(c_0_6486_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6486]) ).
cnf(c_0_6486_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6486]) ).
cnf(c_0_6486_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6486]) ).
cnf(c_0_6486_3,axiom,
( ~ class_Rings_Ono__zero__divisors(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6486]) ).
cnf(c_0_6487_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6487]) ).
cnf(c_0_6487_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6487]) ).
cnf(c_0_6490_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6490]) ).
cnf(c_0_6490_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6490]) ).
cnf(c_0_6490_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6490]) ).
cnf(c_0_6491_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6491]) ).
cnf(c_0_6491_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6491]) ).
cnf(c_0_6491_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6491]) ).
cnf(c_0_6493_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6493]) ).
cnf(c_0_6493_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6493]) ).
cnf(c_0_6493_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(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(literals_permutation,[status(thm)],[c_0_6493]) ).
cnf(c_0_6494_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6494]) ).
cnf(c_0_6494_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6494]) ).
cnf(c_0_6494_2,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(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(literals_permutation,[status(thm)],[c_0_6494]) ).
cnf(c_0_6495_0,axiom,
( X2 = X3
| ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6495]) ).
cnf(c_0_6495_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| X2 = X3
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6495]) ).
cnf(c_0_6495_2,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6495]) ).
cnf(c_0_6496_0,axiom,
( X2 = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6496]) ).
cnf(c_0_6496_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| X2 = X3
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6496]) ).
cnf(c_0_6496_2,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6496]) ).
cnf(c_0_6497_0,axiom,
( X1 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6497]) ).
cnf(c_0_6497_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6497]) ).
cnf(c_0_6498_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6498]) ).
cnf(c_0_6498_1,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6498]) ).
cnf(c_0_6498_2,axiom,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6498]) ).
cnf(c_0_6499_0,axiom,
( c_Nat_OSuc(sk1_esk11_1(X1)) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6499]) ).
cnf(c_0_6499_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Nat_OSuc(sk1_esk11_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6499]) ).
cnf(c_0_6500_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6500]) ).
cnf(c_0_6500_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6500]) ).
cnf(c_0_6500_2,axiom,
( c_Groups_Oplus__class_Oplus(X1,X3,X2) != X3
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6500]) ).
cnf(c_0_6501_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6501]) ).
cnf(c_0_6501_1,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6501]) ).
cnf(c_0_6501_2,axiom,
( X2 != X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6501]) ).
cnf(c_0_6502_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6502]) ).
cnf(c_0_6502_1,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6502]) ).
cnf(c_0_6502_2,axiom,
( X2 != X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6502]) ).
cnf(c_0_6503_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6503]) ).
cnf(c_0_6503_1,axiom,
( ~ class_Rings_Oidom(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6503]) ).
cnf(c_0_6503_2,axiom,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| 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))) ),
inference(literals_permutation,[status(thm)],[c_0_6503]) ).
cnf(c_0_6503_3,axiom,
( 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)
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6503]) ).
cnf(c_0_6504_0,axiom,
( c_Polynomial_OpCons(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6504_1,axiom,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6504_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6504_3,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6505_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6505]) ).
cnf(c_0_6505_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6505]) ).
cnf(c_0_6506_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6506]) ).
cnf(c_0_6506_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6506]) ).
cnf(c_0_6507_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6507]) ).
cnf(c_0_6507_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6507]) ).
cnf(c_0_6508_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6508]) ).
cnf(c_0_6508_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6508]) ).
cnf(c_0_6509_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6509]) ).
cnf(c_0_6509_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6509]) ).
cnf(c_0_6509_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(literals_permutation,[status(thm)],[c_0_6509]) ).
cnf(c_0_6510_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6510_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6510_2,axiom,
( ~ class_Rings_Ozero__neq__one(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6510_3,axiom,
( ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6510_4,axiom,
( ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6510_5,axiom,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6510_6,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6511_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6511]) ).
cnf(c_0_6511_1,axiom,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6511]) ).
cnf(c_0_6511_2,axiom,
( X2 != c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6511]) ).
cnf(c_0_6512_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6512]) ).
cnf(c_0_6512_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6512]) ).
cnf(c_0_6512_2,axiom,
( X2 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6512]) ).
cnf(c_0_6513_0,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6513]) ).
cnf(c_0_6513_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6513]) ).
cnf(c_0_6513_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6513]) ).
cnf(c_0_6514_0,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6514]) ).
cnf(c_0_6514_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6514]) ).
cnf(c_0_6514_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6514]) ).
cnf(c_0_6515_0,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6515]) ).
cnf(c_0_6515_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6515]) ).
cnf(c_0_6515_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6515]) ).
cnf(c_0_6516_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6516]) ).
cnf(c_0_6516_1,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6516]) ).
cnf(c_0_6516_2,axiom,
( X2 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6516]) ).
cnf(c_0_6517_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6517_1,axiom,
( X2 != X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6517_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6518_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6518]) ).
cnf(c_0_6518_1,axiom,
( X2 != X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6518]) ).
cnf(c_0_6518_2,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6518]) ).
cnf(c_0_6519_0,axiom,
( c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6519]) ).
cnf(c_0_6519_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6519]) ).
cnf(c_0_6520_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6520]) ).
cnf(c_0_6520_1,axiom,
( ~ class_Groups_Ozero(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_6520]) ).
cnf(c_0_6521_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6521]) ).
cnf(c_0_6521_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6521]) ).
cnf(c_0_6521_2,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6521]) ).
cnf(c_0_6522_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6522]) ).
cnf(c_0_6522_1,axiom,
( X1 != X3
| 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(literals_permutation,[status(thm)],[c_0_6522]) ).
cnf(c_0_6523_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6523]) ).
cnf(c_0_6523_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6523]) ).
cnf(c_0_6524_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6524]) ).
cnf(c_0_6524_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6524]) ).
cnf(c_0_6525_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6525]) ).
cnf(c_0_6525_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6525]) ).
cnf(c_0_6525_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6525]) ).
cnf(c_0_6526_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6526]) ).
cnf(c_0_6526_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6526]) ).
cnf(c_0_6526_2,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6526]) ).
cnf(c_0_6527_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6527]) ).
cnf(c_0_6527_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_6527]) ).
cnf(c_0_6528_0,axiom,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6528]) ).
cnf(c_0_6528_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6528]) ).
cnf(c_0_6530_0,axiom,
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6530]) ).
cnf(c_0_6530_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6530]) ).
cnf(c_0_6530_2,axiom,
( ~ class_RealVector_Oreal__normed__div__algebra(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6530]) ).
cnf(c_0_6531_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6531]) ).
cnf(c_0_6531_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6531]) ).
cnf(c_0_6531_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6531]) ).
cnf(c_0_6532_0,axiom,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6532]) ).
cnf(c_0_6532_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_6532]) ).
cnf(c_0_6533_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6533]) ).
cnf(c_0_6533_1,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6533]) ).
cnf(c_0_6534_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6534]) ).
cnf(c_0_6534_1,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6534]) ).
cnf(c_0_6535_0,axiom,
( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6535]) ).
cnf(c_0_6535_1,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6535]) ).
cnf(c_0_6539_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6539]) ).
cnf(c_0_6539_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6539]) ).
cnf(c_0_6540_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6540]) ).
cnf(c_0_6540_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6540]) ).
cnf(c_0_6541_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6541]) ).
cnf(c_0_6541_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6541]) ).
cnf(c_0_6542_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6542]) ).
cnf(c_0_6542_1,axiom,
( 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) ),
inference(literals_permutation,[status(thm)],[c_0_6542]) ).
cnf(c_0_6543_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6543]) ).
cnf(c_0_6543_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6543]) ).
cnf(c_0_6544_0,axiom,
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6544]) ).
cnf(c_0_6544_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6544]) ).
cnf(c_0_6544_2,axiom,
( ~ class_RealVector_Oreal__normed__div__algebra(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6544]) ).
cnf(c_0_6545_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6545]) ).
cnf(c_0_6545_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6545]) ).
cnf(c_0_6546_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6546]) ).
cnf(c_0_6546_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6546]) ).
cnf(c_0_6547_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6547]) ).
cnf(c_0_6547_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6547]) ).
cnf(c_0_6548_0,axiom,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),sk1_esk15_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6548]) ).
cnf(c_0_6548_1,axiom,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),sk1_esk15_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6548]) ).
cnf(c_0_6549_0,axiom,
( c_Polynomial_Osmult(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6549]) ).
cnf(c_0_6549_1,axiom,
( ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6549]) ).
cnf(c_0_6549_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6549]) ).
cnf(c_0_6550_0,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6550]) ).
cnf(c_0_6550_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6550]) ).
cnf(c_0_6551_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6551]) ).
cnf(c_0_6551_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6551]) ).
cnf(c_0_6551_2,axiom,
( X2 != c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6551]) ).
cnf(c_0_6552_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6552]) ).
cnf(c_0_6552_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6552]) ).
cnf(c_0_6552_2,axiom,
( X3 != c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6552]) ).
cnf(c_0_6553_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk34_2(X2,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6553]) ).
cnf(c_0_6553_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk34_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6553]) ).
cnf(c_0_6554_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk33_2(X2,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6554]) ).
cnf(c_0_6554_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk33_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6554]) ).
cnf(c_0_6555_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6555]) ).
cnf(c_0_6555_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6555]) ).
cnf(c_0_6556_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6556]) ).
cnf(c_0_6556_1,axiom,
( ~ class_Rings_Osemiring__0(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6556]) ).
cnf(c_0_6556_2,axiom,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6556]) ).
cnf(c_0_6557_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6557]) ).
cnf(c_0_6557_1,axiom,
( ~ class_Rings_Osemiring__0(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6557]) ).
cnf(c_0_6557_2,axiom,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6557]) ).
cnf(c_0_6557_3,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6557]) ).
cnf(c_0_6558_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6558]) ).
cnf(c_0_6558_1,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6558]) ).
cnf(c_0_6562_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6562]) ).
cnf(c_0_6562_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6562]) ).
cnf(c_0_6563_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6563]) ).
cnf(c_0_6563_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6563]) ).
cnf(c_0_6564_0,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6564]) ).
cnf(c_0_6564_1,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6564]) ).
cnf(c_0_6565_0,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6565]) ).
cnf(c_0_6565_1,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6565]) ).
cnf(c_0_6566_0,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6566]) ).
cnf(c_0_6566_1,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6566]) ).
cnf(c_0_6567_0,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6567]) ).
cnf(c_0_6567_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6567]) ).
cnf(c_0_6568_0,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6568]) ).
cnf(c_0_6568_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6568]) ).
cnf(c_0_6569_0,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6569]) ).
cnf(c_0_6569_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6569]) ).
cnf(c_0_6570_0,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6570]) ).
cnf(c_0_6570_1,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6570]) ).
cnf(c_0_6571_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6571]) ).
cnf(c_0_6571_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6571]) ).
cnf(c_0_6572_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6572]) ).
cnf(c_0_6572_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6572]) ).
cnf(c_0_6573_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6573]) ).
cnf(c_0_6573_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6573]) ).
cnf(c_0_6574_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6574]) ).
cnf(c_0_6574_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6574]) ).
cnf(c_0_6575_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6575]) ).
cnf(c_0_6575_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6575]) ).
cnf(c_0_6575_2,axiom,
( ~ class_Rings_Osemiring__0(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6575]) ).
cnf(c_0_6575_3,axiom,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6575]) ).
cnf(c_0_6576_0,axiom,
( 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),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6576]) ).
cnf(c_0_6576_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6576]) ).
cnf(c_0_6576_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6576]) ).
cnf(c_0_6579_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6579]) ).
cnf(c_0_6579_1,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6579]) ).
cnf(c_0_6580_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6580]) ).
cnf(c_0_6580_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6580]) ).
cnf(c_0_6581_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6581]) ).
cnf(c_0_6581_1,axiom,
( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6581]) ).
cnf(c_0_6581_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != X1
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6581]) ).
cnf(c_0_6582_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6582]) ).
cnf(c_0_6582_1,axiom,
( 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) ),
inference(literals_permutation,[status(thm)],[c_0_6582]) ).
cnf(c_0_6583_0,axiom,
( X2 = 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(literals_permutation,[status(thm)],[c_0_6583]) ).
cnf(c_0_6583_1,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6583]) ).
cnf(c_0_6584_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6584]) ).
cnf(c_0_6584_1,axiom,
( 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) ),
inference(literals_permutation,[status(thm)],[c_0_6584]) ).
cnf(c_0_6585_0,axiom,
( X2 = 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(literals_permutation,[status(thm)],[c_0_6585]) ).
cnf(c_0_6585_1,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6585]) ).
cnf(c_0_6586_0,axiom,
( c_Polynomial_Omonom(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6586]) ).
cnf(c_0_6586_1,axiom,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6586]) ).
cnf(c_0_6586_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6586]) ).
cnf(c_0_6587_0,axiom,
( c_Polynomial_Osmult(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6587]) ).
cnf(c_0_6587_1,axiom,
( ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6587]) ).
cnf(c_0_6587_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6587]) ).
cnf(c_0_6588_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6588]) ).
cnf(c_0_6588_1,axiom,
( X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6588]) ).
cnf(c_0_6588_2,axiom,
( X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6588]) ).
cnf(c_0_6589_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6589]) ).
cnf(c_0_6589_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6589]) ).
cnf(c_0_6589_2,axiom,
( X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6589]) ).
cnf(c_0_6590_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6590]) ).
cnf(c_0_6590_1,axiom,
( X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6590]) ).
cnf(c_0_6590_2,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6590]) ).
cnf(c_0_6591_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6591]) ).
cnf(c_0_6591_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6591]) ).
cnf(c_0_6591_2,axiom,
( X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6591]) ).
cnf(c_0_6592_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6592]) ).
cnf(c_0_6592_1,axiom,
( X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6592]) ).
cnf(c_0_6592_2,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6592]) ).
cnf(c_0_6593_0,axiom,
( c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6593]) ).
cnf(c_0_6593_1,axiom,
( ~ class_Rings_Oidom(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)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6593]) ).
cnf(c_0_6593_2,axiom,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6593]) ).
cnf(c_0_6593_3,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6593]) ).
cnf(c_0_6594_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6594]) ).
cnf(c_0_6594_1,axiom,
( X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6594]) ).
cnf(c_0_6596_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6596]) ).
cnf(c_0_6596_1,axiom,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6596]) ).
cnf(c_0_6597_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6597]) ).
cnf(c_0_6597_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6597]) ).
cnf(c_0_6598_0,axiom,
( c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1)) = c_Power_Opower__class_Opower(X1)
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6598]) ).
cnf(c_0_6598_1,axiom,
( ~ class_Power_Opower(X1)
| c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1)) = c_Power_Opower__class_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6598]) ).
cnf(c_0_6600_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6600]) ).
cnf(c_0_6600_1,axiom,
( X2 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6600]) ).
cnf(c_0_6601_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6601]) ).
cnf(c_0_6601_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6601]) ).
cnf(c_0_6602_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6602]) ).
cnf(c_0_6602_1,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6602]) ).
cnf(c_0_6603_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6603]) ).
cnf(c_0_6603_1,axiom,
( ~ class_Rings_Omult__zero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6603]) ).
cnf(c_0_6604_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6604]) ).
cnf(c_0_6604_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6604]) ).
cnf(c_0_6605_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6605]) ).
cnf(c_0_6605_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6605]) ).
cnf(c_0_6606_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6606]) ).
cnf(c_0_6606_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6606]) ).
cnf(c_0_6607_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6607]) ).
cnf(c_0_6607_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6607]) ).
cnf(c_0_6607_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6607]) ).
cnf(c_0_6608_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6608]) ).
cnf(c_0_6608_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6608]) ).
cnf(c_0_6608_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6608]) ).
cnf(c_0_6609_0,axiom,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6609]) ).
cnf(c_0_6609_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6609]) ).
cnf(c_0_6610_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6610]) ).
cnf(c_0_6610_1,axiom,
( ~ class_Groups_Ocomm__monoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6610]) ).
cnf(c_0_6611_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6611]) ).
cnf(c_0_6611_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6611]) ).
cnf(c_0_6612_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6612]) ).
cnf(c_0_6612_1,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6612]) ).
cnf(c_0_6613_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6613]) ).
cnf(c_0_6613_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6613]) ).
cnf(c_0_6614_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6614]) ).
cnf(c_0_6614_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6614]) ).
cnf(c_0_6615_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6615]) ).
cnf(c_0_6615_1,axiom,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6615]) ).
cnf(c_0_6615_2,axiom,
( X2 != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6615]) ).
cnf(c_0_6616_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6616]) ).
cnf(c_0_6616_1,axiom,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6616]) ).
cnf(c_0_6616_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6616]) ).
cnf(c_0_6617_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6617]) ).
cnf(c_0_6617_1,axiom,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6617]) ).
cnf(c_0_6617_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6617]) ).
cnf(c_0_6618_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6618]) ).
cnf(c_0_6618_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6618]) ).
cnf(c_0_6618_2,axiom,
( X2 != X3
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6618]) ).
cnf(c_0_6619_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6619]) ).
cnf(c_0_6619_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6619]) ).
cnf(c_0_6620_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6620]) ).
cnf(c_0_6620_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = X2
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6620]) ).
cnf(c_0_6620_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6620]) ).
cnf(c_0_6621_0,axiom,
( c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6621]) ).
cnf(c_0_6621_1,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6621]) ).
cnf(c_0_6622_0,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk35_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6622]) ).
cnf(c_0_6622_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk35_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6622]) ).
cnf(c_0_6623_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6623]) ).
cnf(c_0_6623_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6623]) ).
cnf(c_0_6624_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6624]) ).
cnf(c_0_6624_1,axiom,
( ~ class_Rings_Omult__zero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6624]) ).
cnf(c_0_6625_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6625]) ).
cnf(c_0_6625_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6625]) ).
cnf(c_0_6626_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6626]) ).
cnf(c_0_6626_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6626]) ).
cnf(c_0_6627_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6627]) ).
cnf(c_0_6627_1,axiom,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Oone__class_Oone(X1)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6627]) ).
cnf(c_0_6627_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6627]) ).
cnf(c_0_6628_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6628]) ).
cnf(c_0_6628_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6628]) ).
cnf(c_0_6628_2,axiom,
( X2 != X3
| ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6628]) ).
cnf(c_0_6629_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6629]) ).
cnf(c_0_6629_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6629]) ).
cnf(c_0_6629_2,axiom,
( X2 != X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6629]) ).
cnf(c_0_6630_0,axiom,
( hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6630]) ).
cnf(c_0_6630_1,axiom,
( ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6630]) ).
cnf(c_0_6630_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6630]) ).
cnf(c_0_6632_0,axiom,
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6632]) ).
cnf(c_0_6632_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6632]) ).
cnf(c_0_6633_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6633]) ).
cnf(c_0_6633_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6633]) ).
cnf(c_0_6634_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6634]) ).
cnf(c_0_6634_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6634]) ).
cnf(c_0_6635_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6635]) ).
cnf(c_0_6635_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6635]) ).
cnf(c_0_6636_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6636]) ).
cnf(c_0_6636_1,axiom,
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6636]) ).
cnf(c_0_6637_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6637]) ).
cnf(c_0_6637_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6637]) ).
cnf(c_0_6638_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6638]) ).
cnf(c_0_6638_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6638]) ).
cnf(c_0_6639_0,axiom,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6639]) ).
cnf(c_0_6639_1,axiom,
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6639]) ).
cnf(c_0_6640_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6640]) ).
cnf(c_0_6640_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6640]) ).
cnf(c_0_6641_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6641]) ).
cnf(c_0_6641_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6641]) ).
cnf(c_0_6642_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6642]) ).
cnf(c_0_6642_1,axiom,
( X1 != c_Nat_OSuc(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6642]) ).
cnf(c_0_6643_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6643]) ).
cnf(c_0_6643_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_6643]) ).
cnf(c_0_6643_2,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6643]) ).
cnf(c_0_6644_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6644]) ).
cnf(c_0_6644_1,axiom,
( ~ class_Groups_Ocomm__monoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6644]) ).
cnf(c_0_6645_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6645]) ).
cnf(c_0_6645_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6645]) ).
cnf(c_0_6646_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6646]) ).
cnf(c_0_6646_1,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6646]) ).
cnf(c_0_6647_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6647]) ).
cnf(c_0_6647_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6647]) ).
cnf(c_0_6648_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6648]) ).
cnf(c_0_6648_1,axiom,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6648]) ).
cnf(c_0_6649_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6649]) ).
cnf(c_0_6649_1,axiom,
( X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6649]) ).
cnf(c_0_6650_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6650]) ).
cnf(c_0_6650_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6650]) ).
cnf(c_0_6651_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6651]) ).
cnf(c_0_6651_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6651]) ).
cnf(c_0_6651_2,axiom,
( X2 != X3
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6651]) ).
cnf(c_0_6652_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6652]) ).
cnf(c_0_6652_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6652]) ).
cnf(c_0_6652_2,axiom,
( X2 != X3
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6652]) ).
cnf(c_0_6653_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6653]) ).
cnf(c_0_6653_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6653]) ).
cnf(c_0_6653_2,axiom,
( X2 != X3
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6653]) ).
cnf(c_0_6654_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6654]) ).
cnf(c_0_6654_1,axiom,
( X2 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6654]) ).
cnf(c_0_6654_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| X2 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6654]) ).
cnf(c_0_6656_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6656]) ).
cnf(c_0_6656_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6656]) ).
cnf(c_0_6657_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6657]) ).
cnf(c_0_6657_1,axiom,
( X1 != c_Nat_OSuc(X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6657]) ).
cnf(c_0_6658_0,axiom,
( X1 = X2
| X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 = c_Groups_Ozero__class_Ozero(X3)
| c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| ~ class_Rings_Odivision__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6658]) ).
cnf(c_0_6658_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 = X2
| X1 = c_Groups_Ozero__class_Ozero(X3)
| c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| ~ class_Rings_Odivision__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6658]) ).
cnf(c_0_6658_2,axiom,
( X1 = c_Groups_Ozero__class_Ozero(X3)
| X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 = X2
| c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| ~ class_Rings_Odivision__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6658]) ).
cnf(c_0_6658_3,axiom,
( c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| X1 = c_Groups_Ozero__class_Ozero(X3)
| X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6658]) ).
cnf(c_0_6658_4,axiom,
( ~ class_Rings_Odivision__ring(X3)
| c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| X1 = c_Groups_Ozero__class_Ozero(X3)
| X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6658]) ).
cnf(c_0_6659_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6659]) ).
cnf(c_0_6659_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6659]) ).
cnf(c_0_6660_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6660]) ).
cnf(c_0_6660_1,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6660]) ).
cnf(c_0_6662_0,axiom,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6662]) ).
cnf(c_0_6662_1,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6662]) ).
cnf(c_0_6664_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6664]) ).
cnf(c_0_6664_1,axiom,
( X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6664]) ).
cnf(c_0_6665_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6665]) ).
cnf(c_0_6665_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6665]) ).
cnf(c_0_6667_0,axiom,
( c_Rings_Odvd__class_Odvd(X1,X2,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6667]) ).
cnf(c_0_6667_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6667]) ).
cnf(c_0_6668_0,axiom,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6668]) ).
cnf(c_0_6668_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6668]) ).
cnf(c_0_6669_0,axiom,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6669]) ).
cnf(c_0_6669_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6669]) ).
cnf(c_0_6670_0,axiom,
( X2 = X3
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6670]) ).
cnf(c_0_6670_1,axiom,
( ~ class_Rings_Oidom(X1)
| X2 = X3
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6670]) ).
cnf(c_0_6670_2,axiom,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| X2 = X3
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6670]) ).
cnf(c_0_6670_3,axiom,
( c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3)
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6670]) ).
cnf(c_0_6671_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6671]) ).
cnf(c_0_6671_1,axiom,
( X2 != 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)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6671]) ).
cnf(c_0_6671_2,axiom,
( X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != 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(literals_permutation,[status(thm)],[c_0_6671]) ).
cnf(c_0_6672_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6672]) ).
cnf(c_0_6672_1,axiom,
( X2 != 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)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6672]) ).
cnf(c_0_6672_2,axiom,
( X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != 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(literals_permutation,[status(thm)],[c_0_6672]) ).
cnf(c_0_6675_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6675]) ).
cnf(c_0_6675_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6675]) ).
cnf(c_0_6676_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6676]) ).
cnf(c_0_6676_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6676]) ).
cnf(c_0_6677_0,axiom,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6677]) ).
cnf(c_0_6677_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6677]) ).
cnf(c_0_6682_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6682]) ).
cnf(c_0_6682_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6682]) ).
cnf(c_0_6684_0,axiom,
( ~ c_Polynomial_Opos__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6684]) ).
cnf(c_0_6684_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6684]) ).
cnf(c_0_6692_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6692]) ).
cnf(c_0_6692_1,axiom,
( X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6692]) ).
cnf(c_0_6693_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6693]) ).
cnf(c_0_6693_1,axiom,
( X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6693]) ).
cnf(c_0_6694_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6694]) ).
cnf(c_0_6694_1,axiom,
( X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6694]) ).
cnf(c_0_6695_0,axiom,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6695]) ).
cnf(c_0_6695_1,axiom,
( X1 != X2
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6695]) ).
cnf(c_0_6696_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6696]) ).
cnf(c_0_6696_1,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6696]) ).
cnf(c_0_6697_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6697]) ).
cnf(c_0_6697_1,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6697]) ).
cnf(c_0_6698_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6698]) ).
cnf(c_0_6698_1,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6698]) ).
cnf(c_0_6699_0,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6699]) ).
cnf(c_0_6699_1,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6699]) ).
cnf(c_0_6704_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6704]) ).
cnf(c_0_6704_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_6704]) ).
cnf(c_0_6711_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6711]) ).
cnf(c_0_6711_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6711]) ).
cnf(c_0_6712_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6712]) ).
cnf(c_0_6712_1,axiom,
( X1 != 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(literals_permutation,[status(thm)],[c_0_6712]) ).
cnf(c_0_6713_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6713]) ).
cnf(c_0_6713_1,axiom,
( X1 != 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(literals_permutation,[status(thm)],[c_0_6713]) ).
cnf(c_0_6714_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6714]) ).
cnf(c_0_6714_1,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6714]) ).
cnf(c_0_6715_0,axiom,
( X2 = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6715]) ).
cnf(c_0_6715_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| X2 = X3
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6715]) ).
cnf(c_0_6715_2,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6715]) ).
cnf(c_0_6716_0,axiom,
( X2 = X3
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Rings_Oinverse__class_Oinverse(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6716]) ).
cnf(c_0_6716_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 = X3
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Rings_Oinverse__class_Oinverse(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6716]) ).
cnf(c_0_6716_2,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Rings_Oinverse__class_Oinverse(X1,X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6716]) ).
cnf(c_0_6717_0,axiom,
( X1 = X2
| c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6717]) ).
cnf(c_0_6717_1,axiom,
( c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| X1 = X2
| ~ class_Rings_Odivision__ring__inverse__zero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6717]) ).
cnf(c_0_6717_2,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X3)
| c_Rings_Oinverse__class_Oinverse(X3,X1) != c_Rings_Oinverse__class_Oinverse(X3,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6717]) ).
cnf(c_0_6718_0,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6718]) ).
cnf(c_0_6718_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6718]) ).
cnf(c_0_6718_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6718]) ).
cnf(c_0_6729_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6729]) ).
cnf(c_0_6729_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6729]) ).
cnf(c_0_6730_0,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6730]) ).
cnf(c_0_6730_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6730]) ).
cnf(c_0_6731_0,axiom,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6731]) ).
cnf(c_0_6731_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6731]) ).
cnf(c_0_6731_2,axiom,
( X3 != c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6731]) ).
cnf(c_0_6732_0,axiom,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6732]) ).
cnf(c_0_6732_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| X3 != c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6732]) ).
cnf(c_0_6732_2,axiom,
( X3 != c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6732]) ).
cnf(c_0_6733_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X3) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6733]) ).
cnf(c_0_6733_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| c_Groups_Ouminus__class_Ouminus(X1,X3) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6733]) ).
cnf(c_0_6733_2,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X3) != X2
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6733]) ).
cnf(c_0_6734_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X3) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6734]) ).
cnf(c_0_6734_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| c_Groups_Ouminus__class_Ouminus(X1,X3) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6734]) ).
cnf(c_0_6734_2,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X3) != X2
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6734]) ).
cnf(c_0_6735_0,axiom,
( c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,X3)
| ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6735]) ).
cnf(c_0_6735_1,axiom,
( ~ class_Rings_Oidom(X1)
| c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,X3)
| ~ class_Int_Oring__char__0(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6735]) ).
cnf(c_0_6735_2,axiom,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6735]) ).
cnf(c_0_6735_3,axiom,
( X2 != X3
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| c_Polynomial_Opoly(X1,X2) = c_Polynomial_Opoly(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6735]) ).
cnf(c_0_6736_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6736]) ).
cnf(c_0_6736_1,axiom,
( ~ class_Groups_Ozero(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_6736]) ).
cnf(c_0_6736_2,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6736]) ).
cnf(c_0_6737_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6737]) ).
cnf(c_0_6737_1,axiom,
( ~ class_Groups_Ozero(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6737]) ).
cnf(c_0_6737_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6737]) ).
cnf(c_0_6738_0,axiom,
( c_Groups_Ozero__class_Ozero(X1) = X2
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6738]) ).
cnf(c_0_6738_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = X2
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6738]) ).
cnf(c_0_6738_2,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6738]) ).
cnf(c_0_6739_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6739]) ).
cnf(c_0_6739_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6739]) ).
cnf(c_0_6739_2,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6739]) ).
cnf(c_0_6740_0,axiom,
( X2 = c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6740]) ).
cnf(c_0_6740_1,axiom,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Oone__class_Oone(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6740]) ).
cnf(c_0_6740_2,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6740]) ).
cnf(c_0_6741_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6741]) ).
cnf(c_0_6741_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6741]) ).
cnf(c_0_6741_2,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6741]) ).
cnf(c_0_6742_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6742]) ).
cnf(c_0_6742_1,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6742]) ).
cnf(c_0_6742_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6742]) ).
cnf(c_0_6743_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Oinverse(X2,X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6743]) ).
cnf(c_0_6743_1,axiom,
( c_Rings_Oinverse__class_Oinverse(X2,X1) != c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6743]) ).
cnf(c_0_6743_2,axiom,
( ~ class_Rings_Odivision__ring(X2)
| c_Rings_Oinverse__class_Oinverse(X2,X1) != c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6743]) ).
cnf(c_0_6744_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6744]) ).
cnf(c_0_6744_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6744]) ).
cnf(c_0_6744_2,axiom,
( X2 != X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6744]) ).
cnf(c_0_6745_0,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Oinverse(X1,X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6745]) ).
cnf(c_0_6745_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Oinverse(X1,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6745]) ).
cnf(c_0_6745_2,axiom,
( X2 != X3
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Oinverse(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6745]) ).
cnf(c_0_6746_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6746]) ).
cnf(c_0_6746_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6746]) ).
cnf(c_0_6746_2,axiom,
( c_RealVector_Onorm__class_Onorm(X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6746]) ).
cnf(c_0_6747_0,axiom,
( class_Orderings_Oord(tc_fun(X1,X2))
| ~ class_Orderings_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6747]) ).
cnf(c_0_6747_1,axiom,
( ~ class_Orderings_Oord(X2)
| class_Orderings_Oord(tc_fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6747]) ).
cnf(c_0_6748_0,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6748]) ).
cnf(c_0_6748_1,axiom,
( ~ class_Orderings_Oorder(X2)
| class_Orderings_Oorder(tc_fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6748]) ).
cnf(c_0_6749_0,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6749]) ).
cnf(c_0_6749_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| class_Orderings_Opreorder(tc_fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6749]) ).
cnf(c_0_6751_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6751]) ).
cnf(c_0_6751_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6751]) ).
cnf(c_0_6751_2,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6751]) ).
cnf(c_0_6752_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6752]) ).
cnf(c_0_6752_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6752]) ).
cnf(c_0_6752_2,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6752]) ).
cnf(c_0_6753_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6753]) ).
cnf(c_0_6753_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6753]) ).
cnf(c_0_6753_2,axiom,
( c_Groups_Ozero__class_Ozero(X1) != X2
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6753]) ).
cnf(c_0_6754_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6754]) ).
cnf(c_0_6754_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6754]) ).
cnf(c_0_6754_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6754]) ).
cnf(c_0_6755_0,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6755]) ).
cnf(c_0_6755_1,axiom,
( ~ class_Fields_Ofield__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Groups_Oone__class_Oone(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6755]) ).
cnf(c_0_6755_2,axiom,
( X2 != c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6755]) ).
cnf(c_0_6756_0,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6756]) ).
cnf(c_0_6756_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6756]) ).
cnf(c_0_6756_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6756]) ).
cnf(c_0_6757_0,axiom,
( c_RealVector_Onorm__class_Onorm(X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6757]) ).
cnf(c_0_6757_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6757]) ).
cnf(c_0_6757_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6757]) ).
cnf(c_0_6758_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6758]) ).
cnf(c_0_6758_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6758]) ).
cnf(c_0_6759_0,axiom,
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6759]) ).
cnf(c_0_6759_1,axiom,
( ~ class_Rings_Odivision__ring(X1)
| c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6759]) ).
cnf(c_0_6760_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6760]) ).
cnf(c_0_6760_1,axiom,
( ~ class_Fields_Ofield__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6760]) ).
cnf(c_0_6761_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_6761]) ).
cnf(c_0_6761_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6761]) ).
cnf(c_0_6762_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6762]) ).
cnf(c_0_6762_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X2
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6762]) ).
cnf(c_0_6762_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6762]) ).
cnf(c_0_6763_0,axiom,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6763]) ).
cnf(c_0_6763_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X2
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6763]) ).
cnf(c_0_6763_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6763]) ).
cnf(c_0_6764_0,axiom,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6764]) ).
cnf(c_0_6764_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6764]) ).
cnf(c_0_6765_0,axiom,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6765]) ).
cnf(c_0_6765_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6765]) ).
cnf(c_0_6770_0,axiom,
( X2 = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Oone(X1)
| c_Groups_Oone__class_Oone(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6770]) ).
cnf(c_0_6770_1,axiom,
( ~ class_Groups_Oone(X1)
| X2 = c_Groups_Oone__class_Oone(X1)
| c_Groups_Oone__class_Oone(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6770]) ).
cnf(c_0_6770_2,axiom,
( c_Groups_Oone__class_Oone(X1) != X2
| ~ class_Groups_Oone(X1)
| X2 = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6770]) ).
cnf(c_0_6771_0,axiom,
( c_Groups_Oone__class_Oone(X1) = X2
| ~ class_Groups_Oone(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6771]) ).
cnf(c_0_6771_1,axiom,
( ~ class_Groups_Oone(X1)
| c_Groups_Oone__class_Oone(X1) = X2
| X2 != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6771]) ).
cnf(c_0_6771_2,axiom,
( X2 != c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Oone(X1)
| c_Groups_Oone__class_Oone(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6771]) ).
cnf(c_0_6772_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6772]) ).
cnf(c_0_6772_1,axiom,
( ~ class_Groups_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6772]) ).
cnf(c_0_6772_2,axiom,
( c_Groups_Ozero__class_Ozero(X1) != X2
| ~ class_Groups_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6772]) ).
cnf(c_0_6773_0,axiom,
( c_Groups_Ozero__class_Ozero(X1) = X2
| ~ class_Groups_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6773]) ).
cnf(c_0_6773_1,axiom,
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) = X2
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6773]) ).
cnf(c_0_6773_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6773]) ).
cnf(c_0_6774_0,axiom,
( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6774]) ).
cnf(c_0_6774_1,axiom,
( ~ class_Rings_Ozero__neq__one(X1)
| c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6774]) ).
cnf(c_0_6775_0,axiom,
( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6775]) ).
cnf(c_0_6775_1,axiom,
( ~ class_Rings_Ozero__neq__one(X1)
| c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6775]) ).
cnf(c_0_6778_0,axiom,
( class_Rings_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6778]) ).
cnf(c_0_6778_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Odvd(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6778]) ).
cnf(c_0_6779_0,axiom,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6779]) ).
cnf(c_0_6779_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Groups_Oone(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6779]) ).
cnf(c_0_6780_0,axiom,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6780]) ).
cnf(c_0_6780_1,axiom,
( ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6780]) ).
cnf(c_0_6781_0,axiom,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6781]) ).
cnf(c_0_6781_1,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Oring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6781]) ).
cnf(c_0_6782_0,axiom,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6782]) ).
cnf(c_0_6782_1,axiom,
( ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6782]) ).
cnf(c_0_6783_0,axiom,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6783]) ).
cnf(c_0_6783_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Power_Opower(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6783]) ).
cnf(c_0_6784_0,axiom,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6784]) ).
cnf(c_0_6784_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6784]) ).
cnf(c_0_6785_0,axiom,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6785]) ).
cnf(c_0_6785_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Orderings_Oord(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6785]) ).
cnf(c_0_6786_0,axiom,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6786]) ).
cnf(c_0_6786_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6786]) ).
cnf(c_0_6787_0,axiom,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6787]) ).
cnf(c_0_6787_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6787]) ).
cnf(c_0_6788_0,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6788]) ).
cnf(c_0_6788_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6788]) ).
cnf(c_0_6789_0,axiom,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6789]) ).
cnf(c_0_6789_1,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6789]) ).
cnf(c_0_6790_0,axiom,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6790]) ).
cnf(c_0_6790_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6790]) ).
cnf(c_0_6791_0,axiom,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6791]) ).
cnf(c_0_6791_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6791]) ).
cnf(c_0_6792_0,axiom,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6792]) ).
cnf(c_0_6792_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6792]) ).
cnf(c_0_6793_0,axiom,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6793]) ).
cnf(c_0_6793_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6793]) ).
cnf(c_0_6794_0,axiom,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6794]) ).
cnf(c_0_6794_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6794]) ).
cnf(c_0_6795_0,axiom,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6795]) ).
cnf(c_0_6795_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6795]) ).
cnf(c_0_6796_0,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6796]) ).
cnf(c_0_6796_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6796]) ).
cnf(c_0_6797_0,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6797]) ).
cnf(c_0_6797_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6797]) ).
cnf(c_0_6798_0,axiom,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6798]) ).
cnf(c_0_6798_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6798]) ).
cnf(c_0_6799_0,axiom,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6799]) ).
cnf(c_0_6799_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6799]) ).
cnf(c_0_6800_0,axiom,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6800]) ).
cnf(c_0_6800_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6800]) ).
cnf(c_0_6801_0,axiom,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6801]) ).
cnf(c_0_6801_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6801]) ).
cnf(c_0_6802_0,axiom,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6802]) ).
cnf(c_0_6802_1,axiom,
( ~ class_Fields_Ofield(X1)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6802]) ).
cnf(c_0_6803_0,axiom,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6803]) ).
cnf(c_0_6803_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6803]) ).
cnf(c_0_6804_0,axiom,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6804]) ).
cnf(c_0_6804_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6804]) ).
cnf(c_0_6805_0,axiom,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6805]) ).
cnf(c_0_6805_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6805]) ).
cnf(c_0_6806_0,axiom,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6806]) ).
cnf(c_0_6806_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6806]) ).
cnf(c_0_6807_0,axiom,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6807]) ).
cnf(c_0_6807_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6807]) ).
cnf(c_0_6808_0,axiom,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6808]) ).
cnf(c_0_6808_1,axiom,
( ~ class_Rings_Oidom(X1)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6808]) ).
cnf(c_0_6809_0,axiom,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6809]) ).
cnf(c_0_6809_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6809]) ).
cnf(c_0_6810_0,axiom,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6810]) ).
cnf(c_0_6810_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6810]) ).
cnf(c_0_6811_0,axiom,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6811]) ).
cnf(c_0_6811_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6811]) ).
cnf(c_0_6812_0,axiom,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6812]) ).
cnf(c_0_6812_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6812]) ).
cnf(c_0_6813_0,axiom,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6813]) ).
cnf(c_0_6813_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6813]) ).
cnf(c_0_6814_0,axiom,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6814]) ).
cnf(c_0_6814_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6814]) ).
cnf(c_0_6815_0,axiom,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6815]) ).
cnf(c_0_6815_1,axiom,
( ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6815]) ).
cnf(c_0_6816_0,axiom,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6816]) ).
cnf(c_0_6816_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6816]) ).
cnf(c_0_6817_0,axiom,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6817]) ).
cnf(c_0_6817_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6817]) ).
cnf(c_0_6818_0,axiom,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6818]) ).
cnf(c_0_6818_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6818]) ).
cnf(c_0_6819_0,axiom,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6819]) ).
cnf(c_0_6819_1,axiom,
( ~ class_Rings_Oidom(X1)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6819]) ).
cnf(c_0_6820_0,axiom,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6820]) ).
cnf(c_0_6820_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6820]) ).
cnf(c_0_6821_0,axiom,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6821]) ).
cnf(c_0_6821_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6821]) ).
cnf(c_0_6822_0,axiom,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6822]) ).
cnf(c_0_6822_1,axiom,
( ~ class_Rings_Oidom(X1)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6822]) ).
cnf(c_0_6823_0,axiom,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6823]) ).
cnf(c_0_6823_1,axiom,
( ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6823]) ).
cnf(c_0_6824_0,axiom,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6824]) ).
cnf(c_0_6824_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6824]) ).
cnf(c_0_6825_0,axiom,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6825]) ).
cnf(c_0_6825_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6825]) ).
cnf(c_0_6826_0,axiom,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6826]) ).
cnf(c_0_6826_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6826]) ).
cnf(c_0_6827_0,axiom,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6827]) ).
cnf(c_0_6827_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6827]) ).
cnf(c_0_6828_0,axiom,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6828]) ).
cnf(c_0_6828_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6828]) ).
cnf(c_0_6829_0,axiom,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6829]) ).
cnf(c_0_6829_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6829]) ).
cnf(c_0_6830_0,axiom,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6830]) ).
cnf(c_0_6830_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6830]) ).
cnf(c_0_6831_0,axiom,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6831]) ).
cnf(c_0_6831_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6831]) ).
cnf(c_0_6832_0,axiom,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6832]) ).
cnf(c_0_6832_1,axiom,
( ~ class_Rings_Oidom(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6832]) ).
cnf(c_0_6833_0,axiom,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6833]) ).
cnf(c_0_6833_1,axiom,
( ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6833]) ).
cnf(c_0_6834_0,axiom,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6834]) ).
cnf(c_0_6834_1,axiom,
( c_Nat_OSuc(X1) != c_Nat_OSuc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6834]) ).
cnf(c_0_6835_0,axiom,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6835]) ).
cnf(c_0_6835_1,axiom,
( c_Nat_OSuc(X1) != c_Nat_OSuc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6835]) ).
cnf(c_0_6836_0,axiom,
( c_Nat_OSuc(X1) = c_Nat_OSuc(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6836]) ).
cnf(c_0_6836_1,axiom,
( X1 != X2
| c_Nat_OSuc(X1) = c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6836]) ).
cnf(c_0_5426_0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),sk1_esk22_0) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),sk1_esk21_0),
inference(literals_permutation,[status(thm)],[c_0_5426]) ).
cnf(c_0_5436_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5456_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
inference(literals_permutation,[status(thm)],[c_0_5456]) ).
cnf(c_0_6024_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,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(literals_permutation,[status(thm)],[c_0_6024]) ).
cnf(c_0_6051_0,axiom,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(literals_permutation,[status(thm)],[c_0_6051]) ).
cnf(c_0_6052_0,axiom,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(literals_permutation,[status(thm)],[c_0_6052]) ).
cnf(c_0_6458_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(literals_permutation,[status(thm)],[c_0_6458]) ).
cnf(c_0_6459_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(literals_permutation,[status(thm)],[c_0_6459]) ).
cnf(c_0_6460_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
inference(literals_permutation,[status(thm)],[c_0_6460]) ).
cnf(c_0_6461_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
inference(literals_permutation,[status(thm)],[c_0_6461]) ).
cnf(c_0_6492_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(literals_permutation,[status(thm)],[c_0_6492]) ).
cnf(c_0_6529_0,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_6529]) ).
cnf(c_0_6559_0,axiom,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(literals_permutation,[status(thm)],[c_0_6559]) ).
cnf(c_0_6560_0,axiom,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(literals_permutation,[status(thm)],[c_0_6560]) ).
cnf(c_0_6561_0,axiom,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(literals_permutation,[status(thm)],[c_0_6561]) ).
cnf(c_0_6577_0,axiom,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(literals_permutation,[status(thm)],[c_0_6577]) ).
cnf(c_0_6578_0,axiom,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(literals_permutation,[status(thm)],[c_0_6578]) ).
cnf(c_0_6666_0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6666]) ).
cnf(c_0_6706_0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6706]) ).
cnf(c_0_6837_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6837]) ).
cnf(c_0_6838_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6838]) ).
cnf(c_0_6839_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6839]) ).
cnf(c_0_6840_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6840]) ).
cnf(c_0_6841_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6841]) ).
cnf(c_0_6842_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6842]) ).
cnf(c_0_6845_0,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6845]) ).
cnf(c_0_6846_0,axiom,
c_Nat_OSuc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_6846]) ).
cnf(c_0_6847_0,axiom,
c_Nat_OSuc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_6847]) ).
cnf(c_0_6848_0,axiom,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6848]) ).
cnf(c_0_6849_0,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != sk1_esk26_0,
inference(literals_permutation,[status(thm)],[c_0_6849]) ).
cnf(c_0_6850_0,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sk1_esk25_0,
inference(literals_permutation,[status(thm)],[c_0_6850]) ).
cnf(c_0_6851_0,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
inference(literals_permutation,[status(thm)],[c_0_6851]) ).
cnf(c_0_6852_0,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
inference(literals_permutation,[status(thm)],[c_0_6852]) ).
cnf(c_0_6853_0,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_w____,
inference(literals_permutation,[status(thm)],[c_0_6853]) ).
cnf(c_0_6854_0,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_a____,
inference(literals_permutation,[status(thm)],[c_0_6854]) ).
cnf(c_0_6855_0,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != v_k____,
inference(literals_permutation,[status(thm)],[c_0_6855]) ).
cnf(c_0_5416_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),sk1_esk25_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,sk1_esk26_0,sk1_esk27_0)),X1))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1),
inference(literals_permutation,[status(thm)],[c_0_5416]) ).
cnf(c_0_5417_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X1))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1),
inference(literals_permutation,[status(thm)],[c_0_5417]) ).
cnf(c_0_5421_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(literals_permutation,[status(thm)],[c_0_5421]) ).
cnf(c_0_5422_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1),
inference(literals_permutation,[status(thm)],[c_0_5422]) ).
cnf(c_0_5424_0,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5453_0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),sk1_esk13_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_5453]) ).
cnf(c_0_5478_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(literals_permutation,[status(thm)],[c_0_5478]) ).
cnf(c_0_5485_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X2),X4),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5493_0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5501_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5502_0,axiom,
hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)) = hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Nat_OSuc(X5)),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5512_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)),
inference(literals_permutation,[status(thm)],[c_0_5512]) ).
cnf(c_0_5513_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2))),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5523_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sk1_esk27_0),sk1_esk25_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(literals_permutation,[status(thm)],[c_0_5523]) ).
cnf(c_0_5524_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5632_0,axiom,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_5632]) ).
cnf(c_0_5633_0,axiom,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5634_0,axiom,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5635_0,axiom,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5636_0,axiom,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5651_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sk1_esk3_0),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_5651]) ).
cnf(c_0_5652_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_5652]) ).
cnf(c_0_5656_0,axiom,
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)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_5656]) ).
cnf(c_0_5661_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____),
inference(literals_permutation,[status(thm)],[c_0_5661]) ).
cnf(c_0_5785_0,axiom,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5786_0,axiom,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5787_0,axiom,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5788_0,axiom,
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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5795_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5808_0,axiom,
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(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5809_0,axiom,
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(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5810_0,axiom,
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(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5811_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_5811]) ).
cnf(c_0_5846_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
inference(literals_permutation,[status(thm)],[c_0_5846]) ).
cnf(c_0_5860_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)),
inference(literals_permutation,[status(thm)],[c_0_5860]) ).
cnf(c_0_5886_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Nat_OSuc(X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_5886]) ).
cnf(c_0_5911_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))),
inference(literals_permutation,[status(thm)],[c_0_5911]) ).
cnf(c_0_5930_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_5930]) ).
cnf(c_0_5931_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)),
inference(literals_permutation,[status(thm)],[c_0_5931]) ).
cnf(c_0_5932_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_5932]) ).
cnf(c_0_5933_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_5933]) ).
cnf(c_0_5934_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_5934]) ).
cnf(c_0_5935_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
inference(literals_permutation,[status(thm)],[c_0_5935]) ).
cnf(c_0_5936_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
inference(literals_permutation,[status(thm)],[c_0_5936]) ).
cnf(c_0_5937_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_5937]) ).
cnf(c_0_6012_0,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(literals_permutation,[status(thm)],[c_0_6012]) ).
cnf(c_0_6013_0,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(literals_permutation,[status(thm)],[c_0_6013]) ).
cnf(c_0_6030_0,axiom,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(literals_permutation,[status(thm)],[c_0_6030]) ).
cnf(c_0_6115_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
inference(literals_permutation,[status(thm)],[c_0_6115]) ).
cnf(c_0_6116_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(literals_permutation,[status(thm)],[c_0_6116]) ).
cnf(c_0_6133_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6133]) ).
cnf(c_0_6163_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_6163]) ).
cnf(c_0_6170_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2)),
inference(literals_permutation,[status(thm)],[c_0_6170]) ).
cnf(c_0_6175_0,axiom,
c_Groups_Ouminus__class_Ouminus(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),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_6175]) ).
cnf(c_0_6227_0,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
inference(literals_permutation,[status(thm)],[c_0_6227]) ).
cnf(c_0_6250_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X2)) = c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6250]) ).
cnf(c_0_6272_0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sk1_esk32_0),X1),
inference(literals_permutation,[status(thm)],[c_0_6272]) ).
cnf(c_0_6273_0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sk1_esk14_0),X1),
inference(literals_permutation,[status(thm)],[c_0_6273]) ).
cnf(c_0_6274_0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1),
inference(literals_permutation,[status(thm)],[c_0_6274]) ).
cnf(c_0_6275_0,axiom,
c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
inference(literals_permutation,[status(thm)],[c_0_6275]) ).
cnf(c_0_6276_0,axiom,
c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),
inference(literals_permutation,[status(thm)],[c_0_6276]) ).
cnf(c_0_6282_0,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Nat_OSuc(X1)),
inference(literals_permutation,[status(thm)],[c_0_6282]) ).
cnf(c_0_6285_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6285]) ).
cnf(c_0_6286_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_6286]) ).
cnf(c_0_6287_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_6287]) ).
cnf(c_0_6288_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
inference(literals_permutation,[status(thm)],[c_0_6288]) ).
cnf(c_0_6289_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(literals_permutation,[status(thm)],[c_0_6289]) ).
cnf(c_0_6290_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6290]) ).
cnf(c_0_6355_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(literals_permutation,[status(thm)],[c_0_6355]) ).
cnf(c_0_6357_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_6357]) ).
cnf(c_0_6393_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),
inference(literals_permutation,[status(thm)],[c_0_6393]) ).
cnf(c_0_6408_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6408]) ).
cnf(c_0_6409_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6409]) ).
cnf(c_0_6410_0,axiom,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6410]) ).
cnf(c_0_6411_0,axiom,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6411]) ).
cnf(c_0_6412_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6412]) ).
cnf(c_0_6437_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6437]) ).
cnf(c_0_6438_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
inference(literals_permutation,[status(thm)],[c_0_6438]) ).
cnf(c_0_6488_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(literals_permutation,[status(thm)],[c_0_6488]) ).
cnf(c_0_6489_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(literals_permutation,[status(thm)],[c_0_6489]) ).
cnf(c_0_6536_0,axiom,
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(literals_permutation,[status(thm)],[c_0_6536]) ).
cnf(c_0_6537_0,axiom,
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(literals_permutation,[status(thm)],[c_0_6537]) ).
cnf(c_0_6538_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(literals_permutation,[status(thm)],[c_0_6538]) ).
cnf(c_0_6595_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6595]) ).
cnf(c_0_6599_0,axiom,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(literals_permutation,[status(thm)],[c_0_6599]) ).
cnf(c_0_6631_0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____),
inference(literals_permutation,[status(thm)],[c_0_6631]) ).
cnf(c_0_6655_0,axiom,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(literals_permutation,[status(thm)],[c_0_6655]) ).
cnf(c_0_6661_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6661]) ).
cnf(c_0_6663_0,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X1)),
inference(literals_permutation,[status(thm)],[c_0_6663]) ).
cnf(c_0_6673_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_OSuc(X1),
inference(literals_permutation,[status(thm)],[c_0_6673]) ).
cnf(c_0_6674_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = c_Nat_OSuc(X1),
inference(literals_permutation,[status(thm)],[c_0_6674]) ).
cnf(c_0_6678_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(literals_permutation,[status(thm)],[c_0_6678]) ).
cnf(c_0_6679_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(literals_permutation,[status(thm)],[c_0_6679]) ).
cnf(c_0_6680_0,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)),
inference(literals_permutation,[status(thm)],[c_0_6680]) ).
cnf(c_0_6681_0,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
inference(literals_permutation,[status(thm)],[c_0_6681]) ).
cnf(c_0_6683_0,axiom,
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(literals_permutation,[status(thm)],[c_0_6683]) ).
cnf(c_0_6685_0,axiom,
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(literals_permutation,[status(thm)],[c_0_6685]) ).
cnf(c_0_6686_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_6686]) ).
cnf(c_0_6687_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6687]) ).
cnf(c_0_6688_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(literals_permutation,[status(thm)],[c_0_6688]) ).
cnf(c_0_6689_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6689]) ).
cnf(c_0_6690_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_6690]) ).
cnf(c_0_6691_0,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6691]) ).
cnf(c_0_6700_0,axiom,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(literals_permutation,[status(thm)],[c_0_6700]) ).
cnf(c_0_6701_0,axiom,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(literals_permutation,[status(thm)],[c_0_6701]) ).
cnf(c_0_6702_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(literals_permutation,[status(thm)],[c_0_6702]) ).
cnf(c_0_6703_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(literals_permutation,[status(thm)],[c_0_6703]) ).
cnf(c_0_6705_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6705]) ).
cnf(c_0_6707_0,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk24_0),
inference(literals_permutation,[status(thm)],[c_0_6707]) ).
cnf(c_0_6708_0,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk19_0),
inference(literals_permutation,[status(thm)],[c_0_6708]) ).
cnf(c_0_6709_0,axiom,
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(literals_permutation,[status(thm)],[c_0_6709]) ).
cnf(c_0_6710_0,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(literals_permutation,[status(thm)],[c_0_6710]) ).
cnf(c_0_6719_0,axiom,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(literals_permutation,[status(thm)],[c_0_6719]) ).
cnf(c_0_6720_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(literals_permutation,[status(thm)],[c_0_6720]) ).
cnf(c_0_6721_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(literals_permutation,[status(thm)],[c_0_6721]) ).
cnf(c_0_6722_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(literals_permutation,[status(thm)],[c_0_6722]) ).
cnf(c_0_6723_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_6723]) ).
cnf(c_0_6724_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_6724]) ).
cnf(c_0_6725_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_6725]) ).
cnf(c_0_6726_0,axiom,
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(literals_permutation,[status(thm)],[c_0_6726]) ).
cnf(c_0_6727_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6727]) ).
cnf(c_0_6728_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6728]) ).
cnf(c_0_6750_0,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6750]) ).
cnf(c_0_6766_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sk1_esk32_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(literals_permutation,[status(thm)],[c_0_6766]) ).
cnf(c_0_6767_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sk1_esk14_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(literals_permutation,[status(thm)],[c_0_6767]) ).
cnf(c_0_6768_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(literals_permutation,[status(thm)],[c_0_6768]) ).
cnf(c_0_6769_0,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii),
inference(literals_permutation,[status(thm)],[c_0_6769]) ).
cnf(c_0_6776_0,axiom,
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(literals_permutation,[status(thm)],[c_0_6776]) ).
cnf(c_0_6777_0,axiom,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6777]) ).
cnf(c_0_6843_0,axiom,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6843]) ).
cnf(c_0_6844_0,axiom,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6844]) ).
cnf(c_0_6856_0,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6856]) ).
cnf(c_0_6857_0,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6857]) ).
cnf(c_0_6858_0,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6858]) ).
cnf(c_0_6859_0,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6859]) ).
cnf(c_0_6860_0,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6860]) ).
cnf(c_0_6861_0,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6861]) ).
cnf(c_0_6862_0,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6862]) ).
cnf(c_0_6863_0,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6863]) ).
cnf(c_0_6864_0,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6864]) ).
cnf(c_0_6865_0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6865]) ).
cnf(c_0_6866_0,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6866]) ).
cnf(c_0_6867_0,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6867]) ).
cnf(c_0_6868_0,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6868]) ).
cnf(c_0_6869_0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6869]) ).
cnf(c_0_6870_0,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6870]) ).
cnf(c_0_6871_0,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6871]) ).
cnf(c_0_6872_0,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6872]) ).
cnf(c_0_6873_0,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6873]) ).
cnf(c_0_6874_0,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6874]) ).
cnf(c_0_6875_0,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6875]) ).
cnf(c_0_6876_0,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6876]) ).
cnf(c_0_6877_0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6877]) ).
cnf(c_0_6878_0,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6878]) ).
cnf(c_0_6879_0,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6879]) ).
cnf(c_0_6880_0,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6880]) ).
cnf(c_0_6881_0,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6881]) ).
cnf(c_0_6882_0,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6882]) ).
cnf(c_0_6883_0,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6883]) ).
cnf(c_0_6884_0,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6884]) ).
cnf(c_0_6885_0,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6885]) ).
cnf(c_0_6886_0,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6886]) ).
cnf(c_0_6887_0,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6887]) ).
cnf(c_0_6888_0,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6888]) ).
cnf(c_0_6889_0,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6889]) ).
cnf(c_0_6890_0,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6890]) ).
cnf(c_0_6891_0,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6891]) ).
cnf(c_0_6892_0,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6892]) ).
cnf(c_0_6893_0,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6893]) ).
cnf(c_0_6894_0,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6894]) ).
cnf(c_0_6895_0,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6895]) ).
cnf(c_0_6896_0,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6896]) ).
cnf(c_0_6897_0,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6897]) ).
cnf(c_0_6898_0,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6898]) ).
cnf(c_0_6899_0,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6899]) ).
cnf(c_0_6900_0,axiom,
class_Power_Opower(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6900]) ).
cnf(c_0_6901_0,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6901]) ).
cnf(c_0_6902_0,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6902]) ).
cnf(c_0_6903_0,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6903]) ).
cnf(c_0_6904_0,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6904]) ).
cnf(c_0_6905_0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6905]) ).
cnf(c_0_6906_0,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6906]) ).
cnf(c_0_6907_0,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6907]) ).
cnf(c_0_6908_0,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6908]) ).
cnf(c_0_6909_0,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6909]) ).
cnf(c_0_6910_0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6910]) ).
cnf(c_0_6911_0,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6911]) ).
cnf(c_0_6912_0,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6912]) ).
cnf(c_0_6913_0,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6913]) ).
cnf(c_0_6914_0,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6914]) ).
cnf(c_0_6915_0,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6915]) ).
cnf(c_0_6916_0,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6916]) ).
cnf(c_0_6917_0,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6917]) ).
cnf(c_0_6918_0,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6918]) ).
cnf(c_0_6919_0,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6919]) ).
cnf(c_0_6920_0,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6920]) ).
cnf(c_0_6921_0,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6921]) ).
cnf(c_0_6922_0,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6922]) ).
cnf(c_0_6923_0,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6923]) ).
cnf(c_0_6924_0,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6924]) ).
cnf(c_0_6925_0,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6925]) ).
cnf(c_0_6926_0,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6926]) ).
cnf(c_0_6927_0,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6927]) ).
cnf(c_0_6928_0,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6928]) ).
cnf(c_0_6929_0,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6929]) ).
cnf(c_0_6930_0,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6930]) ).
cnf(c_0_6931_0,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6931]) ).
cnf(c_0_6932_0,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6932]) ).
cnf(c_0_6933_0,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6933]) ).
cnf(c_0_6934_0,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6934]) ).
cnf(c_0_6935_0,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6935]) ).
cnf(c_0_6936_0,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6936]) ).
cnf(c_0_6937_0,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6937]) ).
cnf(c_0_6938_0,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6938]) ).
cnf(c_0_6939_0,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6939]) ).
cnf(c_0_6940_0,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6940]) ).
cnf(c_0_6941_0,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6941]) ).
cnf(c_0_6942_0,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6942]) ).
cnf(c_0_6943_0,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6943]) ).
cnf(c_0_6944_0,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6944]) ).
cnf(c_0_6945_0,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6945]) ).
cnf(c_0_6946_0,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6946]) ).
cnf(c_0_6947_0,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6947]) ).
cnf(c_0_6948_0,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6948]) ).
cnf(c_0_6949_0,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6949]) ).
cnf(c_0_6950_0,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6950]) ).
cnf(c_0_6951_0,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6951]) ).
cnf(c_0_6952_0,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6952]) ).
cnf(c_0_6953_0,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6953]) ).
cnf(c_0_6954_0,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6954]) ).
cnf(c_0_6955_0,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6955]) ).
cnf(c_0_6956_0,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6956]) ).
cnf(c_0_6957_0,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6957]) ).
cnf(c_0_6958_0,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6958]) ).
cnf(c_0_6959_0,axiom,
class_Orderings_Oord(tc_HOL_Obool),
inference(literals_permutation,[status(thm)],[c_0_6959]) ).
cnf(c_0_6960_0,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
inference(literals_permutation,[status(thm)],[c_0_6960]) ).
cnf(c_0_6961_0,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(literals_permutation,[status(thm)],[c_0_6961]) ).
cnf(c_0_6962_0,axiom,
class_Rings_Odvd(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6962]) ).
cnf(c_0_6963_0,axiom,
class_Groups_Oone(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6963]) ).
cnf(c_0_6964_0,axiom,
class_Groups_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6964]) ).
cnf(c_0_6965_0,axiom,
class_Power_Opower(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6965]) ).
cnf(c_0_6966_0,axiom,
class_Orderings_Oord(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6966]) ).
cnf(c_0_6967_0,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6967]) ).
cnf(c_0_6968_0,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6968]) ).
cnf(c_0_6969_0,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6969]) ).
cnf(c_0_6970_0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6970]) ).
cnf(c_0_6971_0,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6971]) ).
cnf(c_0_6972_0,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6972]) ).
cnf(c_0_6973_0,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6973]) ).
cnf(c_0_6974_0,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6974]) ).
cnf(c_0_6975_0,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6975]) ).
cnf(c_0_6976_0,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6976]) ).
cnf(c_0_6977_0,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6977]) ).
cnf(c_0_6978_0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6978]) ).
cnf(c_0_6979_0,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6979]) ).
cnf(c_0_6980_0,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6980]) ).
cnf(c_0_6981_0,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6981]) ).
cnf(c_0_6982_0,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6982]) ).
cnf(c_0_6983_0,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6983]) ).
cnf(c_0_6984_0,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6984]) ).
cnf(c_0_6985_0,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6985]) ).
cnf(c_0_6986_0,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6986]) ).
cnf(c_0_6987_0,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6987]) ).
cnf(c_0_6988_0,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6988]) ).
cnf(c_0_6989_0,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6989]) ).
cnf(c_0_6990_0,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6990]) ).
cnf(c_0_6991_0,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6991]) ).
cnf(c_0_6992_0,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6992]) ).
cnf(c_0_6993_0,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6993]) ).
cnf(c_0_6994_0,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6994]) ).
cnf(c_0_6995_0,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6995]) ).
cnf(c_0_6996_0,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6996]) ).
cnf(c_0_6997_0,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6997]) ).
cnf(c_0_6998_0,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6998]) ).
cnf(c_0_6999_0,axiom,
class_Rings_Odvd(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6999]) ).
cnf(c_0_7000_0,axiom,
class_Groups_Oone(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7000]) ).
cnf(c_0_7001_0,axiom,
class_Rings_Oidom(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7001]) ).
cnf(c_0_7002_0,axiom,
class_Rings_Oring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7002]) ).
cnf(c_0_7003_0,axiom,
class_Groups_Ozero(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7003]) ).
cnf(c_0_7004_0,axiom,
class_Power_Opower(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7004]) ).
cnf(c_0_7005_0,axiom,
class_Rings_Oring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7005]) ).
cnf(c_0_7006_0,axiom,
class_Orderings_Oord(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7006]) ).
cnf(c_0_7007_0,axiom,
class_Rings_Osemiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7007]) ).
cnf(c_0_7008_0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7008]) ).
cnf(c_0_7009_0,axiom,
class_Orderings_Oorder(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7009]) ).
cnf(c_0_7010_0,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7010]) ).
cnf(c_0_7011_0,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7011]) ).
cnf(c_0_7012_0,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7012]) ).
cnf(c_0_7013_0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7013]) ).
cnf(c_0_7014_0,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7014]) ).
cnf(c_0_7015_0,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7015]) ).
cnf(c_0_7016_0,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7016]) ).
cnf(c_0_7017_0,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7017]) ).
cnf(c_0_7018_0,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7018]) ).
cnf(c_0_7019_0,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7019]) ).
cnf(c_0_7020_0,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7020]) ).
cnf(c_0_7021_0,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7021]) ).
cnf(c_0_7022_0,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7022]) ).
cnf(c_0_7023_0,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7023]) ).
cnf(c_0_7024_0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7024]) ).
cnf(c_0_7025_0,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7025]) ).
cnf(c_0_7026_0,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7026]) ).
cnf(c_0_7027_0,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7027]) ).
cnf(c_0_7028_0,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7028]) ).
cnf(c_0_7029_0,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7029]) ).
cnf(c_0_7030_0,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7030]) ).
cnf(c_0_7031_0,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7031]) ).
cnf(c_0_7032_0,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7032]) ).
cnf(c_0_7033_0,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7033]) ).
cnf(c_0_7034_0,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7034]) ).
cnf(c_0_7035_0,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7035]) ).
cnf(c_0_7036_0,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7036]) ).
cnf(c_0_7037_0,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7037]) ).
cnf(c_0_7038_0,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7038]) ).
cnf(c_0_7039_0,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7039]) ).
cnf(c_0_7040_0,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7040]) ).
cnf(c_0_7041_0,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7041]) ).
cnf(c_0_7042_0,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7042]) ).
cnf(c_0_7043_0,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7043]) ).
cnf(c_0_7044_0,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7044]) ).
cnf(c_0_7045_0,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7045]) ).
cnf(c_0_7046_0,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7046]) ).
cnf(c_0_7047_0,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7047]) ).
cnf(c_0_7048_0,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7048]) ).
cnf(c_0_7049_0,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7049]) ).
cnf(c_0_7050_0,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7050]) ).
cnf(c_0_7051_0,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7051]) ).
cnf(c_0_7052_0,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7052]) ).
cnf(c_0_7053_0,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7053]) ).
cnf(c_0_7054_0,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7054]) ).
cnf(c_0_7055_0,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7055]) ).
cnf(c_0_7056_0,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7056]) ).
cnf(c_0_7057_0,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7057]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,hypothesis,
! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
=> v_thesis____ ) ) ),
file('<stdin>',conj_0) ).
fof(c_0_1_002,conjecture,
v_thesis____,
file('<stdin>',conj_1) ).
fof(c_0_2_003,hypothesis,
! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
=> v_thesis____ ) ) ),
c_0_0 ).
fof(c_0_3_004,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_1])]) ).
fof(c_0_4_005,hypothesis,
! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| v_thesis____ ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])]) ).
fof(c_0_5_006,negated_conjecture,
~ v_thesis____,
c_0_3 ).
cnf(c_0_6_007,hypothesis,
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7_008,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8_009,hypothesis,
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
c_0_6,
[final] ).
cnf(c_0_9_010,negated_conjecture,
~ v_thesis____,
c_0_7,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_4031,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| v_thesis____ ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ae8c12.p',c_0_8) ).
cnf(c_5037,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(global_propositional_subsumption,[status(thm)],[c_4031,c_5037]) ).
cnf(c_5039,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(copy,[status(esa)],[c_5037]) ).
cnf(c_5046,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(copy,[status(esa)],[c_5039]) ).
cnf(c_5049,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(copy,[status(esa)],[c_5046]) ).
cnf(c_5051,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(copy,[status(esa)],[c_5049]) ).
cnf(c_9085,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(copy,[status(esa)],[c_5051]) ).
cnf(c_354501,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk2_1(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ),
inference(instantiation,[status(thm)],[c_9085]) ).
cnf(c_1410,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(X0),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ae8c12.p',c_0_6343_1) ).
cnf(c_6464,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(X0),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(copy,[status(esa)],[c_1410]) ).
cnf(c_180374,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ),
inference(instantiation,[status(thm)],[c_6464]) ).
cnf(c_1510,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk2_1(X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ae8c12.p',c_0_6310_1) ).
cnf(c_6564,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk2_1(X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(copy,[status(esa)],[c_1510]) ).
cnf(c_179872,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sk1_esk2_1(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))) ),
inference(instantiation,[status(thm)],[c_6564]) ).
cnf(c_1508,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ae8c12.p',c_0_6311_1) ).
cnf(c_6562,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(copy,[status(esa)],[c_1508]) ).
cnf(c_179864,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sk1_esk2_1(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(instantiation,[status(thm)],[c_6562]) ).
cnf(c_328,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ae8c12.p',c_0_5424_0) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_354501,c_180374,c_179872,c_179864,c_328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW259+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.13 % Command : iprover_modulo %s %d
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 5 04:57:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.48/0.67 % Orienting using strategy Equiv(ClausalAll)
% 0.48/0.67 % FOF problem with conjecture
% 0.48/0.67 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_08f374.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_ae8c12.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_0110e6 | grep -v "SZS"
% 0.48/0.70
% 0.48/0.70 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.48/0.70
% 0.48/0.70 %
% 0.48/0.70 % ------ iProver source info
% 0.48/0.70
% 0.48/0.70 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.48/0.70 % git: non_committed_changes: true
% 0.48/0.70 % git: last_make_outside_of_git: true
% 0.48/0.70
% 0.48/0.70 %
% 0.48/0.70 % ------ Input Options
% 0.48/0.70
% 0.48/0.70 % --out_options all
% 0.48/0.70 % --tptp_safe_out true
% 0.48/0.70 % --problem_path ""
% 0.48/0.70 % --include_path ""
% 0.48/0.70 % --clausifier .//eprover
% 0.48/0.70 % --clausifier_options --tstp-format
% 0.48/0.70 % --stdin false
% 0.48/0.70 % --dbg_backtrace false
% 0.48/0.70 % --dbg_dump_prop_clauses false
% 0.48/0.70 % --dbg_dump_prop_clauses_file -
% 0.48/0.70 % --dbg_out_stat false
% 0.48/0.70
% 0.48/0.70 % ------ General Options
% 0.48/0.70
% 0.48/0.70 % --fof false
% 0.48/0.70 % --time_out_real 150.
% 0.48/0.70 % --time_out_prep_mult 0.2
% 0.48/0.70 % --time_out_virtual -1.
% 0.48/0.70 % --schedule none
% 0.48/0.70 % --ground_splitting input
% 0.48/0.70 % --splitting_nvd 16
% 0.48/0.70 % --non_eq_to_eq false
% 0.48/0.70 % --prep_gs_sim true
% 0.48/0.70 % --prep_unflatten false
% 0.48/0.70 % --prep_res_sim true
% 0.48/0.70 % --prep_upred true
% 0.48/0.70 % --res_sim_input true
% 0.48/0.70 % --clause_weak_htbl true
% 0.48/0.70 % --gc_record_bc_elim false
% 0.48/0.70 % --symbol_type_check false
% 0.48/0.70 % --clausify_out false
% 0.48/0.70 % --large_theory_mode false
% 0.48/0.70 % --prep_sem_filter none
% 0.48/0.70 % --prep_sem_filter_out false
% 0.48/0.70 % --preprocessed_out false
% 0.48/0.70 % --sub_typing false
% 0.48/0.70 % --brand_transform false
% 0.48/0.70 % --pure_diseq_elim true
% 0.48/0.70 % --min_unsat_core false
% 0.48/0.70 % --pred_elim true
% 0.48/0.70 % --add_important_lit false
% 0.48/0.70 % --soft_assumptions false
% 0.48/0.70 % --reset_solvers false
% 0.48/0.70 % --bc_imp_inh []
% 0.48/0.70 % --conj_cone_tolerance 1.5
% 0.48/0.70 % --prolific_symb_bound 500
% 0.48/0.70 % --lt_threshold 2000
% 0.48/0.70
% 0.48/0.70 % ------ SAT Options
% 0.48/0.70
% 0.48/0.70 % --sat_mode false
% 0.48/0.70 % --sat_fm_restart_options ""
% 0.48/0.70 % --sat_gr_def false
% 0.48/0.70 % --sat_epr_types true
% 0.48/0.70 % --sat_non_cyclic_types false
% 0.48/0.70 % --sat_finite_models false
% 0.48/0.70 % --sat_fm_lemmas false
% 0.48/0.70 % --sat_fm_prep false
% 0.48/0.70 % --sat_fm_uc_incr true
% 0.48/0.70 % --sat_out_model small
% 0.48/0.70 % --sat_out_clauses false
% 0.48/0.70
% 0.48/0.70 % ------ QBF Options
% 0.48/0.70
% 0.48/0.70 % --qbf_mode false
% 0.48/0.70 % --qbf_elim_univ true
% 0.48/0.70 % --qbf_sk_in true
% 0.48/0.70 % --qbf_pred_elim true
% 0.48/0.70 % --qbf_split 32
% 0.48/0.70
% 0.48/0.70 % ------ BMC1 Options
% 0.48/0.70
% 0.48/0.70 % --bmc1_incremental false
% 0.48/0.70 % --bmc1_axioms reachable_all
% 0.48/0.70 % --bmc1_min_bound 0
% 0.48/0.70 % --bmc1_max_bound -1
% 0.48/0.70 % --bmc1_max_bound_default -1
% 0.48/0.70 % --bmc1_symbol_reachability true
% 0.48/0.70 % --bmc1_property_lemmas false
% 0.48/0.70 % --bmc1_k_induction false
% 0.48/0.70 % --bmc1_non_equiv_states false
% 0.48/0.70 % --bmc1_deadlock false
% 0.48/0.70 % --bmc1_ucm false
% 0.48/0.70 % --bmc1_add_unsat_core none
% 0.48/0.70 % --bmc1_unsat_core_children false
% 0.48/0.70 % --bmc1_unsat_core_extrapolate_axioms false
% 0.48/0.70 % --bmc1_out_stat full
% 0.48/0.70 % --bmc1_ground_init false
% 0.48/0.70 % --bmc1_pre_inst_next_state false
% 0.48/0.70 % --bmc1_pre_inst_state false
% 0.48/0.70 % --bmc1_pre_inst_reach_state false
% 0.48/0.70 % --bmc1_out_unsat_core false
% 0.48/0.70 % --bmc1_aig_witness_out false
% 0.48/0.70 % --bmc1_verbose false
% 0.48/0.70 % --bmc1_dump_clauses_tptp false
% 0.54/0.73 % --bmc1_dump_unsat_core_tptp false
% 0.54/0.73 % --bmc1_dump_file -
% 0.54/0.73 % --bmc1_ucm_expand_uc_limit 128
% 0.54/0.73 % --bmc1_ucm_n_expand_iterations 6
% 0.54/0.73 % --bmc1_ucm_extend_mode 1
% 0.54/0.73 % --bmc1_ucm_init_mode 2
% 0.54/0.73 % --bmc1_ucm_cone_mode none
% 0.54/0.73 % --bmc1_ucm_reduced_relation_type 0
% 0.54/0.73 % --bmc1_ucm_relax_model 4
% 0.54/0.73 % --bmc1_ucm_full_tr_after_sat true
% 0.54/0.73 % --bmc1_ucm_expand_neg_assumptions false
% 0.54/0.73 % --bmc1_ucm_layered_model none
% 0.54/0.73 % --bmc1_ucm_max_lemma_size 10
% 0.54/0.73
% 0.54/0.73 % ------ AIG Options
% 0.54/0.73
% 0.54/0.73 % --aig_mode false
% 0.54/0.73
% 0.54/0.73 % ------ Instantiation Options
% 0.54/0.73
% 0.54/0.73 % --instantiation_flag true
% 0.54/0.73 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.54/0.73 % --inst_solver_per_active 750
% 0.54/0.73 % --inst_solver_calls_frac 0.5
% 0.54/0.73 % --inst_passive_queue_type priority_queues
% 0.54/0.73 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.54/0.73 % --inst_passive_queues_freq [25;2]
% 0.54/0.73 % --inst_dismatching true
% 0.54/0.73 % --inst_eager_unprocessed_to_passive true
% 0.54/0.73 % --inst_prop_sim_given true
% 0.54/0.73 % --inst_prop_sim_new false
% 0.54/0.73 % --inst_orphan_elimination true
% 0.54/0.73 % --inst_learning_loop_flag true
% 0.54/0.73 % --inst_learning_start 3000
% 0.54/0.73 % --inst_learning_factor 2
% 0.54/0.73 % --inst_start_prop_sim_after_learn 3
% 0.54/0.73 % --inst_sel_renew solver
% 0.54/0.73 % --inst_lit_activity_flag true
% 0.54/0.73 % --inst_out_proof true
% 0.54/0.73
% 0.54/0.73 % ------ Resolution Options
% 0.54/0.73
% 0.54/0.73 % --resolution_flag true
% 0.54/0.73 % --res_lit_sel kbo_max
% 0.54/0.73 % --res_to_prop_solver none
% 0.54/0.73 % --res_prop_simpl_new false
% 0.54/0.73 % --res_prop_simpl_given false
% 0.54/0.73 % --res_passive_queue_type priority_queues
% 0.54/0.73 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.54/0.73 % --res_passive_queues_freq [15;5]
% 0.54/0.73 % --res_forward_subs full
% 0.54/0.73 % --res_backward_subs full
% 0.54/0.73 % --res_forward_subs_resolution true
% 0.54/0.73 % --res_backward_subs_resolution true
% 0.54/0.73 % --res_orphan_elimination false
% 0.54/0.73 % --res_time_limit 1000.
% 0.54/0.73 % --res_out_proof true
% 0.54/0.73 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_08f374.s
% 0.54/0.73 % --modulo true
% 0.54/0.73
% 0.54/0.73 % ------ Combination Options
% 0.54/0.73
% 0.54/0.73 % --comb_res_mult 1000
% 0.54/0.73 % --comb_inst_mult 300
% 0.54/0.73 % ------
% 0.54/0.73
% 0.54/0.73 % ------ Parsing...%
% 0.54/0.73
% 0.54/0.73
% 0.54/0.73 % ------ Statistics
% 0.54/0.73
% 0.54/0.73 % ------ General
% 0.54/0.73
% 0.54/0.73 % num_of_input_clauses: 751
% 0.54/0.73 % num_of_input_neg_conjectures: 0
% 0.54/0.73 % num_of_splits: 0
% 0.54/0.73 % num_of_split_atoms: 0
% 0.54/0.73 % num_of_sem_filtered_clauses: 0
% 0.54/0.73 % num_of_subtypes: 0
% 0.54/0.73 % monotx_restored_types: 0
% 0.54/0.73 % sat_num_of_epr_types: 0
% 0.54/0.73 % sat_num_of_non_cyclic_types: 0
% 0.54/0.73 % sat_guarded_non_collapsed_types: 0
% 0.54/0.73 % is_epr: 0
% 0.54/0.73 % is_horn: 0
% 0.54/0.73 % has_eq: 0
% 0.54/0.73 % num_pure_diseq_elim: 0
% 0.54/0.73 % simp_replaced_by: 0
% 0.54/0.73 % res_preprocessed: 0
% 0.54/0.73 % prep_upred: 0
% 0.54/0.73 % prep_unflattend: 0
% 0.54/0.73 % pred_elim_cands: 0
% 0.54/0.73 % pred_elim: 0
% 0.54/0.73 % pred_elim_cl: 0
% 0.54/0.73 % pred_elim_cycles: 0
% 0.54/0.73 % forced_gc_time: 0
% 0.54/0.73 % gc_basic_clause_elim: 0
% 0.54/0.73 % parsing_time: 0.
% 0.54/0.73 % sem_filter_time: 0.
% 0.54/0.73 % pred_elim_time: 0.
% 0.54/0.73 % out_proof_time: 0.
% 0.54/0.73 % monotx_time: 0.
% 0.54/0.73 % subtype_inf_time: 0.
% 0.54/0.73 % unif_index_cands_time: 0.
% 0.54/0.73 % Fatal error: exception Failure("Parse error in: /export/starexec/sandbox2/tmp/iprover_modulo_ae8c12.p line: 754 near token: '!='")
% 0.54/0.73 unif_index_add_time: 0.
% 0.54/0.73 % total_time: 0.047
% 0.54/0.73 % num_of_symbols: 150
% 0.54/0.73 % num_of_terms: 1876
% 0.54/0.73
% 0.54/0.73 % ------ Propositional Solver
% 0.54/0.73
% 0.54/0.73 % prop_solver_calls: 0
% 0.54/0.73 % prop_fast_solver_calls: 0
% 0.54/0.73 % prop_num_of_clauses: 0
% 0.54/0.73 % prop_preprocess_simplified: 0
% 0.54/0.73 % prop_fo_subsumed: 0
% 0.54/0.73 % prop_solver_time: 0.
% 0.54/0.73 % prop_fast_solver_time: 0.
% 0.54/0.73 % prop_unsat_core_time: 0.
% 0.54/0.73
% 0.54/0.73 % ------ QBF
% 0.54/0.73
% 0.54/0.73 % qbf_q_res: 0
% 0.54/0.73 % qbf_num_tautologies: 0
% 0.54/0.73 % qbf_prep_cycles: 0
% 0.54/0.73
% 0.54/0.73 % ------ BMC1
% 0.54/0.73
% 0.54/0.73 % bmc1_current_bound: -1
% 0.54/0.73 % bmc1_last_solved_bound: -1
% 0.54/0.73 % bmc1_unsat_core_size: -1
% 0.54/0.73 % bmc1_unsat_core_parents_size: -1
% 0.54/0.73 % bmc1_merge_next_fun: 0
% 0.54/0.73 % bmc1_unsat_core_clauses_time: 0.
% 0.54/0.73
% 0.54/0.73 % ------ Instantiation
% 0.54/0.73
% 0.54/0.73 % inst_num_of_clauses: undef
% 0.54/0.73 % inst_num_in_passive: undef
% 0.54/0.73 % inst_num_in_active: 0
% 0.54/0.73 % inst_num_in_unprocessed: 0
% 0.54/0.73 % inst_num_of_loops: 0
% 0.54/0.73 % inst_num_of_learning_restarts: 0
% 0.54/0.73 % inst_num_moves_active_passive: 0
% 0.54/0.73 % inst_lit_activity: 0
% 0.54/0.73 % inst_lit_activity_moves: 0
% 0.54/0.73 % inst_num_tautologies: 0
% 0.54/0.73 % inst_num_prop_implied: 0
% 0.54/0.73 % inst_num_existing_simplified: 0
% 0.54/0.73 % inst_num_eq_res_simplified: 0
% 0.54/0.73 % inst_num_child_elim: 0
% 0.54/0.73 % inst_num_of_dismatching_blockings: 0
% 0.54/0.73 % inst_num_of_non_proper_insts: 0
% 0.54/0.73 % inst_num_of_duplicates: 0
% 0.54/0.73 % inst_inst_num_from_inst_to_res: 0
% 0.54/0.73 % inst_dismatching_checking_time: 0.
% 0.54/0.73
% 0.54/0.73 % ------ Resolution
% 0.54/0.73
% 0.54/0.73 % res_num_of_clauses: undef
% 0.54/0.73 % res_num_in_passive: undef
% 0.54/0.73 % res_num_in_active: 0
% 0.54/0.73 % res_num_of_loops: 0
% 0.54/0.73 % res_forward_subset_subsumed: 0
% 0.54/0.73 % res_backward_subset_subsumed: 0
% 0.54/0.73 % res_forward_subsumed: 0
% 0.54/0.73 % res_backward_subsumed: 0
% 0.54/0.73 % res_forward_subsumption_resolution: 0
% 0.54/0.73 % res_backward_subsumption_resolution: 0
% 0.54/0.73 % res_clause_to_clause_subsumption: 0
% 0.54/0.73 % res_orphan_elimination: 0
% 0.54/0.73 % res_tautology_del: 0
% 0.54/0.73 % res_num_eq_res_simplified: 0
% 0.54/0.73 % res_num_sel_changes: 0
% 0.54/0.73 % res_moves_from_active_to_pass: 0
% 0.54/0.73
% 0.54/0.73 % Status Unknown
% 0.61/1.01 % Orienting using strategy ClausalAll
% 0.61/1.01 % FOF problem with conjecture
% 0.61/1.01 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_08f374.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_ae8c12.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_209d3e | grep -v "SZS"
% 0.90/1.03
% 0.90/1.03 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.90/1.03
% 0.90/1.03 %
% 0.90/1.03 % ------ iProver source info
% 0.90/1.03
% 0.90/1.03 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.90/1.03 % git: non_committed_changes: true
% 0.90/1.03 % git: last_make_outside_of_git: true
% 0.90/1.03
% 0.90/1.03 %
% 0.90/1.03 % ------ Input Options
% 0.90/1.03
% 0.90/1.03 % --out_options all
% 0.90/1.03 % --tptp_safe_out true
% 0.90/1.03 % --problem_path ""
% 0.90/1.03 % --include_path ""
% 0.90/1.03 % --clausifier .//eprover
% 0.90/1.03 % --clausifier_options --tstp-format
% 0.90/1.03 % --stdin false
% 0.90/1.03 % --dbg_backtrace false
% 0.90/1.03 % --dbg_dump_prop_clauses false
% 0.90/1.03 % --dbg_dump_prop_clauses_file -
% 0.90/1.03 % --dbg_out_stat false
% 0.90/1.03
% 0.90/1.03 % ------ General Options
% 0.90/1.03
% 0.90/1.03 % --fof false
% 0.90/1.03 % --time_out_real 150.
% 0.90/1.03 % --time_out_prep_mult 0.2
% 0.90/1.03 % --time_out_virtual -1.
% 0.90/1.03 % --schedule none
% 0.90/1.03 % --ground_splitting input
% 0.90/1.03 % --splitting_nvd 16
% 0.90/1.03 % --non_eq_to_eq false
% 0.90/1.03 % --prep_gs_sim true
% 0.90/1.03 % --prep_unflatten false
% 0.90/1.03 % --prep_res_sim true
% 0.90/1.03 % --prep_upred true
% 0.90/1.03 % --res_sim_input true
% 0.90/1.03 % --clause_weak_htbl true
% 0.90/1.03 % --gc_record_bc_elim false
% 0.90/1.03 % --symbol_type_check false
% 0.90/1.03 % --clausify_out false
% 0.90/1.03 % --large_theory_mode false
% 0.90/1.03 % --prep_sem_filter none
% 0.90/1.03 % --prep_sem_filter_out false
% 0.90/1.03 % --preprocessed_out false
% 0.90/1.03 % --sub_typing false
% 0.90/1.03 % --brand_transform false
% 0.90/1.03 % --pure_diseq_elim true
% 0.90/1.03 % --min_unsat_core false
% 0.90/1.03 % --pred_elim true
% 0.90/1.03 % --add_important_lit false
% 0.90/1.03 % --soft_assumptions false
% 0.90/1.03 % --reset_solvers false
% 0.90/1.03 % --bc_imp_inh []
% 0.90/1.03 % --conj_cone_tolerance 1.5
% 0.90/1.03 % --prolific_symb_bound 500
% 0.90/1.03 % --lt_threshold 2000
% 0.90/1.03
% 0.90/1.03 % ------ SAT Options
% 0.90/1.03
% 0.90/1.03 % --sat_mode false
% 0.90/1.03 % --sat_fm_restart_options ""
% 0.90/1.03 % --sat_gr_def false
% 0.90/1.03 % --sat_epr_types true
% 0.90/1.03 % --sat_non_cyclic_types false
% 0.90/1.03 % --sat_finite_models false
% 0.90/1.03 % --sat_fm_lemmas false
% 0.90/1.03 % --sat_fm_prep false
% 0.90/1.03 % --sat_fm_uc_incr true
% 0.90/1.03 % --sat_out_model small
% 0.90/1.03 % --sat_out_clauses false
% 0.90/1.03
% 0.90/1.03 % ------ QBF Options
% 0.90/1.03
% 0.90/1.03 % --qbf_mode false
% 0.90/1.03 % --qbf_elim_univ true
% 0.90/1.03 % --qbf_sk_in true
% 0.90/1.03 % --qbf_pred_elim true
% 0.90/1.03 % --qbf_split 32
% 0.90/1.03
% 0.90/1.03 % ------ BMC1 Options
% 0.90/1.03
% 0.90/1.03 % --bmc1_incremental false
% 0.90/1.03 % --bmc1_axioms reachable_all
% 0.90/1.03 % --bmc1_min_bound 0
% 0.90/1.03 % --bmc1_max_bound -1
% 0.90/1.03 % --bmc1_max_bound_default -1
% 0.90/1.03 % --bmc1_symbol_reachability true
% 0.90/1.03 % --bmc1_property_lemmas false
% 0.90/1.03 % --bmc1_k_induction false
% 0.90/1.03 % --bmc1_non_equiv_states false
% 0.90/1.03 % --bmc1_deadlock false
% 0.90/1.03 % --bmc1_ucm false
% 0.90/1.03 % --bmc1_add_unsat_core none
% 0.90/1.03 % --bmc1_unsat_core_children false
% 0.90/1.03 % --bmc1_unsat_core_extrapolate_axioms false
% 0.90/1.03 % --bmc1_out_stat full
% 0.90/1.03 % --bmc1_ground_init false
% 0.90/1.03 % --bmc1_pre_inst_next_state false
% 0.90/1.03 % --bmc1_pre_inst_state false
% 0.90/1.03 % --bmc1_pre_inst_reach_state false
% 0.90/1.03 % --bmc1_out_unsat_core false
% 0.90/1.03 % --bmc1_aig_witness_out false
% 0.90/1.03 % --bmc1_verbose false
% 0.90/1.03 % --bmc1_dump_clauses_tptp false
% 5.24/5.47 % --bmc1_dump_unsat_core_tptp false
% 5.24/5.47 % --bmc1_dump_file -
% 5.24/5.47 % --bmc1_ucm_expand_uc_limit 128
% 5.24/5.47 % --bmc1_ucm_n_expand_iterations 6
% 5.24/5.47 % --bmc1_ucm_extend_mode 1
% 5.24/5.47 % --bmc1_ucm_init_mode 2
% 5.24/5.47 % --bmc1_ucm_cone_mode none
% 5.24/5.47 % --bmc1_ucm_reduced_relation_type 0
% 5.24/5.47 % --bmc1_ucm_relax_model 4
% 5.24/5.47 % --bmc1_ucm_full_tr_after_sat true
% 5.24/5.47 % --bmc1_ucm_expand_neg_assumptions false
% 5.24/5.47 % --bmc1_ucm_layered_model none
% 5.24/5.47 % --bmc1_ucm_max_lemma_size 10
% 5.24/5.47
% 5.24/5.47 % ------ AIG Options
% 5.24/5.47
% 5.24/5.47 % --aig_mode false
% 5.24/5.47
% 5.24/5.47 % ------ Instantiation Options
% 5.24/5.47
% 5.24/5.47 % --instantiation_flag true
% 5.24/5.47 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 5.24/5.47 % --inst_solver_per_active 750
% 5.24/5.47 % --inst_solver_calls_frac 0.5
% 5.24/5.47 % --inst_passive_queue_type priority_queues
% 5.24/5.47 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 5.24/5.47 % --inst_passive_queues_freq [25;2]
% 5.24/5.47 % --inst_dismatching true
% 5.24/5.47 % --inst_eager_unprocessed_to_passive true
% 5.24/5.47 % --inst_prop_sim_given true
% 5.24/5.47 % --inst_prop_sim_new false
% 5.24/5.47 % --inst_orphan_elimination true
% 5.24/5.47 % --inst_learning_loop_flag true
% 5.24/5.47 % --inst_learning_start 3000
% 5.24/5.47 % --inst_learning_factor 2
% 5.24/5.47 % --inst_start_prop_sim_after_learn 3
% 5.24/5.47 % --inst_sel_renew solver
% 5.24/5.47 % --inst_lit_activity_flag true
% 5.24/5.47 % --inst_out_proof true
% 5.24/5.47
% 5.24/5.47 % ------ Resolution Options
% 5.24/5.47
% 5.24/5.47 % --resolution_flag true
% 5.24/5.47 % --res_lit_sel kbo_max
% 5.24/5.47 % --res_to_prop_solver none
% 5.24/5.47 % --res_prop_simpl_new false
% 5.24/5.47 % --res_prop_simpl_given false
% 5.24/5.47 % --res_passive_queue_type priority_queues
% 5.24/5.47 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 5.24/5.47 % --res_passive_queues_freq [15;5]
% 5.24/5.47 % --res_forward_subs full
% 5.24/5.47 % --res_backward_subs full
% 5.24/5.47 % --res_forward_subs_resolution true
% 5.24/5.47 % --res_backward_subs_resolution true
% 5.24/5.47 % --res_orphan_elimination false
% 5.24/5.47 % --res_time_limit 1000.
% 5.24/5.47 % --res_out_proof true
% 5.24/5.47 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_08f374.s
% 5.24/5.47 % --modulo true
% 5.24/5.47
% 5.24/5.47 % ------ Combination Options
% 5.24/5.47
% 5.24/5.47 % --comb_res_mult 1000
% 5.24/5.47 % --comb_inst_mult 300
% 5.24/5.47 % ------
% 5.24/5.47
% 5.24/5.47 % ------ Parsing...% successful
% 5.24/5.47
% 5.24/5.47 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 5.24/5.47
% 5.24/5.47 % ------ Proving...
% 5.24/5.47 % ------ Problem Properties
% 5.24/5.47
% 5.24/5.47 %
% 5.24/5.47 % EPR false
% 5.24/5.47 % Horn false
% 5.24/5.47 % Has equality true
% 5.24/5.47
% 5.24/5.47 % % ------ Input Options Time Limit: Unbounded
% 5.24/5.47
% 5.24/5.47
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 Compiling...
% 5.24/5.47 Loading plugin: done.
% 5.24/5.47 % % ------ Current options:
% 5.24/5.47
% 5.24/5.47 % ------ Input Options
% 5.24/5.47
% 5.24/5.47 % --out_options all
% 5.24/5.47 % --tptp_safe_out true
% 5.24/5.47 % --problem_path ""
% 5.24/5.47 % --include_path ""
% 5.24/5.47 % --clausifier .//eprover
% 5.24/5.47 % --clausifier_options --tstp-format
% 5.24/5.47 % --stdin false
% 5.24/5.47 % --dbg_backtrace false
% 5.24/5.47 % --dbg_dump_prop_clauses false
% 5.24/5.47 % --dbg_dump_prop_clauses_file -
% 5.24/5.47 % --dbg_out_stat false
% 5.24/5.47
% 5.24/5.47 % ------ General Options
% 5.24/5.47
% 5.24/5.47 % --fof false
% 5.24/5.47 % --time_out_real 150.
% 5.24/5.47 % --time_out_prep_mult 0.2
% 5.24/5.47 % --time_out_virtual -1.
% 5.24/5.47 % --schedule none
% 5.24/5.47 % --ground_splitting input
% 5.24/5.47 % --splitting_nvd 16
% 5.24/5.47 % --non_eq_to_eq false
% 5.24/5.47 % --prep_gs_sim true
% 5.24/5.47 % --prep_unflatten false
% 5.24/5.47 % --prep_res_sim true
% 5.24/5.47 % --prep_upred true
% 5.24/5.47 % --res_sim_input true
% 5.24/5.47 % --clause_weak_htbl true
% 5.24/5.47 % --gc_record_bc_elim false
% 5.24/5.47 % --symbol_type_check false
% 5.24/5.47 % --clausify_out false
% 5.24/5.47 % --large_theory_mode false
% 5.24/5.47 % --prep_sem_filter none
% 5.24/5.47 % --prep_sem_filter_out false
% 5.24/5.47 % --preprocessed_out false
% 5.24/5.47 % --sub_typing false
% 5.24/5.47 % --brand_transform false
% 5.24/5.47 % --pure_diseq_elim true
% 5.24/5.47 % --min_unsat_core false
% 5.24/5.47 % --pred_elim true
% 5.24/5.47 % --add_important_lit false
% 5.24/5.47 % --soft_assumptions false
% 5.24/5.47 % --reset_solvers false
% 5.24/5.47 % --bc_imp_inh []
% 5.24/5.47 % --conj_cone_tolerance 1.5
% 5.24/5.47 % --prolific_symb_bound 500
% 5.24/5.47 % --lt_threshold 2000
% 5.24/5.47
% 5.24/5.47 % ------ SAT Options
% 5.24/5.47
% 5.24/5.47 % --sat_mode false
% 5.24/5.47 % --sat_fm_restart_options ""
% 5.24/5.47 % --sat_gr_def false
% 5.24/5.47 % --sat_epr_types true
% 5.24/5.47 % --sat_non_cyclic_types false
% 5.24/5.47 % --sat_finite_models false
% 5.24/5.47 % --sat_fm_lemmas false
% 5.24/5.47 % --sat_fm_prep false
% 5.24/5.47 % --sat_fm_uc_incr true
% 5.24/5.47 % --sat_out_model small
% 5.24/5.47 % --sat_out_clauses false
% 5.24/5.47
% 5.24/5.47 % ------ QBF Options
% 5.24/5.47
% 5.24/5.47 % --qbf_mode false
% 5.24/5.47 % --qbf_elim_univ true
% 5.24/5.47 % --qbf_sk_in true
% 5.24/5.47 % --qbf_pred_elim true
% 5.24/5.47 % --qbf_split 32
% 5.24/5.47
% 5.24/5.47 % ------ BMC1 Options
% 5.24/5.47
% 5.24/5.47 % --bmc1_incremental false
% 5.24/5.47 % --bmc1_axioms reachable_all
% 5.24/5.47 % --bmc1_min_bound 0
% 5.24/5.47 % --bmc1_max_bound -1
% 5.24/5.47 % --bmc1_max_bound_default -1
% 5.24/5.47 % --bmc1_symbol_reachability true
% 5.24/5.47 % --bmc1_property_lemmas false
% 5.24/5.47 % --bmc1_k_induction false
% 5.24/5.47 % --bmc1_non_equiv_states false
% 5.24/5.47 % --bmc1_deadlock false
% 5.24/5.47 % --bmc1_ucm false
% 5.24/5.47 % --bmc1_add_unsat_core none
% 5.24/5.47 % --bmc1_unsat_core_children false
% 5.24/5.47 % --bmc1_unsat_core_extrapolate_axioms false
% 5.24/5.47 % --bmc1_out_stat full
% 5.24/5.47 % --bmc1_ground_init false
% 5.24/5.47 % --bmc1_pre_inst_next_state false
% 5.24/5.47 % --bmc1_pre_inst_state false
% 5.24/5.47 % --bmc1_pre_inst_reach_state false
% 5.24/5.47 % --bmc1_out_unsat_core false
% 5.24/5.47 % --bmc1_aig_witness_out false
% 5.24/5.47 % --bmc1_verbose false
% 5.24/5.47 % --bmc1_dump_clauses_tptp false
% 5.24/5.47 % --bmc1_dump_unsat_core_tptp false
% 5.24/5.47 % --bmc1_dump_file -
% 5.24/5.47 % --bmc1_ucm_expand_uc_limit 128
% 5.24/5.47 % --bmc1_ucm_n_expand_iterations 6
% 5.24/5.47 % --bmc1_ucm_extend_mode 1
% 5.24/5.47 % --bmc1_ucm_init_mode 2
% 5.24/5.47 % --bmc1_ucm_cone_mode none
% 5.24/5.47 % --bmc1_ucm_reduced_relation_type 0
% 5.24/5.47 % --bmc1_ucm_relax_model 4
% 5.24/5.47 % --bmc1_ucm_full_tr_after_sat true
% 5.24/5.47 % --bmc1_ucm_expand_neg_assumptions false
% 5.24/5.47 % --bmc1_ucm_layered_model none
% 12.21/12.43 % --bmc1_ucm_max_lemma_size 10
% 12.21/12.43
% 12.21/12.43 % ------ AIG Options
% 12.21/12.43
% 12.21/12.43 % --aig_mode false
% 12.21/12.43
% 12.21/12.43 % ------ Instantiation Options
% 12.21/12.43
% 12.21/12.43 % --instantiation_flag true
% 12.21/12.43 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 12.21/12.43 % --inst_solver_per_active 750
% 12.21/12.43 % --inst_solver_calls_frac 0.5
% 12.21/12.43 % --inst_passive_queue_type priority_queues
% 12.21/12.43 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 12.21/12.43 % --inst_passive_queues_freq [25;2]
% 12.21/12.43 % --inst_dismatching true
% 12.21/12.43 % --inst_eager_unprocessed_to_passive true
% 12.21/12.43 % --inst_prop_sim_given true
% 12.21/12.43 % --inst_prop_sim_new false
% 12.21/12.43 % --inst_orphan_elimination true
% 12.21/12.43 % --inst_learning_loop_flag true
% 12.21/12.43 % --inst_learning_start 3000
% 12.21/12.43 % --inst_learning_factor 2
% 12.21/12.43 % --inst_start_prop_sim_after_learn 3
% 12.21/12.43 % --inst_sel_renew solver
% 12.21/12.43 % --inst_lit_activity_flag true
% 12.21/12.43 % --inst_out_proof true
% 12.21/12.43
% 12.21/12.43 % ------ Resolution Options
% 12.21/12.43
% 12.21/12.43 % --resolution_flag true
% 12.21/12.43 % --res_lit_sel kbo_max
% 12.21/12.43 % --res_to_prop_solver none
% 12.21/12.43 % --res_prop_simpl_new false
% 12.21/12.43 % --res_prop_simpl_given false
% 12.21/12.43 % --res_passive_queue_type priority_queues
% 12.21/12.43 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 12.21/12.43 % --res_passive_queues_freq [15;5]
% 12.21/12.43 % --res_forward_subs full
% 12.21/12.43 % --res_backward_subs full
% 12.21/12.43 % --res_forward_subs_resolution true
% 12.21/12.43 % --res_backward_subs_resolution true
% 12.21/12.43 % --res_orphan_elimination false
% 12.21/12.43 % --res_time_limit 1000.
% 12.21/12.43 % --res_out_proof true
% 12.21/12.43 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_08f374.s
% 12.21/12.43 % --modulo true
% 12.21/12.43
% 12.21/12.43 % ------ Combination Options
% 12.21/12.43
% 12.21/12.43 % --comb_res_mult 1000
% 12.21/12.43 % --comb_inst_mult 300
% 12.21/12.43 % ------
% 12.21/12.43
% 12.21/12.43
% 12.21/12.43
% 12.21/12.43 % ------ Proving...
% 12.21/12.43 %
% 12.21/12.43
% 12.21/12.43
% 12.21/12.43 % ------ Statistics
% 12.21/12.43
% 12.21/12.43 % ------ General
% 12.21/12.43
% 12.21/12.43 % num_of_input_clauses: 4033
% 12.21/12.43 % num_of_input_neg_conjectures: 1
% 12.21/12.43 % num_of_splits: 0
% 12.21/12.43 % num_of_split_atoms: 0
% 12.21/12.43 % num_of_sem_filtered_clauses: 0
% 12.21/12.43 % num_of_subtypes: 0
% 12.21/12.43 % monotx_restored_types: 0
% 12.21/12.43 % sat_num_of_epr_types: 0
% 12.21/12.43 % sat_num_of_non_cyclic_types: 0
% 12.21/12.43 % sat_guarded_non_collapsed_types: 0
% 12.21/12.43 % is_epr: 0
% 12.21/12.43 % is_horn: 0
% 12.21/12.43 % has_eq: 1
% 12.21/12.43 % num_pure_diseq_elim: 0
% 12.21/12.43 % simp_replaced_by: 0
% 12.21/12.43 % res_preprocessed: 3
% 12.21/12.43 % prep_upred: 0
% 12.21/12.43 % prep_unflattend: 0
% 12.21/12.43 % pred_elim_cands: 1
% 12.21/12.43 % pred_elim: 0
% 12.21/12.43 % pred_elim_cl: 0
% 12.21/12.43 % pred_elim_cycles: 1
% 12.21/12.43 % forced_gc_time: 0
% 12.21/12.43 % gc_basic_clause_elim: 0
% 12.21/12.43 % parsing_time: 0.169
% 12.21/12.43 % sem_filter_time: 0.
% 12.21/12.43 % pred_elim_time: 0.
% 12.21/12.43 % out_proof_time: 0.001
% 12.21/12.43 % monotx_time: 0.
% 12.21/12.43 % subtype_inf_time: 0.
% 12.21/12.43 % unif_index_cands_time: 0.04
% 12.21/12.43 % unif_index_add_time: 0.015
% 12.21/12.43 % total_time: 11.411
% 12.21/12.43 % num_of_symbols: 173
% 12.21/12.43 % num_of_terms: 291179
% 12.21/12.43
% 12.21/12.43 % ------ Propositional Solver
% 12.21/12.43
% 12.21/12.43 % prop_solver_calls: 3
% 12.21/12.43 % prop_fast_solver_calls: 13
% 12.21/12.43 % prop_num_of_clauses: 4619
% 12.21/12.43 % prop_preprocess_simplified: 22131
% 12.21/12.43 % prop_fo_subsumed: 1
% 12.21/12.43 % prop_solver_time: 0.001
% 12.21/12.43 % prop_fast_solver_time: 0.
% 12.21/12.43 % prop_unsat_core_time: 0.
% 12.21/12.43
% 12.21/12.43 % ------ QBF
% 12.21/12.43
% 12.21/12.43 % qbf_q_res: 0
% 12.21/12.43 % qbf_num_tautologies: 0
% 12.21/12.43 % qbf_prep_cycles: 0
% 12.21/12.43
% 12.21/12.43 % ------ BMC1
% 12.21/12.43
% 12.21/12.43 % bmc1_current_bound: -1
% 12.21/12.43 % bmc1_last_solved_bound: -1
% 12.21/12.43 % bmc1_unsat_core_size: -1
% 12.21/12.43 % bmc1_unsat_core_parents_size: -1
% 12.21/12.43 % bmc1_merge_next_fun: 0
% 12.21/12.43 % bmc1_unsat_core_clauses_time: 0.
% 12.21/12.43
% 12.21/12.43 % ------ Instantiation
% 12.21/12.43
% 12.21/12.43 % inst_num_of_clauses: 4810
% 12.21/12.43 % inst_num_in_passive: 3626
% 12.21/12.43 % inst_num_in_active: 922
% 12.21/12.43 % inst_num_in_unprocessed: 260
% 12.21/12.43 % inst_num_of_loops: 962
% 12.21/12.43 % inst_num_of_learning_restarts: 0
% 12.21/12.43 % inst_num_moves_active_passive: 38
% 12.21/12.43 % inst_lit_activity: 100
% 12.21/12.43 % inst_lit_activity_moves: 0
% 12.21/12.43 % inst_num_tautologies: 0
% 12.21/12.43 % inst_num_prop_implied: 0
% 12.21/12.43 % inst_num_existing_simplified: 0
% 12.21/12.43 % inst_num_eq_res_simplified: 0
% 12.21/12.43 % inst_num_child_elim: 0
% 12.21/12.43 % inst_num_of_dismatching_blockings: 395
% 12.21/12.43 % inst_num_of_non_proper_insts: 983
% 12.21/12.43 % inst_num_of_duplicates: 1598
% 12.21/12.43 % inst_inst_num_from_inst_to_res: 0
% 12.21/12.43 % inst_dismatching_checking_time: 0.001
% 12.21/12.43
% 12.21/12.43 % ------ Resolution
% 12.21/12.43
% 12.21/12.43 % res_num_of_clauses: 131281
% 12.21/12.43 % res_num_in_passive: 127810
% 12.21/12.43 % res_num_in_active: 4010
% 12.21/12.43 % res_num_of_loops: 4000
% 12.21/12.43 % res_forward_subset_subsumed: 33015
% 12.21/12.43 % res_backward_subset_subsumed: 3190
% 12.21/12.43 % res_forward_subsumed: 1272
% 12.21/12.43 % res_backward_subsumed: 236
% 12.21/12.43 % res_forward_subsumption_resolution: 155
% 12.21/12.43 % res_backward_subsumption_resolution: 7
% 12.21/12.43 % res_clause_to_clause_subsumption: 17851
% 12.21/12.43 % res_orphan_elimination: 0
% 12.21/12.43 % res_tautology_del: 515
% 12.21/12.43 % res_num_eq_res_simplified: 78
% 12.21/12.43 % res_num_sel_changes: 0
% 12.21/12.43 % res_moves_from_active_to_pass: 0
% 12.21/12.43
% 12.21/12.43 % Status Unsatisfiable
% 12.21/12.43 % SZS status Theorem
% 12.21/12.43 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------