%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWW207+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n019.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 00:28:28 EDT 2022
% Result : Theorem 11.46s 11.69s
% Output : CNFRefutation 11.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1277
% Syntax : Number of formulae : 11210 (2609 unt; 0 def)
% Number of atoms : 29404 (7256 equ)
% Maximal formula atoms : 87 ( 2 avg)
% Number of connectives : 31717 (13523 ~;14635 |; 649 &)
% ( 434 <=>;2476 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 80 ( 78 usr; 1 prp; 0-3 aty)
% Number of functors : 204 ( 204 usr; 26 con; 0-5 aty)
% Number of variables : 26302 ( 961 sgn8099 !; 88 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X14,X7,X26] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X14))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26))),X14)) ),
file('<stdin>',fact_decr__lemma) ).
fof(c_0_1,axiom,
! [X25,X89,X5,X13] :
( ( class_RealVector_Oreal__normed__vector(X13)
& class_Orderings_Oord(X5) )
=> ( ! [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X89),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,c_Groups_Ominus__class_Ominus(X13,hAPP(X25,X89),hAPP(X25,X8)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
=> ! [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X89),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X8))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X89))))) ) ) ),
file('<stdin>',fact_lemmaCauchy) ).
fof(c_0_2,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X22)),X85)),X21)),X52)) ) ),
file('<stdin>',fact_less__add__iff1) ).
fof(c_0_3,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X22)),X85)),X21)),X52)) ) ),
file('<stdin>',fact_le__add__iff1) ).
fof(c_0_4,axiom,
! [X7,X14,X26] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X14))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26)))) ),
file('<stdin>',fact_incr__lemma) ).
fof(c_0_5,axiom,
~ ! [X28] :
( c_SEQ_Osubseq(X28)
=> ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,X28)))) ),
file('<stdin>',fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_Asubseq_Ag_059_Amonoseq_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(c_0_6,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
file('<stdin>',fact_g_I2_J) ).
fof(c_0_7,axiom,
! [X27,X31,X88,X83,X84] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X84),X83))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X83,X84)),X88)),X31)),X27)) ) ),
file('<stdin>',fact_nat__less__add__iff1) ).
fof(c_0_8,axiom,
! [X27,X31,X88,X83,X84] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X84),X83))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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,X83,X84)),X88)),X31)),X27)) ) ),
file('<stdin>',fact_nat__le__add__iff1) ).
fof(c_0_9,axiom,
! [X40,X25,X41,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( ! [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),X40)) )
=> c_SEQ_OBseq(X5,X25) ) ),
file('<stdin>',fact_BseqI2_H) ).
fof(c_0_10,axiom,
! [X33,X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat,X25,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33)))
=> c_SEQ_OBseq(X5,X25) ) ),
file('<stdin>',fact_Bseq__offset) ).
fof(c_0_11,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X22,X6)),X85)),X52))) ) ),
file('<stdin>',fact_less__add__iff2) ).
fof(c_0_12,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X22,X6)),X85)),X52))) ) ),
file('<stdin>',fact_le__add__iff2) ).
fof(c_0_13,axiom,
! [X1,X2,X5,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X13),X2),X1))
<=> ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(X2,X3)),hAPP(X1,X3))) ) ),
file('<stdin>',fact_le__fun__def) ).
fof(c_0_14,axiom,
! [X27,X31,X88,X84,X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83),X84))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),hAPP(hAPP(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,X84,X83)),X88)),X27))) ) ),
file('<stdin>',fact_nat__less__add__iff2) ).
fof(c_0_15,axiom,
! [X27,X31,X88,X84,X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83),X84))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),hAPP(hAPP(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,X84,X83)),X88)),X27))) ) ),
file('<stdin>',fact_nat__le__add__iff2) ).
fof(c_0_16,axiom,
! [X22,X6,X2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X2,X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X2,X22),hAPP(X2,X6))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X22,X6))),X6)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X2,X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X2,X22),hAPP(X2,X6))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X22,X6))),X22)),
file('<stdin>',fact_lemma__MVT) ).
fof(c_0_17,axiom,
! [X11,X4,X12,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X7,X4)),c_Groups_Ominus__class_Ominus(X5,X12,X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X7,X4)),X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ominus__class_Ominus(X5,X12,X11))) ),
file('<stdin>',fact_mult_Oprod__diff__prod) ).
fof(c_0_18,axiom,
! [X29,X11] :
( X11 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X66] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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),X11),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X66),X29))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
file('<stdin>',fact_reduce__poly__simple) ).
fof(c_0_19,axiom,
! [X38,X25,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ( c_SEQ_Oconvergent(X5,X25)
=> ( c_SEQ_Oconvergent(X5,X38)
=> c_SEQ_Oconvergent(X5,c_COMBS(tc_Nat_Onat,X5,X5,c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X5),X25),X38)) ) ) ),
file('<stdin>',fact_mult_Oconvergent) ).
fof(c_0_20,axiom,
! [X38,X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_Oconvergent(X5,X25)
=> ( c_SEQ_Oconvergent(X5,X38)
=> c_SEQ_Oconvergent(X5,c_COMBS(tc_Nat_Onat,X5,X5,c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(X5),X25),X38)) ) ) ),
file('<stdin>',fact_convergent__add) ).
fof(c_0_21,axiom,
! [X26,X15,X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X26)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X4,X15))),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X11,X26))))) ),
file('<stdin>',fact_abs__diff__triangle__ineq) ).
fof(c_0_22,axiom,
! [X9,X25,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_SEQ_Oconvergent(X5,X25)
=> c_SEQ_Oconvergent(X5,c_COMBC(tc_Nat_Onat,X5,X5,c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(X5),X25),X9)) ) ),
file('<stdin>',fact_divide_Oconvergent) ).
fof(c_0_23,axiom,
! [X9,X25,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ( c_SEQ_Oconvergent(X5,X25)
=> c_SEQ_Oconvergent(X5,c_COMBC(tc_Nat_Onat,X5,X5,c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X5),X25),X9)) ) ),
file('<stdin>',fact_mult__left_Oconvergent) ).
fof(c_0_24,axiom,
! [X26,X15,X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X26)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X15))),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X11,X26))))) ),
file('<stdin>',fact_norm__diff__triangle__ineq) ).
fof(c_0_25,axiom,
! [X33,X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X25)
=> c_SEQ_OBseq(X5,c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat,X25,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33))) ) ),
file('<stdin>',fact_Bseq__ignore__initial__segment) ).
fof(c_0_26,axiom,
c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
file('<stdin>',fact_conv1) ).
fof(c_0_27,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
file('<stdin>',fact_f_I2_J) ).
fof(c_0_28,axiom,
! [X12,X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X7,X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X7),hAPP(c_Complex_ORe,X12)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X7),hAPP(c_Complex_OIm,X12)))))),
file('<stdin>',fact_metric__bound__lemma) ).
fof(c_0_29,axiom,
! [X102,X26,X15,X11,X4,X5] :
( class_RealVector_Oreal__field(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X26))),X102) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ominus__class_Ominus(X5,X11,X26)),X102))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ominus__class_Ominus(X5,X4,X15)),X102)),X26)) ),
file('<stdin>',fact_DERIV__mult__lemma) ).
fof(c_0_30,axiom,
! [X23,X49,X67,X68,X11] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X68)),X67)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X49)),X23)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X67))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X67),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X23),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68),X49)) ) ) ) ),
file('<stdin>',fact_unique__quotient__lemma) ).
fof(c_0_31,axiom,
! [X23,X49,X67,X68,X11] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X68)),X67)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X49)),X23)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X11),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X11),X67))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49),X68)) ) ) ) ),
file('<stdin>',fact_unique__quotient__lemma__neg) ).
fof(c_0_32,axiom,
! [X9,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X9))),c_Groups_Ozero__class_Ozero(X5)))
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
& X9 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('<stdin>',fact_sum__squares__le__zero__iff) ).
fof(c_0_33,axiom,
! [X12,X7,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X12))),c_Groups_Ozero__class_Ozero(X5))) ),
file('<stdin>',fact_not__sum__squares__lt__zero) ).
fof(c_0_34,axiom,
! [X29,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X7)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X29))) ),
file('<stdin>',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
fof(c_0_35,axiom,
! [X67,X68,X58,X23,X49,X11] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X49)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X23),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X67))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68),X49)) ) ) ) ) ) ),
file('<stdin>',fact_zdiv__mono2__neg__lemma) ).
fof(c_0_36,axiom,
! [X7,X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_RealDef_Oreal(tc_Nat_Onat,X7)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X29,X7)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('<stdin>',fact_real__of__nat__div3) ).
fof(c_0_37,axiom,
! [X25,X13] :
( class_RealVector_Oreal__normed__vector(X13)
=> ( ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X8))),X37)) )
<=> ? [X77] :
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X8))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X77)))) ) ),
file('<stdin>',fact_lemma__NBseq__def) ).
fof(c_0_38,axiom,
! [X25,X13] :
( class_RealVector_Oreal__normed__vector(X13)
=> ( ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X8))),X37)) )
<=> ? [X77] :
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X8))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X77)))) ) ),
file('<stdin>',fact_lemma__NBseq__def2) ).
fof(c_0_39,axiom,
! [X14] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X14),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X14),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
file('<stdin>',fact_unimodular__reduce__norm) ).
fof(c_0_40,axiom,
! [X44,X45,X12,X4,X7,X5] :
( class_Rings_Olinordered__semiring__1(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X45))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X44))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X45),X44) = c_Groups_Oone__class_Oone(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X45),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X44),X12))),X4)) ) ) ) ) ) ),
file('<stdin>',fact_convex__bound__le) ).
fof(c_0_41,axiom,
! [X44,X45,X12,X4,X7,X5] :
( class_Rings_Olinordered__semiring__1__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X45))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X44))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X45),X44) = c_Groups_Oone__class_Oone(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X45),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X44),X12))),X4)) ) ) ) ) ) ),
file('<stdin>',fact_convex__bound__lt) ).
fof(c_0_42,axiom,
! [X25,X40,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X40))
=> ( ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),X40))
=> c_SEQ_OBseq(X5,X25) ) ) ),
file('<stdin>',fact_BseqI) ).
fof(c_0_43,axiom,
! [X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X25)
<=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),X37)) ) ) ),
file('<stdin>',fact_Bseq__def) ).
fof(c_0_44,axiom,
! [X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X25)
<=> ? [X77] :
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X77)))) ) ),
file('<stdin>',fact_Bseq__iff1a) ).
fof(c_0_45,axiom,
! [X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X25)
<=> ? [X77] :
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X77)))) ) ),
file('<stdin>',fact_Bseq__iff) ).
fof(c_0_46,axiom,
! [X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X53)),X53)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X53),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('<stdin>',fact_odd__less__0) ).
fof(c_0_47,axiom,
! [X67,X68,X58] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X67))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('<stdin>',fact_q__neg__lemma) ).
fof(c_0_48,axiom,
! [X29,X30,X45,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X45)),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X45)),X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,hAPP(hAPP(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,X19)),X45)),X29)) ),
file('<stdin>',fact_nat__diff__add__eq2) ).
fof(c_0_49,axiom,
! [X29,X30,X45,X19,X18] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18),X19))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X45)),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X45)),X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(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,X19,X18)),X45)),X30),X29) ),
file('<stdin>',fact_nat__diff__add__eq1) ).
fof(c_0_50,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
! [X71,X72] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X71),X72))),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(X5,X71)),c_RealVector_Onorm__class_Onorm(X5,X72))),X37))) ),
file('<stdin>',fact_mult_Obounded) ).
fof(c_0_51,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X71,X72] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X71),X72))),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(X5,X71)),c_RealVector_Onorm__class_Onorm(X5,X72))),X37))) ) ),
file('<stdin>',fact_mult_Ononneg__bounded) ).
fof(c_0_52,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X71,X72] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X71),X72))),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(X5,X71)),c_RealVector_Onorm__class_Onorm(X5,X72))),X37))) ) ),
file('<stdin>',fact_mult_Opos__bounded) ).
fof(c_0_53,axiom,
! [X67,X68,X58,X23,X49,X11] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X49)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X67),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49),X68)) ) ) ) ) ) ),
file('<stdin>',fact_zdiv__mono2__lemma) ).
fof(c_0_54,axiom,
! [X12,X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X7),X12) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_ORe,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_OIm,X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_OIm,X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_ORe,X12)))),
file('<stdin>',fact_complex__mult__def) ).
fof(c_0_55,axiom,
! [X10,X25,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ( c_SEQ_Oconvergent(X5,X25)
=> c_SEQ_Oconvergent(X5,c_COMBB(X5,X5,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X25)) ) ),
file('<stdin>',fact_mult__right_Oconvergent) ).
fof(c_0_56,axiom,
! [X107,X108,X35,X5,X109,X13] : hAPP(c_COMBS(X13,X109,X5,X35,X108),X107) = hAPP(hAPP(X35,X107),hAPP(X108,X107)),
file('<stdin>',help_c__COMBS__1) ).
fof(c_0_57,axiom,
! [X107,X108,X35,X5,X109,X13] : hAPP(c_COMBC(X13,X109,X5,X35,X108),X107) = hAPP(hAPP(X35,X107),X108),
file('<stdin>',help_c__COMBC__1) ).
fof(c_0_58,axiom,
! [X107,X108,X35,X109,X5,X13] : hAPP(c_COMBB(X13,X5,X109,X35,X108),X107) = hAPP(X35,hAPP(X108,X107)),
file('<stdin>',help_c__COMBB__1) ).
fof(c_0_59,axiom,
! [X9,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X9))))
<=> ( X10 != c_Groups_Ozero__class_Ozero(X5)
| X9 != c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('<stdin>',fact_sum__squares__gt__zero__iff) ).
fof(c_0_60,axiom,
! [X25] :
( c_SEQ_Oconvergent(tc_Complex_Ocomplex,X25)
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,X25)) ),
file('<stdin>',fact_Im_Oconvergent) ).
fof(c_0_61,axiom,
! [X25] :
( c_SEQ_Oconvergent(tc_Complex_Ocomplex,X25)
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,X25)) ),
file('<stdin>',fact_Re_Oconvergent) ).
fof(c_0_62,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oabs__class_Oabs(X5,X4),c_Groups_Oabs__class_Oabs(X5,X11)))),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)))) ),
file('<stdin>',fact_abs__triangle__ineq3) ).
fof(c_0_63,axiom,
! [X4,X11] : hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X11),X4)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X11))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4))),
file('<stdin>',fact_complex__mod__triangle__ineq2) ).
fof(c_0_64,axiom,
! [X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X11)))),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)))) ),
file('<stdin>',fact_norm__triangle__ineq3) ).
fof(c_0_65,axiom,
! [X86,X6,X10,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X10,X6))),X86))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ominus__class_Ominus(X5,X6,X86)),X10))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X86))) ) ) ),
file('<stdin>',fact_abs__diff__less__iff) ).
fof(c_0_66,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oring(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)
<=> X21 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X22,X6)),X85)),X52) ) ),
file('<stdin>',fact_eq__add__iff2) ).
fof(c_0_67,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oring(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X22)),X85)),X21) = X52 ) ),
file('<stdin>',fact_eq__add__iff1) ).
fof(c_0_68,axiom,
! [X27,X31,X88,X84,X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83),X84))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)
<=> X31 = hAPP(hAPP(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,X84,X83)),X88)),X27) ) ),
file('<stdin>',fact_nat__eq__add__iff2) ).
fof(c_0_69,axiom,
! [X27,X31,X88,X83,X84] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X84),X83))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)
<=> hAPP(hAPP(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,X83,X84)),X88)),X31) = X27 ) ),
file('<stdin>',fact_nat__eq__add__iff1) ).
fof(c_0_70,axiom,
! [X11,X7,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),X11))
=> ? [X87] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X87))
& ! [X73] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X73))),X87))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),X73))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X73),X11)) ) ) ) ) ),
file('<stdin>',fact_lemma__interval) ).
fof(c_0_71,axiom,
! [X7,X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_RealDef_Oreal(tc_Nat_Onat,X7)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X29,X7))))),
file('<stdin>',fact_real__of__nat__div2) ).
fof(c_0_72,axiom,
! [X14,X16] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X16)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X16),X14))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14)))),
file('<stdin>',fact_complex__mod__triangle__sub) ).
fof(c_0_73,axiom,
! [X7,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ? [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X8)),X12)),X7))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X8))),X12))) ) ) ),
file('<stdin>',fact_reals__Archimedean4) ).
fof(c_0_74,axiom,
! [X26,X11,X15,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,X4)),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,X11)),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X26))) ) ) ),
file('<stdin>',fact_abs__mult__less) ).
fof(c_0_75,axiom,
! [X67,X68,X58] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X67),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X68)) ) ) ),
file('<stdin>',fact_q__pos__lemma) ).
fof(c_0_76,axiom,
! [X15,X11,X59,X4,X5] :
( class_Rings_Osemiring(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X59)),X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X59)),X15) ),
file('<stdin>',fact_combine__common__factor) ).
fof(c_0_77,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ) ),
file('<stdin>',fact_power__Suc__less) ).
fof(c_0_78,axiom,
! [X24,X12,X23,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X7)),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X12)),X24))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X24))) ) ) ),
file('<stdin>',fact_norm__mult__less) ).
fof(c_0_79,axiom,
! [X24,X12,X23,X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X7)),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X12)),X24))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X23),X24))) ) ) ),
file('<stdin>',fact_norm__add__less) ).
fof(c_0_80,axiom,
! [X27,X31,X35] :
( hBOOL(hAPP(X35,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X27)))
<=> ( ( X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X98] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X98)),X31))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),c_Nat_OSuc(X98))))
& hBOOL(hAPP(X35,X98)) ) ) ),
file('<stdin>',fact_split__div_H) ).
fof(c_0_81,axiom,
! [X17,X18,X45,X19] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X45)),X17)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X18)),X45)),X17),
file('<stdin>',fact_left__add__mult__distrib) ).
fof(c_0_82,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11)))) ),
file('<stdin>',fact_abs__triangle__ineq4) ).
fof(c_0_83,axiom,
! [X12,X7,X5] :
( class_Rings_Olinordered__ring(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X12)))) ),
file('<stdin>',fact_sum__squares__ge__zero) ).
fof(c_0_84,axiom,
! [X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)),c_RealVector_Onorm__class_Onorm(X5,X11)))) ),
file('<stdin>',fact_norm__triangle__ineq4) ).
fof(c_0_85,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11)))) ),
file('<stdin>',fact_abs__triangle__ineq) ).
fof(c_0_86,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ),
file('<stdin>',fact_mult__right_Obounded) ).
fof(c_0_87,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ),
file('<stdin>',fact_mult__left_Obounded) ).
fof(c_0_88,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ) ),
file('<stdin>',fact_mult__left_Ononneg__bounded) ).
fof(c_0_89,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ) ),
file('<stdin>',fact_mult__right_Ononneg__bounded) ).
fof(c_0_90,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ) ),
file('<stdin>',fact_mult__left_Opos__bounded) ).
fof(c_0_91,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ) ),
file('<stdin>',fact_mult__right_Opos__bounded) ).
fof(c_0_92,axiom,
! [X12,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),c_RealVector_Onorm__class_Onorm(X5,X12)))) ),
file('<stdin>',fact_norm__mult__ineq) ).
fof(c_0_93,axiom,
! [X12,X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),c_RealVector_Onorm__class_Onorm(X5,X12)))) ),
file('<stdin>',fact_norm__triangle__ineq) ).
fof(c_0_94,axiom,
! [X15,X4,X11,X5] :
( class_Fields_Olinordered__field(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X15),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X15),X11))) ) ) ) ),
file('<stdin>',fact_divide__left__mono) ).
fof(c_0_95,axiom,
! [X11,X4,X12,X7,X5] :
( class_Rings_Oring(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),c_Groups_Ominus__class_Ominus(X5,X12,X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X7,X4)),X11)) ),
file('<stdin>',fact_mult__diff__mult) ).
fof(c_0_96,axiom,
! [X15,X11,X4,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X15),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X15),X11))) ) ) ) ),
file('<stdin>',fact_divide__left__mono__neg) ).
fof(c_0_97,axiom,
! [X11,X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_Nat_OSuc(X29))))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ) ),
file('<stdin>',fact_power__le__imp__le__base) ).
fof(c_0_98,axiom,
! [X7,X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X29,X7))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_RealDef_Oreal(tc_Nat_Onat,X7)))),
file('<stdin>',fact_real__of__nat__div4) ).
fof(c_0_99,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X27)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X31))) ),
file('<stdin>',fact_nat__less__real__le) ).
fof(c_0_100,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X27))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X33)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X33)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ) ) ),
file('<stdin>',fact_less__diff__iff) ).
fof(c_0_101,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X27))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X33)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X33)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ) ) ),
file('<stdin>',fact_le__diff__iff) ).
fof(c_0_102,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oabs__class_Oabs(X5,X4),c_Groups_Oabs__class_Oabs(X5,X11))),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)))) ),
file('<stdin>',fact_abs__triangle__ineq2) ).
fof(c_0_103,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oabs__class_Oabs(X5,X4),c_Groups_Oabs__class_Oabs(X5,X11))),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X11,X4)))) ),
file('<stdin>',fact_abs__triangle__ineq2__sym) ).
fof(c_0_104,axiom,
! [X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X11))),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)))) ),
file('<stdin>',fact_norm__triangle__ineq2) ).
fof(c_0_105,axiom,
! [X29,X7,X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X29))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),X29))) ),
file('<stdin>',fact_norm__power__ineq) ).
fof(c_0_106,axiom,
! [X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X11))),c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)))) ),
file('<stdin>',fact_norm__diff__ineq) ).
fof(c_0_107,axiom,
! [X11,X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
file('<stdin>',fact_power__less__imp__less__base) ).
fof(c_0_108,axiom,
! [X11,X4,X15,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ) ),
file('<stdin>',fact_mult__left__le__imp__le) ).
fof(c_0_109,axiom,
! [X11,X15,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ) ),
file('<stdin>',fact_mult__right__le__imp__le) ).
fof(c_0_110,axiom,
! [X11,X4,X15,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
file('<stdin>',fact_mult__less__imp__less__left) ).
fof(c_0_111,axiom,
! [X11,X4,X15,X5] :
( class_Rings_Olinordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
file('<stdin>',fact_mult__left__less__imp__less) ).
fof(c_0_112,axiom,
! [X11,X15,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
file('<stdin>',fact_mult__less__imp__less__right) ).
fof(c_0_113,axiom,
! [X11,X15,X4,X5] :
( class_Rings_Olinordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
file('<stdin>',fact_mult__right__less__imp__less) ).
fof(c_0_114,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X21))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),X22)) ) ) ),
file('<stdin>',fact_mult__le__cancel__left__pos) ).
fof(c_0_115,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X21))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22)) ) ) ),
file('<stdin>',fact_mult__less__cancel__left__pos) ).
fof(c_0_116,axiom,
! [X9,X10,X22,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X22))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X22),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X22),X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10),X9)) ) ) ),
file('<stdin>',fact_power__strict__increasing__iff) ).
fof(c_0_117,axiom,
! [X29,X30,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ) ) ),
file('<stdin>',fact_power__less__imp__less__exp) ).
fof(c_0_118,axiom,
! [X29,X30,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ) ) ),
file('<stdin>',fact_power__le__imp__le__exp) ).
fof(c_0_119,axiom,
! [X9,X10,X22,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X22))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X22),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X22),X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10),X9)) ) ) ),
file('<stdin>',fact_power__increasing__iff) ).
fof(c_0_120,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X22),X6)) ) ) ),
file('<stdin>',fact_mult__le__cancel__left__neg) ).
fof(c_0_121,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X22),X6)) ) ) ),
file('<stdin>',fact_mult__less__cancel__left__neg) ).
fof(c_0_122,axiom,
! [X31,X97,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27))
=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X97)),X31))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),c_Nat_OSuc(X97)))) )
<=> X97 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X27) ) ),
file('<stdin>',fact_split__div__lemma) ).
fof(c_0_123,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X22)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X21))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22)) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X22),X6)) ) ) ) ),
file('<stdin>',fact_mult__less__cancel__left__disj) ).
fof(c_0_124,axiom,
! [X22,X21,X6,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X21)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X21))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22)) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X22),X6)) ) ) ) ),
file('<stdin>',fact_mult__less__cancel__right__disj) ).
fof(c_0_125,axiom,
! [X7] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X7)),
file('<stdin>',fact_abs__add__one__not__less__self) ).
fof(c_0_126,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
file('<stdin>',fact_mult__le__less__imp__less) ).
fof(c_0_127,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
file('<stdin>',fact_mult__less__le__imp__less) ).
fof(c_0_128,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
file('<stdin>',fact_mult__strict__mono_H) ).
fof(c_0_129,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
file('<stdin>',fact_mult__strict__mono) ).
fof(c_0_130,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
file('<stdin>',fact_mult__mono) ).
fof(c_0_131,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
file('<stdin>',fact_mult__mono_H) ).
fof(c_0_132,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Omonoseq(X5,X25)
<=> ( ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,X8)),hAPP(X25,c_Nat_OSuc(X8))))
| ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,c_Nat_OSuc(X8))),hAPP(X25,X8))) ) ) ),
file('<stdin>',fact_monoseq__Suc) ).
fof(c_0_133,axiom,
! [X23] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X23))
=> ? [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X8,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X23))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23),c_RealDef_Oreal(tc_Nat_Onat,X8))) ) ),
file('<stdin>',fact_reals__Archimedean6) ).
fof(c_0_134,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)))) ) ),
file('<stdin>',fact_power__less__power__Suc) ).
fof(c_0_135,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ),
file('<stdin>',fact_Suc__mult__le__cancel1) ).
fof(c_0_136,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ),
file('<stdin>',fact_Suc__mult__less__cancel1) ).
fof(c_0_137,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X4)),c_RComplete_Onatfloor(X11))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X11)))) ) ),
file('<stdin>',fact_le__mult__natfloor) ).
fof(c_0_138,axiom,
! [X26,X15,X11,X4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X4,X11)),c_Complex_Ocomplex_OComplex(X15,X26)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X26)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X15))),
file('<stdin>',fact_complex__mult) ).
fof(c_0_139,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ) ),
file('<stdin>',fact_nat__mult__less__cancel1) ).
fof(c_0_140,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ) ),
file('<stdin>',fact_nat__mult__le__cancel1) ).
fof(c_0_141,axiom,
! [X29,X30,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ) ),
file('<stdin>',fact_nat__power__less__imp__less) ).
fof(c_0_142,axiom,
! [X27,X33,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X33)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ) ),
file('<stdin>',fact_mult__le__cancel2) ).
fof(c_0_143,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ) ),
file('<stdin>',fact_mult__le__cancel1) ).
fof(c_0_144,axiom,
! [X9,X10,X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X53))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X53),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X53),X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9)) ) ),
file('<stdin>',fact_real__mult__le__cancel__iff2) ).
fof(c_0_145,axiom,
! [X9,X10,X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X53))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X53)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9)) ) ),
file('<stdin>',fact_real__mult__le__cancel__iff1) ).
fof(c_0_146,axiom,
! [X9,X10,X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X53))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X53)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),X9)) ) ),
file('<stdin>',fact_real__mult__less__iff1) ).
fof(c_0_147,axiom,
! [X11,X4,X15,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X11)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ),
file('<stdin>',fact_add__less__imp__less__left) ).
fof(c_0_148,axiom,
! [X11,X15,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ),
file('<stdin>',fact_add__less__imp__less__right) ).
fof(c_0_149,axiom,
! [X22,X6,X21,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22)) ) ),
file('<stdin>',fact_add__less__cancel__left) ).
fof(c_0_150,axiom,
! [X22,X21,X6,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X21)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22)) ) ),
file('<stdin>',fact_add__less__cancel__right) ).
fof(c_0_151,axiom,
! [X11,X4,X15,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X11)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ),
file('<stdin>',fact_add__le__imp__le__left) ).
fof(c_0_152,axiom,
! [X11,X15,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ),
file('<stdin>',fact_add__le__imp__le__right) ).
fof(c_0_153,axiom,
! [X22,X6,X21,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),X22)) ) ),
file('<stdin>',fact_add__le__cancel__left) ).
fof(c_0_154,axiom,
! [X22,X21,X6,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X21)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),X22)) ) ),
file('<stdin>',fact_add__le__cancel__right) ).
fof(c_0_155,axiom,
! [X53,X10,X9,X54,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X54),X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X53)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X54),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X9))
<=> ( X54 = X10
| X9 = X53 ) ) ),
file('<stdin>',fact_crossproduct__eq) ).
fof(c_0_156,axiom,
! [X52,X21,X22,X6,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( ( X6 != X22
& X21 != X52 )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X52)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X52)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X21)) ) ),
file('<stdin>',fact_crossproduct__noteq) ).
fof(c_0_157,axiom,
! [X4,X62,X29,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X62))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X62)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ) ) ),
file('<stdin>',fact_power__strict__decreasing) ).
fof(c_0_158,axiom,
! [X4,X62,X29,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X62))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X62)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ) ) ),
file('<stdin>',fact_power__decreasing) ).
fof(c_0_159,axiom,
! [X29,X11,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29))) ) ) ) ),
file('<stdin>',fact_power__strict__mono) ).
fof(c_0_160,axiom,
! [X11,X58,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X58))) ) ) ),
file('<stdin>',fact_zdiv__mono2) ).
fof(c_0_161,axiom,
! [X83,X84,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X84))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X84,X33)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X83),X33)),X84)) ) ),
file('<stdin>',fact_le__diff__conv2) ).
fof(c_0_162,axiom,
! [X11,X58,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X58)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11))) ) ) ),
file('<stdin>',fact_zdiv__mono2__neg) ).
fof(c_0_163,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7))),X7)) ),
file('<stdin>',fact_ln__add__one__self__le__self) ).
fof(c_0_164,axiom,
! [X27,X33,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X33)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ) ),
file('<stdin>',fact_mult__less__cancel2) ).
fof(c_0_165,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ) ),
file('<stdin>',fact_mult__less__cancel1) ).
fof(c_0_166,axiom,
! [X33,X27,X35] :
( hBOOL(hAPP(X35,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X27,X33)))
<=> ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [X42,X82] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X82),X33))
=> ( X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X42)),X82)
=> hBOOL(hAPP(X35,X42)) ) ) ) ) ),
file('<stdin>',fact_split__div) ).
fof(c_0_167,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ),
file('<stdin>',fact_nat__add__left__cancel__less) ).
fof(c_0_168,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ),
file('<stdin>',fact_nat__add__left__cancel__le) ).
fof(c_0_169,axiom,
! [X83,X33,X84] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X84,X33)),X83))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X83),X33))) ),
file('<stdin>',fact_le__diff__conv) ).
fof(c_0_170,axiom,
! [X7,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X29)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
=> c_RComplete_Onatceiling(X7) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('<stdin>',fact_natceiling__eq) ).
fof(c_0_171,axiom,
! [X22,X6,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X22)),c_Groups_Ozero__class_Ozero(X5)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X6))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X22),c_Groups_Ozero__class_Ozero(X5))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X22)) ) ) ) ),
file('<stdin>',fact_mult__le__0__iff) ).
fof(c_0_172,axiom,
! [X6,X22] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X22)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('<stdin>',fact_pos__imp__zdiv__neg__iff) ).
fof(c_0_173,axiom,
! [X29,X11,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29))) ) ) ),
file('<stdin>',fact_power__mono) ).
fof(c_0_174,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Olinordered__comm__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
file('<stdin>',fact_comm__mult__strict__left__mono) ).
fof(c_0_175,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
file('<stdin>',fact_mult__strict__left__mono) ).
fof(c_0_176,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15))) ) ) ),
file('<stdin>',fact_mult__strict__right__mono) ).
fof(c_0_177,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Oordered__comm__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
file('<stdin>',fact_comm__mult__left__mono) ).
fof(c_0_178,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
file('<stdin>',fact_mult__left__mono) ).
fof(c_0_179,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15))) ) ) ),
file('<stdin>',fact_mult__right__mono) ).
fof(c_0_180,axiom,
! [X6,X22] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X22),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X22)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) ),
file('<stdin>',fact_neg__imp__zdiv__neg__iff) ).
fof(c_0_181,axiom,
! [X29,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X14)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14),c_RealDef_Oreal(tc_Nat_Onat,X29))) ),
file('<stdin>',fact_ge__natfloor__plus__one__imp__gt) ).
fof(c_0_182,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ! [X73] :
? [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X73),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X8)),X7))) ),
file('<stdin>',fact_reals__Archimedean3) ).
fof(c_0_183,axiom,
! [X4,X62,X29,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X62))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X62))) ) ) ),
file('<stdin>',fact_power__increasing) ).
fof(c_0_184,axiom,
! [X4,X62,X29,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X62))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X62))) ) ) ),
file('<stdin>',fact_power__strict__increasing) ).
fof(c_0_185,axiom,
! [X12,X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X7)),X7)) ) ) ) ),
file('<stdin>',fact_mult__left__le__one__le) ).
fof(c_0_186,axiom,
! [X12,X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12)),X7)) ) ) ) ),
file('<stdin>',fact_mult__right__le__one__le) ).
fof(c_0_187,axiom,
! [X15,X4,X11,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
file('<stdin>',fact_mult__strict__left__mono__neg) ).
fof(c_0_188,axiom,
! [X15,X4,X11,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15))) ) ) ),
file('<stdin>',fact_mult__strict__right__mono__neg) ).
fof(c_0_189,axiom,
! [X15,X4,X11,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
file('<stdin>',fact_mult__left__mono__neg) ).
fof(c_0_190,axiom,
! [X15,X4,X11,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15))) ) ) ),
file('<stdin>',fact_mult__right__mono__neg) ).
fof(c_0_191,axiom,
! [X7,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X29)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
=> c_RComplete_Onatfloor(X7) = X29 ) ),
file('<stdin>',fact_natfloor__eq) ).
fof(c_0_192,axiom,
! [X33,X84,X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X83),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X84,X33)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X83),X33)),X84)) ),
file('<stdin>',fact_less__diff__conv) ).
fof(c_0_193,axiom,
! [X12,X29,X50,X5] :
( class_Groups_Omonoid__mult(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X29))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X29),X50)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X50))),X12) ) ),
file('<stdin>',fact_lemma__realpow__diff) ).
fof(c_0_194,axiom,
! [X26,X15,X11,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26))) ) ) ),
file('<stdin>',fact_add__le__less__mono) ).
fof(c_0_195,axiom,
! [X26,X15,X11,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26))) ) ) ),
file('<stdin>',fact_add__less__le__mono) ).
fof(c_0_196,axiom,
! [X26,X15,X11,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26))) ) ) ),
file('<stdin>',fact_add__strict__mono) ).
fof(c_0_197,axiom,
! [X26,X15,X11,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26))) ) ) ),
file('<stdin>',fact_add__mono) ).
fof(c_0_198,axiom,
! [X17,X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X17,X29)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X17,X30))) ) ),
file('<stdin>',fact_div__le__mono2) ).
fof(c_0_199,axiom,
! [X11,X56,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),X56))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X56,X11))) ) ),
file('<stdin>',fact_zdiv__mono1) ).
fof(c_0_200,axiom,
! [X11,X56,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),X56))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X56,X11)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11))) ) ),
file('<stdin>',fact_zdiv__mono1__neg) ).
fof(c_0_201,axiom,
! [X15,X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X15)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X15))) ) ),
file('<stdin>',fact_diff__less__mono) ).
fof(c_0_202,axiom,
! [X34,X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X29)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X30))) ) ),
file('<stdin>',fact_diff__less__mono2) ).
fof(c_0_203,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27),X31))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X31)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
file('<stdin>',fact_nat__le__real__less) ).
fof(c_0_204,axiom,
! [X46,X47,X51,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),X46)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(c_0_205,axiom,
! [X90,X12,X91,X92] :
( X92 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),X12)),X90)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X90),X91)) ) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),X90))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> ( X91 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X92,X91) = X12 ) ) ),
file('<stdin>',fact_divmod__int__rel__div__eq) ).
fof(c_0_206,axiom,
! [X22,X6,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),X22))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,X6,X22)),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('<stdin>',fact_le__iff__diff__le__0) ).
fof(c_0_207,axiom,
! [X22,X6,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ominus__class_Ominus(X5,X6,X22)),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('<stdin>',fact_less__iff__diff__less__0) ).
fof(c_0_208,axiom,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X8)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('<stdin>',fact_th) ).
fof(c_0_209,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)))) ) ),
file('<stdin>',fact_power__gt1__lemma) ).
fof(c_0_210,axiom,
! [X7,X29,X5] :
( class_Groups_Omonoid__mult(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X29) ) ),
file('<stdin>',fact_realpow__minus__mult) ).
fof(c_0_211,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('<stdin>',fact_even__less__0__iff) ).
fof(c_0_212,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('<stdin>',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(c_0_213,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('<stdin>',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(c_0_214,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Oincseq(X5,X25)
<=> ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,X20)),hAPP(X25,X8))) ) ) ),
file('<stdin>',fact_incseq__def) ).
fof(c_0_215,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Odecseq(X5,X25)
<=> ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,X8)),hAPP(X25,X20))) ) ) ),
file('<stdin>',fact_decseq__def) ).
fof(c_0_216,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Omonoseq(X5,X25)
<=> ( ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,X20)),hAPP(X25,X8))) )
| ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,X8)),hAPP(X25,X20))) ) ) ) ),
file('<stdin>',fact_monoseq__def) ).
fof(c_0_217,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29))),c_Groups_Oone__class_Oone(X5))) ) ) ),
file('<stdin>',fact_power__Suc__less__one) ).
fof(c_0_218,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X18))) ) ),
file('<stdin>',fact_zmult__zless__mono2) ).
fof(c_0_219,axiom,
! [X12,X7,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X14))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X12))) ) ),
file('<stdin>',fact_real__mult__less__mono2) ).
fof(c_0_220,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X18))) ) ),
file('<stdin>',fact_mult__less__mono2) ).
fof(c_0_221,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X17))) ) ),
file('<stdin>',fact_mult__less__mono1) ).
fof(c_0_222,axiom,
! [X12,X7,X15,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),c_RealVector_Onorm__class_Onorm(X5,X12))))
=> X7 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('<stdin>',fact_norm__ratiotest__lemma) ).
fof(c_0_223,axiom,
! [X29,X23,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X23),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X23),c_Nat_OSuc(X29))),X23)) ) ) ),
file('<stdin>',fact_realpow__Suc__le__self) ).
fof(c_0_224,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X10,X9)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
file('<stdin>',fact_real__le__eq__diff) ).
fof(c_0_225,axiom,
! [X39,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X33),X39))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X33,X39)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('<stdin>',fact_less__bin__lemma) ).
fof(c_0_226,axiom,
! [X14,X64,X16,X65] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X65),X16))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X64),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X65),X64)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),X14))) ) ),
file('<stdin>',fact_zadd__zless__mono) ).
fof(c_0_227,axiom,
! [X34,X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X34))) ) ),
file('<stdin>',fact_mult__le__mono) ).
fof(c_0_228,axiom,
! [X34,X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X34))) ) ),
file('<stdin>',fact_add__less__mono) ).
fof(c_0_229,axiom,
! [X34,X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X34))) ) ),
file('<stdin>',fact_add__le__mono) ).
fof(c_0_230,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X11))) ) ),
file('<stdin>',fact_add__strict__left__mono) ).
fof(c_0_231,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15))) ) ),
file('<stdin>',fact_add__strict__right__mono) ).
fof(c_0_232,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X11))) ) ),
file('<stdin>',fact_add__left__mono) ).
fof(c_0_233,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15))) ) ),
file('<stdin>',fact_add__right__mono) ).
fof(c_0_234,axiom,
! [X12,X7] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_OIm,X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_ORe,X12))),
file('<stdin>',fact_complex__Im__mult) ).
fof(c_0_235,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('<stdin>',fact_mult__neg__pos) ).
fof(c_0_236,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X4)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('<stdin>',fact_mult__pos__neg2) ).
fof(c_0_237,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('<stdin>',fact_mult__pos__neg) ).
fof(c_0_238,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11)) ) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('<stdin>',fact_split__mult__neg__le) ).
fof(c_0_239,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('<stdin>',fact_mult__nonpos__nonneg) ).
fof(c_0_240,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X4)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('<stdin>',fact_mult__nonneg__nonpos2) ).
fof(c_0_241,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('<stdin>',fact_mult__nonneg__nonpos) ).
fof(c_0_242,axiom,
! [X12,X7,X15] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X12))))
=> X7 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('<stdin>',fact_rabs__ratiotest__lemma) ).
fof(c_0_243,axiom,
! [X17,X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X17)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X29,X17))) ),
file('<stdin>',fact_div__le__mono) ).
fof(c_0_244,axiom,
! [X34,X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X29)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X30))) ),
file('<stdin>',fact_diff__le__mono2) ).
fof(c_0_245,axiom,
! [X34,X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X34)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X34))) ),
file('<stdin>',fact_diff__le__mono) ).
fof(c_0_246,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('<stdin>',fact_add__nonpos__neg) ).
fof(c_0_247,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('<stdin>',fact_add__neg__nonpos) ).
fof(c_0_248,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('<stdin>',fact_add__neg__neg) ).
fof(c_0_249,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('<stdin>',fact_add__nonpos__nonpos) ).
fof(c_0_250,axiom,
! [X27,X6,X69,X70,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X70,X69),X6),c_Nat_OSuc(X27)) = hAPP(hAPP(X69,X6),hAPP(hAPP(c_Power_Opower_Opower(X5,X70,X69),X6),X27)),
file('<stdin>',fact_power_Opower_Opower__Suc) ).
fof(c_0_251,axiom,
! [X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X54),c_Groups_Oone__class_Oone(tc_Int_Oint))),X53))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),X53)) ),
file('<stdin>',fact_add1__zle__eq) ).
fof(c_0_252,axiom,
! [X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4)),c_Groups_Ozero__class_Ozero(X5))) ),
file('<stdin>',fact_not__square__less__zero) ).
fof(c_0_253,axiom,
! [X4,X11,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X4)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11)) ) ) ),
file('<stdin>',fact_zero__less__mult__pos2) ).
fof(c_0_254,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11)) ) ) ),
file('<stdin>',fact_zero__less__mult__pos) ).
fof(c_0_255,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29)),X30)) ) ),
file('<stdin>',fact_div__less__dividend) ).
fof(c_0_256,axiom,
! [X17,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X7,X17)),X7)) ) ),
file('<stdin>',fact_int__div__less__self) ).
fof(c_0_257,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)),X30)) ) ),
file('<stdin>',fact_diff__less) ).
fof(c_0_258,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('<stdin>',fact_div__nonneg__neg__le0) ).
fof(c_0_259,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('<stdin>',fact_div__nonpos__pos__le0) ).
fof(c_0_260,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('<stdin>',fact_div__neg__pos__less0) ).
fof(c_0_261,axiom,
! [X30,X29,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X30),X17))) ),
file('<stdin>',fact_le__add__diff) ).
fof(c_0_262,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X18)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X17)) ),
file('<stdin>',fact_add__lessD1) ).
fof(c_0_263,axiom,
! [X29,X17,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X17)),X29))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X29)) ) ),
file('<stdin>',fact_add__leE) ).
fof(c_0_264,axiom,
! [X29,X17,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X17)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ),
file('<stdin>',fact_add__leD1) ).
fof(c_0_265,axiom,
! [X29,X17,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X17)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X29)) ),
file('<stdin>',fact_add__leD2) ).
fof(c_0_266,axiom,
! [X12,X7,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X7,X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12)) ),
file('<stdin>',fact_realpow__two__diff) ).
fof(c_0_267,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17),X18))) ),
file('<stdin>',fact_zadd__left__mono) ).
fof(c_0_268,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18),X17))) ),
file('<stdin>',fact_zadd__strict__right__mono) ).
fof(c_0_269,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X17))) ),
file('<stdin>',fact_mult__le__mono1) ).
fof(c_0_270,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X18))) ),
file('<stdin>',fact_mult__le__mono2) ).
fof(c_0_271,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X17))) ),
file('<stdin>',fact_add__less__mono1) ).
fof(c_0_272,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X17))) ),
file('<stdin>',fact_add__le__mono1) ).
fof(c_0_273,axiom,
! [X14,X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X14),X7)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X14),X12))) ),
file('<stdin>',fact_real__add__left__mono) ).
fof(c_0_274,axiom,
! [X46,X47,X51,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X47)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X51),X46)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(c_0_275,axiom,
! [X46,X47,X51,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46))) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(c_0_276,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(c_0_277,axiom,
! [X27,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X10)),X27)))
<=> ( X10 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_zero__less__zpower__abs__iff) ).
fof(c_0_278,axiom,
? [X37] :
! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))),
file('<stdin>',fact_Re_Obounded) ).
fof(c_0_279,axiom,
? [X37] :
! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))),
file('<stdin>',fact_Im_Obounded) ).
fof(c_0_280,axiom,
? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))) ),
file('<stdin>',fact_Re_Ononneg__bounded) ).
fof(c_0_281,axiom,
? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))) ),
file('<stdin>',fact_Im_Ononneg__bounded) ).
fof(c_0_282,axiom,
? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))) ),
file('<stdin>',fact_Re_Opos__bounded) ).
fof(c_0_283,axiom,
? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))) ),
file('<stdin>',fact_Im_Opos__bounded) ).
fof(c_0_284,axiom,
! [X27,X31] :
( hBOOL(hAPP(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),X31),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27)) ) ),
file('<stdin>',fact_one__le__mult__iff) ).
fof(c_0_285,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X30))
=> hBOOL(hAPP(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),X30),X29))) ) ),
file('<stdin>',fact_one__less__mult) ).
fof(c_0_286,axiom,
! [X22,X6,X35] :
( hBOOL(hAPP(X35,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X22)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6),X22))
=> hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X87] :
( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X87)
=> hBOOL(hAPP(X35,X87)) ) ) ),
file('<stdin>',fact_nat__diff__split) ).
fof(c_0_287,axiom,
! [X22,X6,X35] :
( hBOOL(hAPP(X35,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X22)))
<=> ~ ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6),X22))
& ~ hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X87] :
( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X87)
& ~ hBOOL(hAPP(X35,X87)) ) ) ),
file('<stdin>',fact_nat__diff__split__asm) ).
fof(c_0_288,axiom,
! [X22,X6,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X22)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X6))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X22)) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X22),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ),
file('<stdin>',fact_zero__le__mult__iff) ).
fof(c_0_289,axiom,
! [X22,X6] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X22)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22),X6))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22)) ) ) ),
file('<stdin>',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(c_0_290,axiom,
! [X6,X22] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
=> ( hBOOL(hAPP(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,X6,X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) ),
file('<stdin>',fact_pos__imp__zdiv__nonneg__iff) ).
fof(c_0_291,axiom,
! [X18,X19] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X18)),X19)),
file('<stdin>',fact_not__add__less1) ).
fof(c_0_292,axiom,
! [X19,X18] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X19)),X19)),
file('<stdin>',fact_not__add__less2) ).
fof(c_0_293,axiom,
! [X83,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X83,X33)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33),X83)) ) ),
file('<stdin>',fact_pos__imp__zdiv__pos__iff) ).
fof(c_0_294,axiom,
! [X19,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Nat_OSuc(X19))),X29)) ),
file('<stdin>',fact_diff__Suc__less) ).
fof(c_0_295,axiom,
! [X6,X22] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X22),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(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,X6,X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('<stdin>',fact_neg__imp__zdiv__nonneg__iff) ).
fof(c_0_296,axiom,
! [X1,X2,X5,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X13),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X13),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X13),X1),X2)) ) ) ),
file('<stdin>',fact_less__fun__def) ).
fof(c_0_297,axiom,
! [X4,X29] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X29))),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X4))),
file('<stdin>',fact_cis__real__of__nat__Suc__mult) ).
fof(c_0_298,axiom,
! [X29,X30,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X30),X29))) ) ) ),
file('<stdin>',fact_less__1__mult) ).
fof(c_0_299,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11))) ) ) ),
file('<stdin>',fact_mult__pos__pos) ).
fof(c_0_300,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11)) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5))) ) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11))) ) ),
file('<stdin>',fact_split__mult__pos__le) ).
fof(c_0_301,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11))) ) ) ),
file('<stdin>',fact_mult__nonneg__nonneg) ).
fof(c_0_302,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11))) ) ) ),
file('<stdin>',fact_add__nonneg__pos) ).
fof(c_0_303,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11))) ) ) ),
file('<stdin>',fact_add__pos__nonneg) ).
fof(c_0_304,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11))) ) ) ),
file('<stdin>',fact_add__pos__pos) ).
fof(c_0_305,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11))) ) ) ),
file('<stdin>',fact_add__nonneg__nonneg) ).
fof(c_0_306,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29))) ) ),
file('<stdin>',fact_n__less__m__mult__n) ).
fof(c_0_307,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X30))) ) ),
file('<stdin>',fact_n__less__n__mult__m) ).
fof(c_0_308,axiom,
! [X11,X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> X4 = X11 ) ) ) ) ),
file('<stdin>',fact_power__eq__imp__eq__base) ).
fof(c_0_309,axiom,
! [X30,X29,X4,X5] :
( class_Fields_Ofield(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) ) ) ),
file('<stdin>',fact_power__diff) ).
fof(c_0_310,axiom,
! [X26,X11,X15,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ominus__class_Ominus(X5,X4,X11)),c_Groups_Ominus__class_Ominus(X5,X15,X26)) ),
file('<stdin>',fact_Deriv_Oadd__diff__add) ).
fof(c_0_311,axiom,
! [X29,X4,X11,X5] :
( class_Fields_Ofield(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X11)),X29) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29)) ) ),
file('<stdin>',fact_nonzero__power__divide) ).
fof(c_0_312,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),X29)) ) ),
file('<stdin>',fact_le__div__geq) ).
fof(c_0_313,axiom,
! [X29,X30] :
( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29)) ) ),
file('<stdin>',fact_mult__eq__if) ).
fof(c_0_314,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ) ),
file('<stdin>',fact_one__less__power) ).
fof(c_0_315,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X15)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X15)) ),
file('<stdin>',fact_add__divide__distrib) ).
fof(c_0_316,axiom,
! [X55,X12,X7,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12)),X55) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X7),X55)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X12),X55)) ),
file('<stdin>',fact_divide_Oadd) ).
fof(c_0_317,axiom,
! [X29,X11,X4,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X11)),X29) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29)) ),
file('<stdin>',fact_power__divide) ).
fof(c_0_318,axiom,
! [X29,X11,X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),X29) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29)) ),
file('<stdin>',fact_power__mult__distrib) ).
fof(c_0_319,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Ocomm__semiring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)) ),
file('<stdin>',fact_comm__semiring__class_Odistrib) ).
fof(c_0_320,axiom,
! [X11,X56,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X56)),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),X11)) ),
file('<stdin>',fact_mult_Oadd__left) ).
fof(c_0_321,axiom,
! [X55,X12,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12)),X55) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X55)) ),
file('<stdin>',fact_mult__left_Oadd) ).
fof(c_0_322,axiom,
! [X11,X30,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X30)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X30) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(c_0_323,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(c_0_324,axiom,
! [X49,X12,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12)),X49) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X49)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X49)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(c_0_325,axiom,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X30)))),
file('<stdin>',fact_le__cube) ).
fof(c_0_326,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11))) ) ) ),
file('<stdin>',fact_mult__neg__neg) ).
fof(c_0_327,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11))) ) ) ),
file('<stdin>',fact_mult__nonpos__nonpos) ).
fof(c_0_328,axiom,
! [X29,X17,X18] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X29)),X17)) ),
file('<stdin>',fact_less__imp__diff__less) ).
fof(c_0_329,axiom,
! [X12,X7] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X7),X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_ORe,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_OIm,X12))),
file('<stdin>',fact_complex__Re__mult) ).
fof(c_0_330,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
file('<stdin>',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(c_0_331,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
file('<stdin>',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(c_0_332,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27)) ) ),
file('<stdin>',fact_add__gr__0) ).
fof(c_0_333,axiom,
! [X17,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17))
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17),X30),X17) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
file('<stdin>',fact_int__power__div__base) ).
fof(c_0_334,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X10),X9)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X9)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ),
file('<stdin>',fact_real__0__le__divide__iff) ).
fof(c_0_335,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15))) ) ) ),
file('<stdin>',fact_pos__add__strict) ).
fof(c_0_336,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15))) ) ) ),
file('<stdin>',fact_add__strict__increasing2) ).
fof(c_0_337,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15))) ) ) ),
file('<stdin>',fact_add__strict__increasing) ).
fof(c_0_338,axiom,
! [X4,X11,X15,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15))) ) ) ),
file('<stdin>',fact_add__increasing2) ).
fof(c_0_339,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15))) ) ) ),
file('<stdin>',fact_add__increasing) ).
fof(c_0_340,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__ring__abs(X5)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5))) ) )
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11)) ) ),
file('<stdin>',fact_abs__eq__mult) ).
fof(c_0_341,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7)))),
file('<stdin>',fact_real__natfloor__gt__diff__one) ).
fof(c_0_342,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),X29)) ) ) ),
file('<stdin>',fact_div__if) ).
fof(c_0_343,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),X29)) ) ),
file('<stdin>',fact_div__geq) ).
fof(c_0_344,axiom,
! [X29,X30] :
( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29) = X29 )
& ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29)) ) ),
file('<stdin>',fact_add__eq__if) ).
fof(c_0_345,axiom,
! [X9,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X9)) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
& X9 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('<stdin>',fact_sum__squares__eq__zero__iff) ).
fof(c_0_346,axiom,
! [X14,X16] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X16),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),c_Groups_Oone__class_Oone(tc_Int_Oint))),X14)) ),
file('<stdin>',fact_zless__imp__add1__zle) ).
fof(c_0_347,axiom,
! [X49,X23,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
=> ( X4 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X49))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ),
file('<stdin>',fact_self__quotient__aux2) ).
fof(c_0_348,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
=> hBOOL(hAPP(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,X7,X12))) ) ),
file('<stdin>',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
fof(c_0_349,axiom,
! [X7,X5] :
( class_Rings_Oring__1(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X7),c_Groups_Oone__class_Oone(X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),c_Groups_Oone__class_Oone(X5))),c_Groups_Ominus__class_Ominus(X5,X7,c_Groups_Oone__class_Oone(X5))) ),
file('<stdin>',fact_real__squared__diff__one__factored) ).
fof(c_0_350,axiom,
! [X49,X23,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
=> ( X4 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X49))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X23),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X49)) ) ) ),
file('<stdin>',fact_self__quotient__aux1) ).
fof(c_0_351,axiom,
! [X2] :
( c_SEQ_Osubseq(X2)
<=> ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X8)),hAPP(X2,c_Nat_OSuc(X8)))) ),
file('<stdin>',fact_subseq__Suc__iff) ).
fof(c_0_352,axiom,
! [X29,X30,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X29))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X17),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X17)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29) ) ),
file('<stdin>',fact_Nat_Odiff__diff__eq) ).
fof(c_0_353,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('<stdin>',fact_real__natfloor__add__one__gt) ).
fof(c_0_354,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7),X12))) ) ),
file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(c_0_355,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
=> hBOOL(hAPP(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),X7),X12))) ) ),
file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(c_0_356,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
=> hBOOL(hAPP(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),X7),X12))) ) ),
file('<stdin>',fact_real__mult__order) ).
fof(c_0_357,axiom,
! [X27,X31] :
( hBOOL(hAPP(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),X31),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27)) ) ),
file('<stdin>',fact_nat__0__less__mult__iff) ).
fof(c_0_358,axiom,
! [X30,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X30)),X30) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Oone__class_Oone(X5))),X30) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(c_0_359,axiom,
! [X16,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),X60)),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X16)),
file('<stdin>',fact_zadd__zmult__distrib) ).
fof(c_0_360,axiom,
! [X16,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X61),X60)),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X61),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X60),X16)),
file('<stdin>',fact_real__add__mult__distrib) ).
fof(c_0_361,axiom,
! [X17,X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X17)),
file('<stdin>',fact_add__mult__distrib) ).
fof(c_0_362,axiom,
! [X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X53,c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),X53)) ),
file('<stdin>',fact_zle__diff1__eq) ).
fof(c_0_363,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ),
file('<stdin>',fact_zero__less__diff) ).
fof(c_0_364,axiom,
! [X10,X1,X2,X5,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X13),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(X2,X10)),hAPP(X1,X10))) ) ),
file('<stdin>',fact_le__funD) ).
fof(c_0_365,axiom,
! [X10,X1,X2,X5,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X13),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(X2,X10)),hAPP(X1,X10))) ) ),
file('<stdin>',fact_le__funE) ).
fof(c_0_366,axiom,
! [X30,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)),X30) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X30)) ),
file('<stdin>',fact_diff__Suc__diff__eq2) ).
fof(c_0_367,axiom,
! [X30,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X17),c_Nat_OSuc(X18)) ),
file('<stdin>',fact_diff__Suc__diff__eq1) ).
fof(c_0_368,axiom,
! [X12,X7] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X12)),c_Transcendental_Ocos(X7))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X12)),c_Transcendental_Osin(X7))),
file('<stdin>',fact_cos__diff2) ).
fof(c_0_369,axiom,
! [X12,X7] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X7)),c_Transcendental_Ocos(X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X7)),c_Transcendental_Osin(X12))),
file('<stdin>',fact_cos__diff) ).
fof(c_0_370,axiom,
! [X15,X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),c_Divides_Odiv__class_Odiv(X5,X4,X11)) ) ),
file('<stdin>',fact_div__mult__self2) ).
fof(c_0_371,axiom,
! [X15,X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),c_Divides_Odiv__class_Odiv(X5,X4,X11)) ) ),
file('<stdin>',fact_div__mult__self1) ).
fof(c_0_372,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ominus__class_Ominus(X5,X4,X11)),X15) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X15)) ),
file('<stdin>',fact_diff__divide__distrib) ).
fof(c_0_373,axiom,
! [X55,X12,X7,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ominus__class_Ominus(X5,X7,X12)),X55) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X7),X55),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X12),X55)) ),
file('<stdin>',fact_divide_Odiff) ).
fof(c_0_374,axiom,
! [X55,X12,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X7,X12)),X55) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X55)) ),
file('<stdin>',fact_mult__left_Odiff) ).
fof(c_0_375,axiom,
! [X11,X56,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X56)),X11) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),X11)) ),
file('<stdin>',fact_mult_Odiff__left) ).
fof(c_0_376,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X9))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X10)),c_Transcendental_Oln(X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9)) ) ) ),
file('<stdin>',fact_ln__le__cancel__iff) ).
fof(c_0_377,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X9))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X10)),c_Transcendental_Oln(X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),X9)) ) ) ),
file('<stdin>',fact_ln__less__cancel__iff) ).
fof(c_0_378,axiom,
! [X11,X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_Nat_OSuc(X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> X4 = X11 ) ) ) ),
file('<stdin>',fact_power__inject__base) ).
fof(c_0_379,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oabs__class_Oabs(X5,X4)),X29))) ),
file('<stdin>',fact_zero__le__power__abs) ).
fof(c_0_380,axiom,
! [X58,X11,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X58)) ),
file('<stdin>',fact_mult_Oadd__right) ).
fof(c_0_381,axiom,
! [X12,X7,X57,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),X12)) ),
file('<stdin>',fact_mult__right_Oadd) ).
fof(c_0_382,axiom,
! [X14,X12,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X12),X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X14)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(c_0_383,axiom,
! [X47,X51,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),X47) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X47)),X51) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(c_0_384,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),X11) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(c_0_385,axiom,
! [X12,X7] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X7)),c_Transcendental_Ocos(X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X7)),c_Transcendental_Osin(X12))),
file('<stdin>',fact_sin__add) ).
fof(c_0_386,axiom,
! [X19,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X19),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)),X19) ),
file('<stdin>',fact_diff__add__assoc2) ).
fof(c_0_387,axiom,
! [X19,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)),X19) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X19),X17) ),
file('<stdin>',fact_add__diff__assoc2) ).
fof(c_0_388,axiom,
! [X12,X7] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X7),X12) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_ORe,X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_OIm,X12))),
file('<stdin>',fact_complex__add__def) ).
fof(c_0_389,axiom,
! [X27,X35] :
( ~ hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X35,X27))
=> ? [X32] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X27))
& ! [X42] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42),X32))
=> ~ hBOOL(hAPP(X35,X42)) )
& hBOOL(hAPP(X35,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('<stdin>',fact_ex__least__nat__less) ).
fof(c_0_390,axiom,
! [X27,X10] :
( hBOOL(hAPP(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),X10),X27)))
<=> ( X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)) ) ),
file('<stdin>',fact_zero__less__power__nat__eq) ).
fof(c_0_391,axiom,
! [X27,X10] :
( hBOOL(hAPP(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),X10),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))
| X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_nat__zero__less__power__iff) ).
fof(c_0_392,axiom,
! [X25] :
( c_SEQ_OBseq(tc_RealDef_Oreal,X25)
=> ( ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(X25,X20)),hAPP(X25,X8))) )
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,X25) ) ),
file('<stdin>',fact_Bseq__mono__convergent) ).
fof(c_0_393,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29)))) ) ),
file('<stdin>',fact_power__gt1) ).
fof(c_0_394,axiom,
! [X29,X30,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) ),
file('<stdin>',fact_power__add) ).
fof(c_0_395,axiom,
! [X49,X50,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X50)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X49)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X49)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(c_0_396,axiom,
! [X4,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4))
=> ? [X3] :
( hBOOL(hAPP(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),X29) = X4
& ! [X73] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X73))
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X73),X29) = X4 )
=> X73 = X3 ) ) ) ),
file('<stdin>',fact_realpow__pos__nth__unique) ).
fof(c_0_397,axiom,
! [X9,X10] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X10 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X9 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('<stdin>',fact_real__two__squares__add__zero__iff) ).
fof(c_0_398,axiom,
! [X26,X15,X11,X4,X23,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X23 != c_Groups_Ozero__class_Ozero(X5)
=> ( ( X4 = X11
& X15 != X26 )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X15)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X26)) ) ) ),
file('<stdin>',fact_add__scale__eq__noteq) ).
fof(c_0_399,axiom,
! [X29,X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)),c_Nat_OSuc(X30))),
file('<stdin>',fact_diff__less__Suc) ).
fof(c_0_400,axiom,
! [X29,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19))
=> hBOOL(hAPP(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),X19),X29))) ),
file('<stdin>',fact_nat__one__le__power) ).
fof(c_0_401,axiom,
! [X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),X53))
| X54 = X53 ) ),
file('<stdin>',fact_zless__add1__eq) ).
fof(c_0_402,axiom,
! [X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54),X53)) ),
file('<stdin>',fact_zle__add1__eq__le) ).
fof(c_0_403,axiom,
! [X29,X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29)),X30)),
file('<stdin>',fact_div__le__dividend) ).
fof(c_0_404,axiom,
! [X29,X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)),X30)),
file('<stdin>',fact_diff__le__self) ).
fof(c_0_405,axiom,
! [X6,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6),c_RComplete_Onatfloor(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X6)),X10)) ) ),
file('<stdin>',fact_le__natfloor__eq) ).
fof(c_0_406,axiom,
! [X16,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X61,X60)),X16) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X16)),
file('<stdin>',fact_zdiff__zmult__distrib) ).
fof(c_0_407,axiom,
! [X17,X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)),X17) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X17)),
file('<stdin>',fact_diff__mult__distrib) ).
fof(c_0_408,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ),
file('<stdin>',fact_one__le__power) ).
fof(c_0_409,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ),
file('<stdin>',fact_zero__less__power) ).
fof(c_0_410,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ),
file('<stdin>',fact_zero__le__power) ).
fof(c_0_411,axiom,
! [X2] :
( c_SEQ_Osubseq(X2)
<=> ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X20)),hAPP(X2,X8))) ) ),
file('<stdin>',fact_subseq__def) ).
fof(c_0_412,axiom,
! [X29,X4,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Oone__class_Oone(X5)),X4)),X29) ),
file('<stdin>',fact_power__one__over) ).
fof(c_0_413,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X7),c_RealDef_Oreal(tc_Nat_Onat,X12))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X7),X12) ) ),
file('<stdin>',fact_natfloor__div__nat) ).
fof(c_0_414,axiom,
! [X7,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4)),X7))
=> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,X4))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X7),X4) ),
file('<stdin>',fact_natceiling__subtract) ).
fof(c_0_415,axiom,
! [X7,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4)),X7))
=> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,X4))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X7),X4) ),
file('<stdin>',fact_natfloor__subtract) ).
fof(c_0_416,axiom,
! [X35,X27,X31] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
=> hBOOL(hAPP(hAPP(X35,X27),X31)) )
=> ( ( X31 = X27
=> hBOOL(hAPP(hAPP(X35,X27),X31)) )
=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31))
=> hBOOL(hAPP(hAPP(X35,X27),X31)) )
=> hBOOL(hAPP(hAPP(X35,X27),X31)) ) ) ),
file('<stdin>',fact_nat__less__cases) ).
fof(c_0_417,axiom,
! [X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X25)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),X37)) ) ) ),
file('<stdin>',fact_BseqD) ).
fof(c_0_418,axiom,
! [X60,X61,X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),X60)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X61)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X60)),
file('<stdin>',fact_zadd__zmult__distrib2) ).
fof(c_0_419,axiom,
! [X14,X12,X7] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X12)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X14)),
file('<stdin>',fact_zpower__zadd__distrib) ).
fof(c_0_420,axiom,
! [X29,X30,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X29)),
file('<stdin>',fact_add__mult__distrib2) ).
fof(c_0_421,axiom,
! [X29,X7] : hBOOL(hAPP(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X7)),X29))),
file('<stdin>',fact_zero__le__zpower__abs) ).
fof(c_0_422,axiom,
! [X30,X19] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X19)))),
file('<stdin>',fact_less__add__Suc2) ).
fof(c_0_423,axiom,
! [X30,X19] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X30)))),
file('<stdin>',fact_less__add__Suc1) ).
fof(c_0_424,axiom,
! [X4,X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X30)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Oone__class_Oone(X5))),X30) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(c_0_425,axiom,
! [X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X4),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Divides_Odiv__class_Odiv(X5,X4,X11)),c_Groups_Oone__class_Oone(X5)) ) ),
file('<stdin>',fact_div__add__self1) ).
fof(c_0_426,axiom,
! [X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Divides_Odiv__class_Odiv(X5,X4,X11)),c_Groups_Oone__class_Oone(X5)) ) ),
file('<stdin>',fact_div__add__self2) ).
fof(c_0_427,axiom,
! [X11,X4,X15] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15))
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X15)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11),X15) ),
file('<stdin>',fact_zdiv__zmult2__eq) ).
fof(c_0_428,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
=> c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X7),X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(X7),c_Transcendental_Oln(X12)) ) ),
file('<stdin>',fact_ln__div) ).
fof(c_0_429,axiom,
! [X30,X29,X5] :
( class_Power_Opower(X5)
=> ( ( X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X30),X29) = c_Groups_Oone__class_Oone(X5) )
& ( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X30),X29) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X30),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X30),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('<stdin>',fact_realpow__num__eq__if) ).
fof(c_0_430,axiom,
! [X9,X10,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X9))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X10),X9) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
& X9 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ) ),
file('<stdin>',fact_add__nonneg__eq__0__iff) ).
fof(c_0_431,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
=> c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(X7)),c_Transcendental_Oln(X12)) ) ),
file('<stdin>',fact_ln__mult) ).
fof(c_0_432,axiom,
! [X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14))) ),
file('<stdin>',fact_le__imp__0__less) ).
fof(c_0_433,axiom,
! [X29,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),c_RealDef_Oreal(tc_Nat_Onat,X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X7)),X29)) ) ),
file('<stdin>',fact_less__natfloor) ).
fof(c_0_434,axiom,
! [X6,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X10)),X6))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_RealDef_Oreal(tc_Nat_Onat,X6))) ) ),
file('<stdin>',fact_natceiling__le__eq) ).
fof(c_0_435,axiom,
! [X33,X27,X35] :
( hBOOL(hAPP(X35,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X27,X33)))
<=> ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
=> ! [X42] :
( ? [X82] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X82))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X82),X33))
& X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X82) )
=> hBOOL(hAPP(X35,X42)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X42] :
( ? [X82] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X33),X82))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X82),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X82) )
=> hBOOL(hAPP(X35,X42)) ) ) ) ),
file('<stdin>',fact_split__zdiv) ).
fof(c_0_436,axiom,
! [X7] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X7)),c_Transcendental_Ocos(X7))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X7)),c_Transcendental_Osin(X7))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('<stdin>',fact_sin__cos__squared__add3) ).
fof(c_0_437,axiom,
! [X10] :
( ~ hBOOL(hAPP(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),X10),X10)))
<=> X10 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('<stdin>',fact_not__real__square__gt__zero) ).
fof(c_0_438,axiom,
! [X12,X7,X57,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),c_Groups_Ominus__class_Ominus(X5,X7,X12)) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),X12)) ),
file('<stdin>',fact_mult__right_Odiff) ).
fof(c_0_439,axiom,
! [X58,X11,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ominus__class_Ominus(X5,X11,X58)) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X58)) ),
file('<stdin>',fact_mult_Odiff__right) ).
fof(c_0_440,axiom,
! [X29,X30,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X29)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) ),
file('<stdin>',fact_nat__mult__div__cancel1) ).
fof(c_0_441,axiom,
! [X19,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17),X18) ),
file('<stdin>',fact_diff__diff__right) ).
fof(c_0_442,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X7,X12))) ) ),
file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(c_0_443,axiom,
! [X4,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4))
=> ? [X74] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X74))
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X74),X29) = X4 ) ) ),
file('<stdin>',fact_realpow__pos__nth) ).
fof(c_0_444,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X15)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),X15) ),
file('<stdin>',fact_times__divide__eq__right) ).
fof(c_0_445,axiom,
! [X29,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) ),
file('<stdin>',fact_power__commutes) ).
fof(c_0_446,axiom,
! [X47,X51,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),X47) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X51),X47)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(c_0_447,axiom,
! [X46,X47,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X47)),X46) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(c_0_448,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oab__semigroup__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)) ),
file('<stdin>',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(c_0_449,axiom,
! [X26,X15,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),X26) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(c_0_450,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(c_0_451,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oab__semigroup__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15)) ),
file('<stdin>',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(c_0_452,axiom,
! [X12,X7] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X7)),c_Transcendental_Ocos(X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X7)),c_Transcendental_Osin(X12))),
file('<stdin>',fact_sin__diff) ).
fof(c_0_453,axiom,
! [X12,X7] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X12)),c_Transcendental_Osin(X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X12)),c_Transcendental_Ocos(X7))),
file('<stdin>',fact_sin__diff2) ).
fof(c_0_454,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Osgn__class_Osgn(X5,X6)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('<stdin>',fact_sgn__less) ).
fof(c_0_455,axiom,
! [X19,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X18),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)) ),
file('<stdin>',fact_diff__add__assoc) ).
fof(c_0_456,axiom,
! [X19,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X18),X17) ),
file('<stdin>',fact_add__diff__assoc) ).
fof(c_0_457,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X27)),c_RealDef_Oreal(tc_Nat_Onat,X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27),X31)) ),
file('<stdin>',fact_real__of__nat__le__iff) ).
fof(c_0_458,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X27)),c_RealDef_Oreal(tc_Nat_Onat,X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31)) ),
file('<stdin>',fact_real__of__nat__less__iff) ).
fof(c_0_459,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11)) ),
file('<stdin>',fact_abs__add__abs) ).
fof(c_0_460,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X27))
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X33) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X33)
<=> X31 = X27 ) ) ),
file('<stdin>',fact_eq__diff__iff) ).
fof(c_0_461,axiom,
! [X29,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> hBOOL(hAPP(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),X7),X29))) ),
file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(c_0_462,axiom,
! [X29,X30,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X30)),X29) ),
file('<stdin>',fact_power__mult) ).
fof(c_0_463,axiom,
! [X49,X50,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X50)),X49) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X49)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(c_0_464,axiom,
! [X50,X30] :
( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X50),X30) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X50),X30) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X50),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('<stdin>',fact_power__eq__if) ).
fof(c_0_465,axiom,
! [X12,X7] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X7)),c_Transcendental_Ocos(X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X7)),c_Transcendental_Osin(X12))),
file('<stdin>',fact_cos__add) ).
fof(c_0_466,axiom,
! [X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14)),X14) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('<stdin>',fact_odd__nonzero) ).
fof(c_0_467,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X7))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7))),
file('<stdin>',fact_abs__Re__le__cmod) ).
fof(c_0_468,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X7))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7))),
file('<stdin>',fact_abs__Im__le__cmod) ).
fof(c_0_469,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
file('<stdin>',fact__096cmod_A_Is_A0_J_A_060_061_Ar_096) ).
fof(c_0_470,axiom,
! [X12,X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X7))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X12)),X7) = c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X7)) ) ),
file('<stdin>',fact_abs__mult__pos) ).
fof(c_0_471,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5)))) ),
file('<stdin>',fact_zero__less__two) ).
fof(c_0_472,axiom,
! [X52,X21,X22,X6,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X6,X22) = c_Groups_Ominus__class_Ominus(X5,X21,X52)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),X52)) ) ) ),
file('<stdin>',fact_diff__eq__diff__less) ).
fof(c_0_473,axiom,
! [X52,X21,X22,X6,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X6,X22) = c_Groups_Ominus__class_Ominus(X5,X21,X52)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),X22))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X21),X52)) ) ) ),
file('<stdin>',fact_diff__eq__diff__less__eq) ).
fof(c_0_474,axiom,
! [X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X30) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5))),X30) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(c_0_475,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X10)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
file('<stdin>',fact_ln__less__zero__iff) ).
fof(c_0_476,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10)) ) ),
file('<stdin>',fact_ln__ge__zero__iff) ).
fof(c_0_477,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X7)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7)) ) ),
file('<stdin>',fact_ln__ge__zero__imp__ge__one) ).
fof(c_0_478,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10)) ) ),
file('<stdin>',fact_ln__gt__zero__iff) ).
fof(c_0_479,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X7)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7)) ) ),
file('<stdin>',fact_ln__gt__zero__imp__gt__one) ).
fof(c_0_480,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7)))),
file('<stdin>',fact_abs__add__one__gt__zero) ).
fof(c_0_481,axiom,
! [X29,X4,X23] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X23,X4)),X29) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X23),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X4)),
file('<stdin>',fact_DeMoivre2) ).
fof(c_0_482,axiom,
! [X60,X61,X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X61,X60)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X60)),
file('<stdin>',fact_zdiff__zmult__distrib2) ).
fof(c_0_483,axiom,
! [X29,X30,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X29)),
file('<stdin>',fact_diff__mult__distrib2) ).
fof(c_0_484,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X4)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ),
file('<stdin>',fact_abs__le__D1) ).
fof(c_0_485,axiom,
! [X14,X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14))) ),
file('<stdin>',fact_termination__basic__simps_I3_J) ).
fof(c_0_486,axiom,
! [X12,X14,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14))) ),
file('<stdin>',fact_termination__basic__simps_I4_J) ).
fof(c_0_487,axiom,
! [X12,X14,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14))) ),
file('<stdin>',fact_termination__basic__simps_I2_J) ).
fof(c_0_488,axiom,
! [X14,X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14))) ),
file('<stdin>',fact_termination__basic__simps_I1_J) ).
fof(c_0_489,axiom,
! [X30,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X30))) ),
file('<stdin>',fact_trans__less__add1) ).
fof(c_0_490,axiom,
! [X30,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X18))) ),
file('<stdin>',fact_trans__less__add2) ).
fof(c_0_491,axiom,
! [X30,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X18))) ),
file('<stdin>',fact_trans__le__add2) ).
fof(c_0_492,axiom,
! [X30,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X30))) ),
file('<stdin>',fact_trans__le__add1) ).
fof(c_0_493,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X7)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ),
file('<stdin>',fact_ln__less__zero) ).
fof(c_0_494,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)),X29) = X30 ),
file('<stdin>',fact_le__add__diff__inverse2) ).
fof(c_0_495,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Osgn__class_Osgn(X5,X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
file('<stdin>',fact_sgn__greater) ).
fof(c_0_496,axiom,
! [X4,X23] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X23)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X4),X23),
file('<stdin>',fact_real__divide__square__eq) ).
fof(c_0_497,axiom,
! [X63,X60,X61] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),X60)),X63) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X63)),
file('<stdin>',fact_zadd__assoc) ).
fof(c_0_498,axiom,
! [X63,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X60)),X63) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X63)),
file('<stdin>',fact_zmult__assoc) ).
fof(c_0_499,axiom,
! [X63,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X61),X60)),X63) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X60),X63)),
file('<stdin>',fact_real__mult__assoc) ).
fof(c_0_500,axiom,
! [X17,X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X17)),
file('<stdin>',fact_nat__mult__assoc) ).
fof(c_0_501,axiom,
! [X14,X12,X7] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X12)),X14) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X14)),
file('<stdin>',fact_zpower__zpower) ).
fof(c_0_502,axiom,
! [X17,X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X17)),
file('<stdin>',fact_nat__add__assoc) ).
fof(c_0_503,axiom,
! [X23] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X23))
=> ? [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X8)),X23))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X8)))) ) ),
file('<stdin>',fact_reals__Archimedean6a) ).
fof(c_0_504,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7))),X7)) ),
file('<stdin>',fact_real__natfloor__le) ).
fof(c_0_505,axiom,
! [X4,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X7)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),c_RComplete_Onatfloor(X4))) ),
file('<stdin>',fact_le__natfloor) ).
fof(c_0_506,axiom,
! [X14,X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X14)) ) ) ),
file('<stdin>',fact_order__less__le__trans) ).
fof(c_0_507,axiom,
! [X14,X7,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X14),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X14),X7)) ) ) ),
file('<stdin>',fact_xt1_I7_J) ).
fof(c_0_508,axiom,
! [X14,X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X14)) ) ) ),
file('<stdin>',fact_order__le__less__trans) ).
fof(c_0_509,axiom,
! [X14,X7,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X14),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X14),X7)) ) ) ),
file('<stdin>',fact_xt1_I8_J) ).
fof(c_0_510,axiom,
! [X14,X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X14)) ) ) ),
file('<stdin>',fact_order__less__trans) ).
fof(c_0_511,axiom,
! [X14,X7,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X14),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X14),X7)) ) ) ),
file('<stdin>',fact_xt1_I10_J) ).
fof(c_0_512,axiom,
! [X14,X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X14)) ) ) ),
file('<stdin>',fact_order__trans) ).
fof(c_0_513,axiom,
! [X14,X7,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X14),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X14),X7)) ) ) ),
file('<stdin>',fact_xt1_I6_J) ).
fof(c_0_514,axiom,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X8))),v_r)),
file('<stdin>',fact_assms) ).
fof(c_0_515,axiom,
! [X27,X31,X6,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X6))
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X31) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X27)
<=> X31 = X27 ) ) ),
file('<stdin>',fact_power__inject__exp) ).
fof(c_0_516,axiom,
! [X29,X30,X34,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17),X34))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X29)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ) ),
file('<stdin>',fact_less__add__eq__less) ).
fof(c_0_517,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19)),X17)) ) ),
file('<stdin>',fact_less__trans__Suc) ).
fof(c_0_518,axiom,
! [X4,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),c_RealDef_Oreal(tc_Nat_Onat,X4))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X7)),X4) ),
file('<stdin>',fact_natceiling__add) ).
fof(c_0_519,axiom,
! [X4,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),c_RealDef_Oreal(tc_Nat_Onat,X4))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X7)),X4) ),
file('<stdin>',fact_natfloor__add) ).
fof(c_0_520,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),c_RealDef_Oreal(tc_Nat_Onat,X29)) ),
file('<stdin>',fact_real__of__nat__diff) ).
fof(c_0_521,axiom,
! [X17,X29,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X30),X29),c_Nat_OSuc(X17)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),X17),
file('<stdin>',fact_Suc__diff__diff) ).
fof(c_0_522,axiom,
! [X29,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X7),X29)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_Transcendental_Oln(X7)) ),
file('<stdin>',fact_ln__realpow) ).
fof(c_0_523,axiom,
! [X26,X15,X11,X4] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X4,X11),c_Complex_Ocomplex_OComplex(X15,X26)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4,X15),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X11,X26)),
file('<stdin>',fact_complex__diff) ).
fof(c_0_524,axiom,
! [X11,X4,X15,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X15 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)) = c_Divides_Odiv__class_Odiv(X5,X4,X11) ) ),
file('<stdin>',fact_div__mult__mult1) ).
fof(c_0_525,axiom,
! [X11,X4,X15,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X15 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)) = c_Divides_Odiv__class_Odiv(X5,X4,X11) ) ),
file('<stdin>',fact_div__mult__mult2) ).
fof(c_0_526,axiom,
! [X11,X4,X15,X5] :
( class_Divides_Osemiring__div(X5)
=> ( ( X15 = c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)) = c_Groups_Ozero__class_Ozero(X5) )
& ( X15 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)) = c_Divides_Odiv__class_Odiv(X5,X4,X11) ) ) ),
file('<stdin>',fact_div__mult__mult1__if) ).
fof(c_0_527,axiom,
! [X6,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X6)),c_Groups_Ozero__class_Ozero(X5)))
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_abs__le__zero__iff) ).
fof(c_0_528,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),c_Nat_OSuc(X27)))
<=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X82] :
( X31 = c_Nat_OSuc(X82)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X82),X27)) ) ) ),
file('<stdin>',fact_less__Suc__eq__0__disj) ).
fof(c_0_529,axiom,
! [X49,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X49)),X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Nat_OSuc(X49)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(c_0_530,axiom,
! [X29,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),X4) ),
file('<stdin>',fact_power__Suc2) ).
fof(c_0_531,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Ozero__class_Ozero(X5))) ),
file('<stdin>',fact_abs__not__less__zero) ).
fof(c_0_532,axiom,
! [X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4))) ),
file('<stdin>',fact_zero__le__square) ).
fof(c_0_533,axiom,
! [X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Oone__class_Oone(X5)))) ),
file('<stdin>',fact_less__add__one) ).
fof(c_0_534,axiom,
! [X26,X15,X11,X4] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X4,X11)),c_Complex_Ocomplex_OComplex(X15,X26)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X11),X26)),
file('<stdin>',fact_complex__add) ).
fof(c_0_535,axiom,
! [X11,X75,X4,X76] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X76,X4)),c_Complex_Orcis(X75,X11)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X76),X75),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X11)),
file('<stdin>',fact_rcis__mult) ).
fof(c_0_536,axiom,
! [X46,X47,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X46)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(c_0_537,axiom,
! [X26,X15,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X26)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(c_0_538,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X19),X17)) ) ),
file('<stdin>',fact_zle__trans) ).
fof(c_0_539,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X17)) ) ),
file('<stdin>',fact_le__trans) ).
fof(c_0_540,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X17)) ) ),
file('<stdin>',fact_real__le__trans) ).
fof(c_0_541,axiom,
! [X33,X83] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X83,X33) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( X33 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X83))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X83),X33)) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X83),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X33),X83)) ) ) ),
file('<stdin>',fact_zdiv__eq__0__iff) ).
fof(c_0_542,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X11))
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('<stdin>',fact_div__pos__pos__trivial) ).
fof(c_0_543,axiom,
! [X17,X18,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18),X17) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X17),X18),
file('<stdin>',fact_diff__commute) ).
fof(c_0_544,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X10)) ) ),
file('<stdin>',fact_convergent__realpow) ).
fof(c_0_545,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X10)) ) ),
file('<stdin>',fact_monoseq__realpow) ).
fof(c_0_546,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X10)) ) ),
file('<stdin>',fact_Bseq__realpow) ).
fof(c_0_547,axiom,
! [X4,X29] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X4)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),X29)),
file('<stdin>',fact_sin__n__Im__cis__pow__n) ).
fof(c_0_548,axiom,
! [X4,X29] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X4)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),X29)),
file('<stdin>',fact_cos__n__Re__cis__pow__n) ).
fof(c_0_549,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X11),X4))
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('<stdin>',fact_div__neg__neg__trivial) ).
fof(c_0_550,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X10)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_norm__le__zero__iff) ).
fof(c_0_551,axiom,
! [X9,X10,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10)) ) ) ),
file('<stdin>',fact_less__le__not__le) ).
fof(c_0_552,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X7)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('<stdin>',fact_natfloor__add__one) ).
fof(c_0_553,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X7)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('<stdin>',fact_natceiling__add__one) ).
fof(c_0_554,axiom,
! [X15,X11,X4] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X15)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4,X11),X15),
file('<stdin>',fact_div__mult2__eq) ).
fof(c_0_555,axiom,
! [X17,X18,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18),X17) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X17)),
file('<stdin>',fact_diff__diff__left) ).
fof(c_0_556,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X7)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
file('<stdin>',fact_norm__not__less__zero) ).
fof(c_0_557,axiom,
! [X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27)) ),
file('<stdin>',fact_real__of__nat__gt__zero__cancel__iff) ).
fof(c_0_558,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X9))
=> ( c_Transcendental_Oln(X10) = c_Transcendental_Oln(X9)
<=> X10 = X9 ) ) ),
file('<stdin>',fact_ln__inj__iff) ).
fof(c_0_559,axiom,
! [X4,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),c_RealDef_Oreal(tc_Nat_Onat,X4)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X7)),X4)) ),
file('<stdin>',fact_natceiling__le) ).
fof(c_0_560,axiom,
! [X29,X30,X17] :
( ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X29)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X29)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) ) ),
file('<stdin>',fact_nat__mult__div__cancel__disj) ).
fof(c_0_561,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X30),X29) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) ),
file('<stdin>',fact_Suc__diff__le) ).
fof(c_0_562,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)
<=> X31 = X27 ) ),
file('<stdin>',fact_nat__mult__eq__cancel1) ).
fof(c_0_563,axiom,
! [X29,X30,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),
file('<stdin>',fact_diff__cancel) ).
fof(c_0_564,axiom,
! [X29,X17,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X17)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),
file('<stdin>',fact_diff__cancel2) ).
fof(c_0_565,axiom,
! [X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X12)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_Transcendental_Ocos(c_Transcendental_Oarccos(X12)) = X12 ),
file('<stdin>',fact_cos__arccos__abs) ).
fof(c_0_566,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X30),X29) = X30 ),
file('<stdin>',fact_div__mult__self1__is__m) ).
fof(c_0_567,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29),X29) = X30 ),
file('<stdin>',fact_div__mult__self__is__m) ).
fof(c_0_568,axiom,
! [X29,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4))
=> ? [X74] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X74))
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X74),c_Nat_OSuc(X29)) = X4 ) ),
file('<stdin>',fact_realpow__pos__nth2) ).
fof(c_0_569,axiom,
! [X27,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X27)),X31)) ),
file('<stdin>',fact_not__less__eq__eq) ).
fof(c_0_570,axiom,
! [X29,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X29))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X19)) = X19 ),
file('<stdin>',fact_diff__diff__cancel) ).
fof(c_0_571,axiom,
! [X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X27)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
<=> X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_real__of__nat__le__zero__cancel__iff) ).
fof(c_0_572,axiom,
! [X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X53)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> X53 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('<stdin>',fact_zabs__less__one__iff) ).
fof(c_0_573,axiom,
! [X11,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ominus__class_Ominus(X5,X4,X11)),X11) = X4 ),
file('<stdin>',fact_diff__add__cancel) ).
fof(c_0_574,axiom,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X29)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
file('<stdin>',fact_not__real__of__nat__less__zero) ).
fof(c_0_575,axiom,
! [X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X29 ),
file('<stdin>',fact_Suc__pred) ).
fof(c_0_576,axiom,
! [X14,X12,X7] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7),X14)),
file('<stdin>',fact_zadd__left__commute) ).
fof(c_0_577,axiom,
! [X14,X12,X7] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X14)),
file('<stdin>',fact_nat__add__left__commute) ).
fof(c_0_578,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) = X30 ),
file('<stdin>',fact_le__add__diff__inverse) ).
fof(c_0_579,axiom,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> X10 = X9 ) ) ),
file('<stdin>',fact_linorder__antisym__conv2) ).
fof(c_0_580,axiom,
! [X9,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( X10 = X9
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10)) ) ) ),
file('<stdin>',fact_order__eq__iff) ).
fof(c_0_581,axiom,
! [X10,X9,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
<=> X10 = X9 ) ) ),
file('<stdin>',fact_order__antisym__conv) ).
fof(c_0_582,axiom,
! [X12,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> X7 = X12 ) ) ),
file('<stdin>',fact_order__antisym) ).
fof(c_0_583,axiom,
! [X7,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> X7 = X12 ) ) ),
file('<stdin>',fact_xt1_I5_J) ).
fof(c_0_584,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
<=> ? [X32] : X27 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32)) ),
file('<stdin>',fact_less__iff__Suc__add) ).
fof(c_0_585,axiom,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10)) ) ),
file('<stdin>',fact_linorder__not__less) ).
fof(c_0_586,axiom,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X9),X10)) ) ),
file('<stdin>',fact_linorder__not__le) ).
fof(c_0_587,axiom,
! [X7,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12)) ) ),
file('<stdin>',fact_leD) ).
fof(c_0_588,axiom,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X9),X10))
| X10 = X9 ) ) ),
file('<stdin>',fact_not__less__iff__gr__or__eq) ).
fof(c_0_589,axiom,
! [X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ),
file('<stdin>',fact_order__less__not__sym) ).
fof(c_0_590,axiom,
! [X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ),
file('<stdin>',fact_order__less__imp__not__less) ).
fof(c_0_591,axiom,
! [X11,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4)) ) ),
file('<stdin>',fact_order__less__asym_H) ).
fof(c_0_592,axiom,
! [X4,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ),
file('<stdin>',fact_xt1_I9_J) ).
fof(c_0_593,axiom,
! [X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ),
file('<stdin>',fact_order__less__asym) ).
fof(c_0_594,axiom,
! [X6,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oabs__class_Oabs(X5,X6)))
<=> X6 != c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_zero__less__abs__iff) ).
fof(c_0_595,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),c_Nat_OSuc(X31)))
<=> X27 = X31 ) ),
file('<stdin>',fact_le__less__Suc__eq) ).
fof(c_0_596,axiom,
! [X27,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),c_Nat_OSuc(X31))) ),
file('<stdin>',fact_not__less__eq) ).
fof(c_0_597,axiom,
! [X6,X69,X70,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X70,X69),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X70,
file('<stdin>',fact_power_Opower_Opower__0) ).
fof(c_0_598,axiom,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X30))),
file('<stdin>',fact_le__square) ).
fof(c_0_599,axiom,
! [X30,X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X30))),
file('<stdin>',fact_le__add1) ).
fof(c_0_600,axiom,
! [X30,X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29))),
file('<stdin>',fact_le__add2) ).
fof(c_0_601,axiom,
! [X11,X4,X5] :
( ( class_Fields_Ofield__inverse__zero(X5)
& class_RealVector_Oreal__normed__field(X5) )
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X11)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)),c_RealVector_Onorm__class_Onorm(X5,X11)) ),
file('<stdin>',fact_norm__divide) ).
fof(c_0_602,axiom,
! [X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X29 ),
file('<stdin>',fact_Suc__diff__1) ).
fof(c_0_603,axiom,
! [X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> X29 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('<stdin>',fact_Suc__pred_H) ).
fof(c_0_604,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X27)),c_Nat_OSuc(X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27),X31)) ),
file('<stdin>',fact_Suc__le__mono) ).
fof(c_0_605,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X31)),c_Nat_OSuc(X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ),
file('<stdin>',fact_Suc__less__eq) ).
fof(c_0_606,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X30)),c_Nat_OSuc(X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ),
file('<stdin>',fact_Suc__less__SucD) ).
fof(c_0_607,axiom,
! [X12,X7,X5] :
( class_RealVector_Oreal__normed__div__algebra(X5)
=> c_Groups_Osgn__class_Osgn(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Osgn__class_Osgn(X5,X7)),c_Groups_Osgn__class_Osgn(X5,X12)) ),
file('<stdin>',fact_sgn__mult) ).
fof(c_0_608,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Osgn__class_Osgn(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Osgn__class_Osgn(X5,X4)),c_Groups_Osgn__class_Osgn(X5,X11)) ),
file('<stdin>',fact_sgn__times) ).
fof(c_0_609,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11)) ),
file('<stdin>',fact_abs__mult) ).
fof(c_0_610,axiom,
! [X4,X11,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X11)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)),c_RealVector_Onorm__class_Onorm(X5,X11)) ) ),
file('<stdin>',fact_nonzero__norm__divide) ).
fof(c_0_611,axiom,
! [X33,X84,X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83),X84))
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X84,X83) = X33
<=> X84 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X83) ) ),
file('<stdin>',fact_le__imp__diff__is__add) ).
fof(c_0_612,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X10)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
file('<stdin>',fact_natceiling__le__eq__one) ).
fof(c_0_613,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)) = c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X11,X4)) ),
file('<stdin>',fact_abs__minus__commute) ).
fof(c_0_614,axiom,
! [X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X11,X4)) ),
file('<stdin>',fact_norm__minus__commute) ).
fof(c_0_615,axiom,
! [X12,X7,X5] :
( class_RealVector_Oreal__normed__div__algebra(X5)
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),c_RealVector_Onorm__class_Onorm(X5,X12)) ),
file('<stdin>',fact_norm__mult) ).
fof(c_0_616,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10)) ),
file('<stdin>',fact_le__natfloor__eq__one) ).
fof(c_0_617,axiom,
! [X29,X4] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),X29) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X4)),
file('<stdin>',fact_DeMoivre) ).
fof(c_0_618,axiom,
! [X16,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14),X16))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16),X14))
=> X14 = X16 ) ),
file('<stdin>',fact_zle__antisym) ).
fof(c_0_619,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> X30 = X29 ) ),
file('<stdin>',fact_le__antisym) ).
fof(c_0_620,axiom,
! [X16,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X16))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16),X14))
=> X14 = X16 ) ),
file('<stdin>',fact_real__le__antisym) ).
fof(c_0_621,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X7))) ),
file('<stdin>',fact_ln__gt__zero) ).
fof(c_0_622,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X7))) ),
file('<stdin>',fact_ln__ge__zero) ).
fof(c_0_623,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X7)),X7)) ),
file('<stdin>',fact_ln__less__self) ).
fof(c_0_624,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X5,X10)))
<=> X10 != c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_zero__less__norm__iff) ).
fof(c_0_625,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X27)),X31)) ),
file('<stdin>',fact_less__eq__Suc__le) ).
fof(c_0_626,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X31)),X27))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ),
file('<stdin>',fact_Suc__le__eq) ).
fof(c_0_627,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X30)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ),
file('<stdin>',fact_Suc__le__lessD) ).
fof(c_0_628,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X30)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ),
file('<stdin>',fact_Suc__leD) ).
fof(c_0_629,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X30)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ),
file('<stdin>',fact_Suc__lessD) ).
fof(c_0_630,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X30)),c_Nat_OSuc(X29))) ),
file('<stdin>',fact_Suc__mono) ).
fof(c_0_631,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X7)),c_RComplete_Onatceiling(X12))) ),
file('<stdin>',fact_natceiling__mono) ).
fof(c_0_632,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X7)),c_RComplete_Onatfloor(X12))) ),
file('<stdin>',fact_natfloor__mono) ).
fof(c_0_633,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
=> ( X7 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X7 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('<stdin>',fact_nat__lt__two__imp__zero__or__one) ).
fof(c_0_634,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oabs__class_Oabs(X5,X4)),X29) ),
file('<stdin>',fact_power__abs) ).
fof(c_0_635,axiom,
! [X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X53))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X53)) ),
file('<stdin>',fact_int__one__le__iff__zero__less) ).
fof(c_0_636,axiom,
! [X29,X30] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) = X30 ),
file('<stdin>',fact_add__diff__inverse) ).
fof(c_0_637,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> ( c_Nat_OSuc(X30) != X29
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X30)),X29)) ) ),
file('<stdin>',fact_Suc__lessI) ).
fof(c_0_638,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X7))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('<stdin>',fact_abs__cos__le__one) ).
fof(c_0_639,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(X7))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('<stdin>',fact_abs__sin__le__one) ).
fof(c_0_640,axiom,
! [X10,X9,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X9),X10))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> X10 = X9 ) ) ),
file('<stdin>',fact_linorder__antisym__conv3) ).
fof(c_0_641,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oord(X5)
=> ( X4 = X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X15)) ) ) ),
file('<stdin>',fact_ord__eq__less__trans) ).
fof(c_0_642,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 = X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X4)) ) ) ),
file('<stdin>',fact_xt1_I1_J) ).
fof(c_0_643,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oord(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( X11 = X15
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X15)) ) ) ),
file('<stdin>',fact_ord__less__eq__trans) ).
fof(c_0_644,axiom,
! [X15,X4,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4))
=> ( X11 = X15
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X4)) ) ) ),
file('<stdin>',fact_xt1_I2_J) ).
fof(c_0_645,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oord(X5)
=> ( X4 = X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X15)) ) ) ),
file('<stdin>',fact_ord__eq__le__trans) ).
fof(c_0_646,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 = X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X4)) ) ) ),
file('<stdin>',fact_xt1_I3_J) ).
fof(c_0_647,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oord(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( X11 = X15
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X15)) ) ) ),
file('<stdin>',fact_ord__le__eq__trans) ).
fof(c_0_648,axiom,
! [X15,X4,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> ( X11 = X15
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X4)) ) ) ),
file('<stdin>',fact_xt1_I4_J) ).
fof(c_0_649,axiom,
! [X29,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Nat_OSuc(X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X29),
file('<stdin>',fact_diff__Suc__eq__diff__pred) ).
fof(c_0_650,axiom,
! [X29,X7,X5] :
( class_RealVector_Oreal__normed__div__algebra(X5)
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),X29) ),
file('<stdin>',fact_norm__power) ).
fof(c_0_651,axiom,
! [X9,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
& X10 != X9 ) ) ),
file('<stdin>',fact_order__less__le) ).
fof(c_0_652,axiom,
! [X9,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
| X10 = X9 ) ) ),
file('<stdin>',fact_order__le__less) ).
fof(c_0_653,axiom,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
<=> X10 = X9 ) ) ),
file('<stdin>',fact_linorder__antisym__conv1) ).
fof(c_0_654,axiom,
! [X11,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 != X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
file('<stdin>',fact_order__neq__le__trans) ).
fof(c_0_655,axiom,
! [X11,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 != X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4)) ) ) ),
file('<stdin>',fact_xt1_I12_J) ).
fof(c_0_656,axiom,
! [X12,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
| X7 = X12 ) ) ),
file('<stdin>',fact_order__le__imp__less__or__eq) ).
fof(c_0_657,axiom,
! [X11,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( X4 != X11
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
file('<stdin>',fact_order__le__neq__trans) ).
fof(c_0_658,axiom,
! [X4,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> ( X4 != X11
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4)) ) ) ),
file('<stdin>',fact_xt1_I11_J) ).
fof(c_0_659,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),c_Nat_OSuc(X29)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> X30 = c_Nat_OSuc(X29) ) ),
file('<stdin>',fact_le__SucE) ).
fof(c_0_660,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),c_Nat_OSuc(X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
| X31 = c_Nat_OSuc(X27) ) ),
file('<stdin>',fact_le__Suc__eq) ).
fof(c_0_661,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X30)),X29)) ),
file('<stdin>',fact_Suc__leI) ).
fof(c_0_662,axiom,
! [X49,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Nat_OSuc(X49)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X49)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
fof(c_0_663,axiom,
! [X49,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X49)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Nat_OSuc(X49)) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(c_0_664,axiom,
! [X29,X4,X5] :
( class_Power_Opower(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) ),
file('<stdin>',fact_power__Suc) ).
fof(c_0_665,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),X27) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X31 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X27 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('<stdin>',fact_pos__zmult__eq__1__iff) ).
fof(c_0_666,axiom,
! [X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12)) ) ),
file('<stdin>',fact_order__less__imp__le) ).
fof(c_0_667,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),c_Nat_OSuc(X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
| X31 = X27 ) ),
file('<stdin>',fact_less__Suc__eq) ).
fof(c_0_668,axiom,
! [X31,X27] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),c_Nat_OSuc(X31)))
<=> X27 = X31 ) ),
file('<stdin>',fact_not__less__less__Suc__eq) ).
fof(c_0_669,axiom,
! [X30,X29] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),c_Nat_OSuc(X30)))
=> X30 = X29 ) ),
file('<stdin>',fact_less__antisym) ).
fof(c_0_670,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),c_Nat_OSuc(X29)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> X30 = X29 ) ),
file('<stdin>',fact_less__SucE) ).
fof(c_0_671,axiom,
! [X29,X30] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),c_RealDef_Oreal(tc_Nat_Onat,X29)),
file('<stdin>',fact_real__of__nat__add) ).
fof(c_0_672,axiom,
! [X29,X30] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),c_RealDef_Oreal(tc_Nat_Onat,X29)),
file('<stdin>',fact_real__of__nat__mult) ).
fof(c_0_673,axiom,
! [X12,X7] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_OIm,X12)),
file('<stdin>',fact_Im_Oadd) ).
fof(c_0_674,axiom,
! [X12,X7] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_ORe,X12)),
file('<stdin>',fact_Re_Oadd) ).
fof(c_0_675,axiom,
! [X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
=> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('<stdin>',fact_cos__arg__i__mult__zero__pos) ).
fof(c_0_676,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),c_Nat_OSuc(X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ),
file('<stdin>',fact_less__Suc__eq__le) ).
fof(c_0_677,axiom,
! [X12,X7] : hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X7,X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X7),hAPP(c_Complex_OIm,X12)),
file('<stdin>',fact_Im_Odiff) ).
fof(c_0_678,axiom,
! [X12,X7] : hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X7,X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X7),hAPP(c_Complex_ORe,X12)),
file('<stdin>',fact_Re_Odiff) ).
fof(c_0_679,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X7)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7))),
file('<stdin>',fact_complex__Re__le__cmod) ).
fof(c_0_680,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),c_Nat_OSuc(X29))) ),
file('<stdin>',fact_le__imp__less__Suc) ).
fof(c_0_681,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),c_Nat_OSuc(X29))) ),
file('<stdin>',fact_le__SucI) ).
fof(c_0_682,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),c_Nat_OSuc(X29))) ),
file('<stdin>',fact_less__SucI) ).
fof(c_0_683,axiom,
! [X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('<stdin>',fact_cos__arg__i__mult__zero__neg) ).
fof(c_0_684,axiom,
! [X54,X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X53),X54))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53),X54))
& X53 != X54 ) ),
file('<stdin>',fact_zless__le) ).
fof(c_0_685,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
& X31 != X27 ) ),
file('<stdin>',fact_nat__less__le) ).
fof(c_0_686,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
| X31 = X27 ) ),
file('<stdin>',fact_le__eq__less__or__eq) ).
fof(c_0_687,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> ( X30 != X29
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ) ),
file('<stdin>',fact_le__neq__implies__less) ).
fof(c_0_688,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),X9))
| X10 = X9 ) ),
file('<stdin>',fact_less__eq__real__def) ).
fof(c_0_689,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9))
& X10 != X9 ) ),
file('<stdin>',fact_real__less__def) ).
fof(c_0_690,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),X12)) ),
file('<stdin>',fact_termination__basic__simps_I5_J) ).
fof(c_0_691,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ),
file('<stdin>',fact_less__imp__le__nat) ).
fof(c_0_692,axiom,
! [X29,X30] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
| X30 = X29 )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ),
file('<stdin>',fact_less__or__eq__imp__le) ).
fof(c_0_693,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X30)),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)),
file('<stdin>',fact_mult__Suc) ).
fof(c_0_694,axiom,
! [X29,X30] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),X29) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X29)),
file('<stdin>',fact_power__real__of__nat) ).
fof(c_0_695,axiom,
! [X29,X30] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),X29),
file('<stdin>',fact_real__of__nat__power) ).
fof(c_0_696,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(X5))) ),
file('<stdin>',fact_not__one__le__zero) ).
fof(c_0_697,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(X5))) ),
file('<stdin>',fact_not__one__less__zero) ).
fof(c_0_698,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Groups_Osgn__class_Osgn(X5,X6) = c_Groups_Oone__class_Oone(X5)
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
file('<stdin>',fact_sgn__1__pos) ).
fof(c_0_699,axiom,
! [X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> c_Groups_Osgn__class_Osgn(X5,X4) = c_Groups_Oone__class_Oone(X5) ) ),
file('<stdin>',fact_sgn__pos) ).
fof(c_0_700,axiom,
! [X39,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X39))
<=> ? [X8] : X39 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X8) ),
file('<stdin>',fact_le__Suc__ex__iff) ).
fof(c_0_701,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
<=> ? [X32] : X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32) ),
file('<stdin>',fact_le__iff__add) ).
fof(c_0_702,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> c_Groups_Oabs__class_Oabs(X5,X4) = X4 ) ),
file('<stdin>',fact_abs__of__nonneg) ).
fof(c_0_703,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> c_Groups_Oabs__class_Oabs(X5,X4) = X4 ) ),
file('<stdin>',fact_abs__of__pos) ).
fof(c_0_704,axiom,
! [X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4) ),
file('<stdin>',fact_abs__mult__self) ).
fof(c_0_705,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),c_Nat_OSuc(X29)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)),
file('<stdin>',fact_mult__Suc__right) ).
fof(c_0_706,axiom,
! [X7,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12),X7))
=> c_Nat__Transfer_Otsub(X7,X12) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X12) ),
file('<stdin>',fact_tsub__eq) ).
fof(c_0_707,axiom,
! [X7,X12] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12),X7))
=> c_Nat__Transfer_Otsub(X7,X12) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X12) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12),X7))
=> c_Nat__Transfer_Otsub(X7,X12) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('<stdin>',fact_tsub__def) ).
fof(c_0_708,axiom,
! [X27,X31,X33] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X27)
<=> X31 = X27 ),
file('<stdin>',fact_Suc__mult__cancel1) ).
fof(c_0_709,axiom,
! [X52,X21,X22,X6,X5] :
( class_Groups_Oab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X6,X22) = c_Groups_Ominus__class_Ominus(X5,X21,X52)
=> ( X6 = X22
<=> X21 = X52 ) ) ),
file('<stdin>',fact_diff__eq__diff__eq) ).
fof(c_0_710,axiom,
! [X29,X7] :
( X7 = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X7),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X7)),X29) ),
file('<stdin>',fact_natfloor__power) ).
fof(c_0_711,axiom,
! [X29,X30] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X29)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X30) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('<stdin>',fact_abs__zmult__eq__1) ).
fof(c_0_712,axiom,
! [X29,X30] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X30 = X29 ) ),
file('<stdin>',fact_diffs0__imp__equal) ).
fof(c_0_713,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_div__less) ).
fof(c_0_714,axiom,
! [X27,X31] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X27) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ),
file('<stdin>',fact_diff__is__0__eq) ).
fof(c_0_715,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_diff__is__0__eq_H) ).
fof(c_0_716,axiom,
! [X12,X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X7 != X12
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ) ),
file('<stdin>',fact_linorder__neqE__linordered__idom) ).
fof(c_0_717,axiom,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( X10 != X9
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X9),X10)) ) ) ),
file('<stdin>',fact_linorder__neq__iff) ).
fof(c_0_718,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
| X7 = X12
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ),
file('<stdin>',fact_linorder__less__linear) ).
fof(c_0_719,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( X7 != X12
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ) ),
file('<stdin>',fact_linorder__neqE) ).
fof(c_0_720,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ( X7 != X12
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ) ),
file('<stdin>',fact_linorder__cases) ).
fof(c_0_721,axiom,
! [X15,X4,X11,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4)
=> X11 = X15 ) ),
file('<stdin>',fact_add__right__imp__eq) ).
fof(c_0_722,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Ocancel__ab__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)
=> X11 = X15 ) ),
file('<stdin>',fact_add__imp__eq) ).
fof(c_0_723,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)
=> X11 = X15 ) ),
file('<stdin>',fact_add__left__imp__eq) ).
fof(c_0_724,axiom,
! [X21,X6,X22,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X6)
<=> X22 = X21 ) ),
file('<stdin>',fact_add__right__cancel) ).
fof(c_0_725,axiom,
! [X21,X22,X6,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X22) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21)
<=> X22 = X21 ) ),
file('<stdin>',fact_add__left__cancel) ).
fof(c_0_726,axiom,
! [X11,X4] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),c_Complex_Ocis(X11)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4,X11)),
file('<stdin>',fact_cis__divide) ).
fof(c_0_727,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ),
file('<stdin>',fact_linorder__le__less__linear) ).
fof(c_0_728,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7)) ) ),
file('<stdin>',fact_leI) ).
fof(c_0_729,axiom,
! [X7,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12)) ) ),
file('<stdin>',fact_not__leE) ).
fof(c_0_730,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7)) ) ),
file('<stdin>',fact_linorder__linear) ).
fof(c_0_731,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7)) ) ),
file('<stdin>',fact_linorder__le__cases) ).
fof(c_0_732,axiom,
! [X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X4),X11) = X4 ) ),
file('<stdin>',fact_div__mult__self1__is__id) ).
fof(c_0_733,axiom,
! [X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11),X11) = X4 ) ),
file('<stdin>',fact_div__mult__self2__is__id) ).
fof(c_0_734,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oabs__class_Oabs(X5,X4))) ),
file('<stdin>',fact_abs__ge__zero) ).
fof(c_0_735,axiom,
! [X11,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11),X11) = X4 ),
file('<stdin>',fact_add__diff__cancel) ).
fof(c_0_736,axiom,
! [X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_less__Suc0) ).
fof(c_0_737,axiom,
! [X11,X4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),c_Complex_Ocis(X11)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X11)),
file('<stdin>',fact_cis__mult) ).
fof(c_0_738,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X29)))),
file('<stdin>',fact_real__of__nat__Suc__gt__zero) ).
fof(c_0_739,axiom,
! [X11,X4] : c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X4),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X4)),c_Complex_Oexpi(X11)),
file('<stdin>',fact_expi__add) ).
fof(c_0_740,axiom,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X29)),X29)),
file('<stdin>',fact_Suc__n__not__le__n) ).
fof(c_0_741,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X7),X12))
| X7 = X12
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X12),X7)) ),
file('<stdin>',fact_zless__linear) ).
fof(c_0_742,axiom,
! [X27,X31] :
( X31 != X27
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31)) ) ),
file('<stdin>',fact_nat__neq__iff) ).
fof(c_0_743,axiom,
! [X12,X7] :
( X7 != X12
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12),X7)) ) ),
file('<stdin>',fact_linorder__neqE__nat) ).
fof(c_0_744,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X7) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('<stdin>',fact_real__sgn__pos) ).
fof(c_0_745,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( c_Transcendental_Oln(X10) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X10 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
file('<stdin>',fact_ln__eq__zero__iff) ).
fof(c_0_746,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X30)),X29) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)),
file('<stdin>',fact_add__Suc) ).
fof(c_0_747,axiom,
! [X16,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16),X14)) ),
file('<stdin>',fact_zle__linear) ).
fof(c_0_748,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30)) ),
file('<stdin>',fact_nat__le__linear) ).
fof(c_0_749,axiom,
! [X16,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16),X14)) ),
file('<stdin>',fact_real__le__linear) ).
fof(c_0_750,axiom,
! [X27,X31,X33] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)
<=> ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X31 = X27 ) ),
file('<stdin>',fact_nat__mult__eq__cancel__disj) ).
fof(c_0_751,axiom,
! [X22,X6,X21] :
( X21 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X22)
<=> X6 = X22 ) ),
file('<stdin>',fact_real__mult__left__cancel) ).
fof(c_0_752,axiom,
! [X22,X6,X21] :
( X21 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X21)
<=> X6 = X22 ) ),
file('<stdin>',fact_real__mult__right__cancel) ).
fof(c_0_753,axiom,
! [X27,X33,X31] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X33)
<=> ( X31 = X27
| X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_mult__cancel2) ).
fof(c_0_754,axiom,
! [X27,X31,X33] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)
<=> ( X31 = X27
| X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_mult__cancel1) ).
fof(c_0_755,axiom,
! [X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27))
<=> ? [X20] : X27 = c_Nat_OSuc(X20) ),
file('<stdin>',fact_gr0__conv__Suc) ).
fof(c_0_756,axiom,
! [X14] : hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X14)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X14)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14)),
file('<stdin>',fact_Re__sgn) ).
fof(c_0_757,axiom,
! [X14] : hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X14)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X14)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14)),
file('<stdin>',fact_Im__sgn) ).
fof(c_0_758,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X21 != c_Groups_Ozero__class_Ozero(X5)
=> ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X22),X21)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21) = X22 ) ) ),
file('<stdin>',fact_nonzero__eq__divide__eq) ).
fof(c_0_759,axiom,
! [X6,X22,X21,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X21 != c_Groups_Ozero__class_Ozero(X5)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X22),X21) = X6
<=> X22 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21) ) ) ),
file('<stdin>',fact_nonzero__divide__eq__eq) ).
fof(c_0_760,axiom,
! [X4,X11,X15,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X15 != c_Groups_Ozero__class_Ozero(X5)
=> ( X11 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X15) = X4 ) ) ),
file('<stdin>',fact_divide__eq__imp) ).
fof(c_0_761,axiom,
! [X11,X4,X15,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X15 != c_Groups_Ozero__class_Ozero(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15) = X11
=> X4 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X15) ) ) ),
file('<stdin>',fact_eq__divide__imp) ).
fof(c_0_762,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X5,X7))) ),
file('<stdin>',fact_norm__ge__zero) ).
fof(c_0_763,axiom,
! [X27,X31,X33] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X27)
<=> X31 = X27 ),
file('<stdin>',fact_nat__add__left__cancel) ).
fof(c_0_764,axiom,
! [X27,X33,X31] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X33)
<=> X31 = X27 ),
file('<stdin>',fact_nat__add__right__cancel) ).
fof(c_0_765,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Nat_OSuc(X29)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)),
file('<stdin>',fact_add__Suc__right) ).
fof(c_0_766,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X7)))),
file('<stdin>',fact_real__natceiling__ge) ).
fof(c_0_767,axiom,
! [X30,X29] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X30)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_diff__add__0) ).
fof(c_0_768,axiom,
! [X27] :
( X27 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27)) ),
file('<stdin>',fact_neq0__conv) ).
fof(c_0_769,axiom,
! [X29,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29),X29) = X30,
file('<stdin>',fact_diff__add__inverse2) ).
fof(c_0_770,axiom,
! [X30,X29] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X30),X29) = X30,
file('<stdin>',fact_diff__add__inverse) ).
fof(c_0_771,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Oabs__class_Oabs(X5,X4))) ),
file('<stdin>',fact_abs__ge__self) ).
fof(c_0_772,axiom,
! [X12,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> X7 != X12 ) ),
file('<stdin>',fact_less__imp__neq) ).
fof(c_0_773,axiom,
! [X12,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> X7 != X12 ) ),
file('<stdin>',fact_order__less__imp__not__eq) ).
fof(c_0_774,axiom,
! [X12,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> X12 != X7 ) ),
file('<stdin>',fact_order__less__imp__not__eq2) ).
fof(c_0_775,axiom,
! [X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Osgn__class_Osgn(X5,X7)),c_Groups_Oabs__class_Oabs(X5,X7)) = X7 ),
file('<stdin>',fact_mult__sgn__abs) ).
fof(c_0_776,axiom,
! [X7,X5] :
( class_Orderings_Opreorder(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X7)) ),
file('<stdin>',fact_order__less__irrefl) ).
fof(c_0_777,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_natceiling__neg) ).
fof(c_0_778,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> c_RComplete_Onatfloor(X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_natfloor__neg) ).
fof(c_0_779,axiom,
! [X27,X2] :
( c_SEQ_Osubseq(X2)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27),hAPP(X2,X27))) ),
file('<stdin>',fact_seq__suble) ).
fof(c_0_780,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X29))),
file('<stdin>',fact_real__of__nat__ge__zero) ).
fof(c_0_781,axiom,
! [X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_le__0__eq) ).
fof(c_0_782,axiom,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('<stdin>',fact_not__less0) ).
fof(c_0_783,axiom,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('<stdin>',fact_less__nat__zero__code) ).
fof(c_0_784,axiom,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('<stdin>',fact_less__zeroE) ).
fof(c_0_785,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('<stdin>',fact_ext) ).
fof(c_0_786,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oone__class_Oone(X5))) ),
file('<stdin>',fact_zero__le__one) ).
fof(c_0_787,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oone__class_Oone(X5))) ),
file('<stdin>',fact_zero__less__one) ).
fof(c_0_788,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_gr__implies__not0) ).
fof(c_0_789,axiom,
! [X21,X5] :
( class_RealVector_Ometric__space(X5)
=> c_SEQ_Oconvergent(X5,c_COMBK(X5,tc_Nat_Onat,X21)) ),
file('<stdin>',fact_convergent__const) ).
fof(c_0_790,axiom,
! [X27,X6,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Omult__zero(X5)
& class_Rings_Ono__zero__divisors(X5)
& class_Rings_Ozero__neq__one(X5) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X27) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X6 = c_Groups_Ozero__class_Ozero(X5)
& X27 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('<stdin>',fact_power__eq__0__iff) ).
fof(c_0_791,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X30))
=> X30 != X29 ),
file('<stdin>',fact_less__not__refl2) ).
fof(c_0_792,axiom,
! [X36,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24),X36))
=> X24 != X36 ),
file('<stdin>',fact_less__not__refl3) ).
fof(c_0_793,axiom,
! [X105,X106,X13,X5] : hAPP(c_COMBK(X5,X13,X106),X105) = X106,
file('<stdin>',help_c__COMBK__1) ).
fof(c_0_794,axiom,
! [X95,X96,X101,X5] : c_Complex_Ocomplex_Ocomplex__case(X5,X101,c_Complex_Ocomplex_OComplex(X96,X95)) = hAPP(hAPP(X101,X96),X95),
file('<stdin>',fact_complex_Osimps_I2_J) ).
fof(c_0_795,axiom,
! [X95,X96,X101,X5] : c_Complex_Ocomplex_Ocomplex__rec(X5,X101,c_Complex_Ocomplex_OComplex(X96,X95)) = hAPP(hAPP(X101,X96),X95),
file('<stdin>',fact_complex_Orecs) ).
fof(c_0_796,axiom,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X29)),
file('<stdin>',fact_less__not__refl) ).
fof(c_0_797,axiom,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X29)),
file('<stdin>',fact_less__irrefl__nat) ).
fof(c_0_798,axiom,
! [X29,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X30),c_Nat_OSuc(X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),
file('<stdin>',fact_diff__Suc__Suc) ).
fof(c_0_799,axiom,
! [X29] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X29)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('<stdin>',fact_real__of__nat__Suc) ).
fof(c_0_800,axiom,
! [X11,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X4) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(c_0_801,axiom,
! [X15,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(c_0_802,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X30)),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Nat_OSuc(X29)),
file('<stdin>',fact_add__Suc__shift) ).
fof(c_0_803,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(X7)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('<stdin>',fact_sin__le__one) ).
fof(c_0_804,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(X7)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('<stdin>',fact_cos__le__one) ).
fof(c_0_805,axiom,
! [X11,X4,X5] :
( class_Rings_Ono__zero__divisors(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11) = c_Groups_Ozero__class_Ozero(X5)
=> ( X4 = c_Groups_Ozero__class_Ozero(X5)
| X11 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('<stdin>',fact_divisors__zero) ).
fof(c_0_806,axiom,
! [X11,X4,X5] :
( class_Rings_Ono__zero__divisors(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11) != c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('<stdin>',fact_no__zero__divisors) ).
fof(c_0_807,axiom,
! [X22,X6,X5] :
( class_Rings_Oring__no__zero__divisors(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X22) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X6 = c_Groups_Ozero__class_Ozero(X5)
| X22 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('<stdin>',fact_mult__eq__0__iff) ).
fof(c_0_808,axiom,
! [X6,X22,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X22 != c_Groups_Ozero__class_Ozero(X5)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X22) = c_Groups_Oone__class_Oone(X5)
<=> X6 = X22 ) ) ),
file('<stdin>',fact_right__inverse__eq) ).
fof(c_0_809,axiom,
! [X22,X6,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X6,X22) = c_Groups_Ozero__class_Ozero(X5)
<=> X6 = X22 ) ),
file('<stdin>',fact_right__minus__eq) ).
fof(c_0_810,axiom,
! [X22,X6,X5] :
( class_Groups_Oab__group__add(X5)
=> ( X6 = X22
<=> c_Groups_Ominus__class_Ominus(X5,X6,X22) = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_eq__iff__diff__eq__0) ).
fof(c_0_811,axiom,
! [X29,X4,X5] :
( class_Rings_Oring__1__no__zero__divisors(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29) != c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_field__power__not__zero) ).
fof(c_0_812,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6) = c_Groups_Ozero__class_Ozero(X5)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_double__eq__0__iff) ).
fof(c_0_813,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_double__zero__sym) ).
fof(c_0_814,axiom,
! [X27,X31] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X27) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X31 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X27 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('<stdin>',fact_add__is__1) ).
fof(c_0_815,axiom,
! [X27,X31] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X27)
<=> ( ( X31 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X27 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('<stdin>',fact_one__is__add) ).
fof(c_0_816,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(X29))),
file('<stdin>',fact_zero__less__Suc) ).
fof(c_0_817,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(X7))),
file('<stdin>',fact_zero__le__natceiling) ).
fof(c_0_818,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X7))),
file('<stdin>',fact_zero__le__natfloor) ).
fof(c_0_819,axiom,
! [X17,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),c_Groups_Osgn__class_Osgn(X5,X17)) ),
file('<stdin>',fact_abs__sgn) ).
fof(c_0_820,axiom,
! [X6,X22,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X22 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X6)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_add__0__iff) ).
fof(c_0_821,axiom,
! [X31,X10] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X10),X31) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X10 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('<stdin>',fact_nat__power__eq__Suc__0__iff) ).
fof(c_0_822,axiom,
hBOOL(hAPP(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_823,axiom,
hBOOL(hAPP(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_824,axiom,
hBOOL(hAPP(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_825,axiom,
! [X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( X7 = X12
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12)) ) ),
file('<stdin>',fact_order__eq__refl) ).
fof(c_0_826,axiom,
! [X27,X31] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X27) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X31 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X27 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('<stdin>',fact_mult__eq__1__iff) ).
fof(c_0_827,axiom,
! [X16,X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),X14),
file('<stdin>',fact_zadd__commute) ).
fof(c_0_828,axiom,
! [X16,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X14),
file('<stdin>',fact_zmult__commute) ).
fof(c_0_829,axiom,
! [X16,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X14),
file('<stdin>',fact_real__mult__commute) ).
fof(c_0_830,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X30),
file('<stdin>',fact_nat__mult__commute) ).
fof(c_0_831,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X30),
file('<stdin>',fact_nat__add__commute) ).
fof(c_0_832,axiom,
! [X29] :
( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)) ),
file('<stdin>',fact_gr0I) ).
fof(c_0_833,axiom,
! [X4,X23] : hAPP(c_Complex_ORe,c_Complex_Orcis(X23,X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),c_Transcendental_Ocos(X4)),
file('<stdin>',fact_Re__rcis) ).
fof(c_0_834,axiom,
! [X4,X23] : hAPP(c_Complex_OIm,c_Complex_Orcis(X23,X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),c_Transcendental_Osin(X4)),
file('<stdin>',fact_Im__rcis) ).
fof(c_0_835,axiom,
! [X7,X5] :
( class_Orderings_Opreorder(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X7)) ),
file('<stdin>',fact_order__refl) ).
fof(c_0_836,axiom,
! [X29,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Osemiring__0(X5) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),c_Nat_OSuc(X29)) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_power__0__Suc) ).
fof(c_0_837,axiom,
! [X29,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Osemiring__0(X5) )
=> ( ( X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),X29) = c_Groups_Oone__class_Oone(X5) )
& ( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),X29) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('<stdin>',fact_power__0__left) ).
fof(c_0_838,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),c_Nat_OSuc(X29))),
file('<stdin>',fact_lessI) ).
fof(c_0_839,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)),
file('<stdin>',fact_less__eq__nat_Osimps_I1_J) ).
fof(c_0_840,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)),
file('<stdin>',fact_le0) ).
fof(c_0_841,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('<stdin>',fact_rp) ).
fof(c_0_842,axiom,
! [X27,X31] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X27) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_mult__is__0) ).
fof(c_0_843,axiom,
! [X29,X30] :
( X30 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)
=> ( X29 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_mult__eq__self__implies__10) ).
fof(c_0_844,axiom,
! [X7] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X7) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X7),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7)),
file('<stdin>',fact_real__sgn__eq) ).
fof(c_0_845,axiom,
! [X9,X10] :
( X10 = X9
<=> ( hAPP(c_Complex_ORe,X10) = hAPP(c_Complex_ORe,X9)
& hAPP(c_Complex_OIm,X10) = hAPP(c_Complex_OIm,X9) ) ),
file('<stdin>',fact_expand__complex__eq) ).
fof(c_0_846,axiom,
! [X12,X7] :
( hAPP(c_Complex_ORe,X7) = hAPP(c_Complex_ORe,X12)
=> ( hAPP(c_Complex_OIm,X7) = hAPP(c_Complex_OIm,X12)
=> X7 = X12 ) ),
file('<stdin>',fact_complex__equality) ).
fof(c_0_847,axiom,
! [X12] :
( X12 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('<stdin>',fact_cos__arg__i__mult__zero) ).
fof(c_0_848,axiom,
! [X27,X31] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X27) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X31 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X27 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('<stdin>',fact_nat__mult__eq__1__iff) ).
fof(c_0_849,axiom,
! [X27,X31] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X27)
<=> ( X31 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X27 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('<stdin>',fact_nat__1__eq__mult__iff) ).
fof(c_0_850,axiom,
! [X27,X31] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X27) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('<stdin>',fact_add__is__0) ).
fof(c_0_851,axiom,
! [X29,X30] :
( X30 = X29
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ),
file('<stdin>',fact_eq__imp__le) ).
fof(c_0_852,axiom,
! [X5] :
( class_Power_Opower(X5)
=> c_Power_Opower__class_Opower(X5) = c_Power_Opower_Opower(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Otimes__class_Otimes(X5)) ),
file('<stdin>',fact_power__power__power) ).
fof(c_0_853,axiom,
! [X29,X30] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29) = X30
=> X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_add__eq__self__zero) ).
fof(c_0_854,axiom,
! [X29] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X29) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('<stdin>',fact_power__Suc__0) ).
fof(c_0_855,axiom,
! [X16] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16),X16)),
file('<stdin>',fact_zle__refl) ).
fof(c_0_856,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X29)),
file('<stdin>',fact_le__refl) ).
fof(c_0_857,axiom,
! [X16] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16),X16)),
file('<stdin>',fact_real__le__refl) ).
fof(c_0_858,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_divide__zero__left) ).
fof(c_0_859,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ozero__class_Ozero(X5)),X12) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_divide_Ozero) ).
fof(c_0_860,axiom,
! [X29,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oone__class_Oone(X5)),X29) = c_Groups_Oone__class_Oone(X5) ),
file('<stdin>',fact_power__one) ).
fof(c_0_861,axiom,
! [X4,X5] :
( class_Rings_Omult__zero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_mult__zero__left) ).
fof(c_0_862,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X12) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_mult__left_Ozero) ).
fof(c_0_863,axiom,
! [X11,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X11) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_mult_Ozero__left) ).
fof(c_0_864,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(c_0_865,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
file('<stdin>',fact_mult__1) ).
fof(c_0_866,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
file('<stdin>',fact_mult__1__left) ).
fof(c_0_867,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(c_0_868,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = X4 ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(c_0_869,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = X4 ),
file('<stdin>',fact_add__0) ).
fof(c_0_870,axiom,
! [X4,X5] :
( class_Groups_Omonoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = X4 ),
file('<stdin>',fact_add__0__left) ).
fof(c_0_871,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> ( ( X4 = c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X4) = c_Groups_Ozero__class_Ozero(X5) )
& ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X4) = c_Groups_Oone__class_Oone(X5) ) ) ),
file('<stdin>',fact_divide__self__if) ).
fof(c_0_872,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Odiv(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_div__by__0) ).
fof(c_0_873,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Odiv(X5,c_Groups_Ozero__class_Ozero(X5),X4) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_div__0) ).
fof(c_0_874,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,X4,X4) = c_Groups_Oone__class_Oone(X5) ) ),
file('<stdin>',fact_div__self) ).
fof(c_0_875,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_divide__zero) ).
fof(c_0_876,axiom,
! [X4,X5] :
( class_Rings_Omult__zero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_mult__zero__right) ).
fof(c_0_877,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_mult__right_Ozero) ).
fof(c_0_878,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_mult_Ozero__right) ).
fof(c_0_879,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(c_0_880,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X4) = c_Groups_Oone__class_Oone(X5) ) ),
file('<stdin>',fact_divide__self) ).
fof(c_0_881,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Odiv(X5,X4,c_Groups_Oone__class_Oone(X5)) = X4 ),
file('<stdin>',fact_div__by__1) ).
fof(c_0_882,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('<stdin>',fact_diff__0__right) ).
fof(c_0_883,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('<stdin>',fact_divide__1) ).
fof(c_0_884,axiom,
! [X4,X5] :
( class_Power_Opower(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5) ),
file('<stdin>',fact_power__0) ).
fof(c_0_885,axiom,
! [X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5) ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(c_0_886,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('<stdin>',fact_mult_Ocomm__neutral) ).
fof(c_0_887,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('<stdin>',fact_mult__1__right) ).
fof(c_0_888,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(c_0_889,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(c_0_890,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('<stdin>',fact_add_Ocomm__neutral) ).
fof(c_0_891,axiom,
! [X4,X5] :
( class_Groups_Omonoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('<stdin>',fact_add__0__right) ).
fof(c_0_892,axiom,
! [X30] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X30,
file('<stdin>',fact_div__1) ).
fof(c_0_893,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X4,X4) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_diff__self) ).
fof(c_0_894,axiom,
! [X4] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X4),c_Transcendental_Osin(X4))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('<stdin>',fact_cmod__unit__one) ).
fof(c_0_895,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4 ),
file('<stdin>',fact_power__one__right) ).
fof(c_0_896,axiom,
! [X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X7 ),
file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(c_0_897,axiom,
! [X29] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X29),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X29,
file('<stdin>',fact_diff__Suc__1) ).
fof(c_0_898,axiom,
! [X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Osgn__class_Osgn(X5,c_Groups_Osgn__class_Osgn(X5,X4)) = c_Groups_Osgn__class_Osgn(X5,X4) ),
file('<stdin>',fact_sgn__sgn) ).
fof(c_0_899,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Oabs__class_Oabs(X5,X4)) = c_Groups_Oabs__class_Oabs(X5,X4) ),
file('<stdin>',fact_abs__idempotent) ).
fof(c_0_900,axiom,
! [X14] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X14),hAPP(c_Complex_OIm,X14)) = X14,
file('<stdin>',fact_complex__surj) ).
fof(c_0_901,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4)) = c_RealVector_Onorm__class_Onorm(X5,X4) ),
file('<stdin>',fact_abs__norm__cancel) ).
fof(c_0_902,axiom,
! [X4] :
( X4 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X4) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('<stdin>',fact_zdiv__self) ).
fof(c_0_903,axiom,
! [X11] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('<stdin>',fact_zdiv__zero) ).
fof(c_0_904,axiom,
! [X29] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_diff__0__eq__0) ).
fof(c_0_905,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( ( X7 = c_Groups_Ozero__class_Ozero(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Osgn__class_Osgn(X5,X7)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X7 != c_Groups_Ozero__class_Ozero(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Osgn__class_Osgn(X5,X7)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
file('<stdin>',fact_norm__sgn) ).
fof(c_0_906,axiom,
! [X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X30,
file('<stdin>',fact_minus__nat_Odiff__0) ).
fof(c_0_907,axiom,
! [X29] : c_Nat_OSuc(X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X29),
file('<stdin>',fact_Suc__eq__plus1__left) ).
fof(c_0_908,axiom,
! [X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_diff__self__eq__0) ).
fof(c_0_909,axiom,
! [X29] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_mult__0) ).
fof(c_0_910,axiom,
! [X25] :
( c_SEQ_OBseq(tc_RealDef_Oreal,X25)
=> ( c_SEQ_Omonoseq(tc_RealDef_Oreal,X25)
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,X25) ) ),
file('<stdin>',fact_Bseq__monoseq__convergent) ).
fof(c_0_911,axiom,
! [X29] : c_Nat_OSuc(X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('<stdin>',fact_Suc__eq__plus1) ).
fof(c_0_912,axiom,
! [X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14) = X14,
file('<stdin>',fact_zadd__0) ).
fof(c_0_913,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14) = X14,
file('<stdin>',fact_zmult__1) ).
fof(c_0_914,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X14) = X14,
file('<stdin>',fact_real__mult__1) ).
fof(c_0_915,axiom,
! [X29] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X29) = X29,
file('<stdin>',fact_nat__mult__1) ).
fof(c_0_916,axiom,
! [X29] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29) = X29,
file('<stdin>',fact_plus__nat_Oadd__0) ).
fof(c_0_917,axiom,
! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),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_918,axiom,
! [X4,X23] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X23,X4)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23),
file('<stdin>',fact_complex__mod__rcis) ).
fof(c_0_919,axiom,
! [X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X14,
file('<stdin>',fact_zadd__0__right) ).
fof(c_0_920,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X14,
file('<stdin>',fact_zmult__1__right) ).
fof(c_0_921,axiom,
! [X29] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X29,
file('<stdin>',fact_nat__mult__1__right) ).
fof(c_0_922,axiom,
! [X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X30,
file('<stdin>',fact_Nat_Oadd__0__right) ).
fof(c_0_923,axiom,
! [X7] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X7)) = c_RealDef_Oreal(tc_Nat_Onat,X7),
file('<stdin>',fact_abs__real__of__nat__cancel) ).
fof(c_0_924,axiom,
! [X93,X94,X95,X96] :
( c_Complex_Ocomplex_OComplex(X96,X95) = c_Complex_Ocomplex_OComplex(X94,X93)
<=> ( X96 = X94
& X95 = X93 ) ),
file('<stdin>',fact_complex_Oinject) ).
fof(c_0_925,axiom,
! [X43,X5] :
( class_Groups_Ozero(X5)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X5,X43) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X43 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ),
file('<stdin>',fact_psize__eq__0__iff) ).
fof(c_0_926,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Odecseq(X5,X25)
=> c_SEQ_Omonoseq(X5,X25) ) ),
file('<stdin>',fact_decseq__imp__monoseq) ).
fof(c_0_927,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Oincseq(X5,X25)
=> c_SEQ_Omonoseq(X5,X25) ) ),
file('<stdin>',fact_incseq__imp__monoseq) ).
fof(c_0_928,axiom,
! [X31,X27] :
( c_RealDef_Oreal(tc_Nat_Onat,X27) = c_RealDef_Oreal(tc_Nat_Onat,X31)
<=> X27 = X31 ),
file('<stdin>',fact_real__of__nat__inject) ).
fof(c_0_929,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Groups_Osgn__class_Osgn(X5,X10) = c_Groups_Ozero__class_Ozero(X5)
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_sgn__zero__iff) ).
fof(c_0_930,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Groups_Osgn__class_Osgn(X5,X6) = c_Groups_Ozero__class_Ozero(X5)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_sgn__0__0) ).
fof(c_0_931,axiom,
! [X6,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Groups_Oabs__class_Oabs(X5,X6) = c_Groups_Ozero__class_Ozero(X5)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_abs__eq__0) ).
fof(c_0_932,axiom,
! [X99,X100] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X100,X99)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_complex_Osize_I2_J) ).
fof(c_0_933,axiom,
! [X12,X7] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X7,X12)) = X7,
file('<stdin>',fact_Re) ).
fof(c_0_934,axiom,
! [X12,X7] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X7,X12)) = X12,
file('<stdin>',fact_Im) ).
fof(c_0_935,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_RealVector_Onorm__class_Onorm(X5,X10) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_norm__eq__zero) ).
fof(c_0_936,axiom,
! [X104,X103] :
( class_Orderings_Oord(X103)
=> class_Orderings_Oord(tc_fun(X104,X103)) ),
file('<stdin>',arity_fun__Orderings_Oord) ).
fof(c_0_937,axiom,
! [X104,X103] :
( class_Orderings_Oorder(X103)
=> class_Orderings_Oorder(tc_fun(X104,X103)) ),
file('<stdin>',arity_fun__Orderings_Oorder) ).
fof(c_0_938,axiom,
! [X104,X103] :
( class_Orderings_Opreorder(X103)
=> class_Orderings_Opreorder(tc_fun(X104,X103)) ),
file('<stdin>',arity_fun__Orderings_Opreorder) ).
fof(c_0_939,axiom,
! [X99,X100] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(X100,X99)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_complex_Osize_I1_J) ).
fof(c_0_940,axiom,
! [X7] :
( c_Transcendental_Osin(X7) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X7)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('<stdin>',fact_sin__zero__abs__cos__one) ).
fof(c_0_941,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> c_Groups_Osgn__class_Osgn(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(X5) ),
file('<stdin>',fact_sgn__one) ).
fof(c_0_942,axiom,
! [X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Groups_Osgn__class_Osgn(X5,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_sgn__zero) ).
fof(c_0_943,axiom,
! [X5] :
( class_Groups_Osgn__if(X5)
=> c_Groups_Osgn__class_Osgn(X5,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_sgn0) ).
fof(c_0_944,axiom,
! [X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(X5) ),
file('<stdin>',fact_abs__one) ).
fof(c_0_945,axiom,
! [X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_abs__zero) ).
fof(c_0_946,axiom,
! [X27] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X27)),
file('<stdin>',fact_less__eq__Suc__le__raw) ).
fof(c_0_947,axiom,
! [X4] : c_Complex_Ocis(X4) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X4),c_Transcendental_Osin(X4)),
file('<stdin>',fact_cis__def) ).
fof(c_0_948,axiom,
! [X22,X6] :
( c_Complex_Ocomplex_OComplex(X6,X22) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
<=> ( X6 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
& X22 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('<stdin>',fact_Complex__eq__1) ).
fof(c_0_949,axiom,
! [X22,X6] :
( c_Complex_Ocomplex_OComplex(X6,X22) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
<=> ( X6 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X22 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('<stdin>',fact_Complex__eq__0) ).
fof(c_0_950,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('<stdin>',fact_norm__one) ).
fof(c_0_951,axiom,
! [X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('<stdin>',fact_norm__zero) ).
fof(c_0_952,axiom,
! [X29] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X29)) = X29,
file('<stdin>',fact_natceiling__real__of__nat) ).
fof(c_0_953,axiom,
! [X29] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X29)) = X29,
file('<stdin>',fact_natfloor__real__of__nat) ).
fof(c_0_954,axiom,
! [X27] :
( c_RealDef_Oreal(tc_Nat_Onat,X27) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('<stdin>',fact_real__of__nat__zero__iff) ).
fof(c_0_955,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('<stdin>',fact_real__of__nat__one) ).
fof(c_0_956,axiom,
! [X9,X10] :
( c_Complex_Ocomplex_OComplex(X10,X9) = c_Complex_Oii
<=> ( X10 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X9 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
file('<stdin>',fact_Complex__eq__i) ).
fof(c_0_957,axiom,
! [X23] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X23) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23),
file('<stdin>',fact_real__norm__def) ).
fof(c_0_958,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('<stdin>',fact_complex__one__def) ).
fof(c_0_959,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('<stdin>',fact_complex__zero__def) ).
fof(c_0_960,axiom,
! [X4] : hAPP(c_Complex_ORe,c_Complex_Ocis(X4)) = c_Transcendental_Ocos(X4),
file('<stdin>',fact_Re__cis) ).
fof(c_0_961,axiom,
! [X4] : hAPP(c_Complex_OIm,c_Complex_Ocis(X4)) = c_Transcendental_Osin(X4),
file('<stdin>',fact_Im__cis) ).
fof(c_0_962,axiom,
! [X4] : c_Complex_Ocis(X4) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4),
file('<stdin>',fact_cis__rcis__eq) ).
fof(c_0_963,axiom,
! [X10,X5] :
( class_Groups_Oone(X5)
=> ( c_Groups_Oone__class_Oone(X5) = X10
<=> X10 = c_Groups_Oone__class_Oone(X5) ) ),
file('<stdin>',fact_one__reorient) ).
fof(c_0_964,axiom,
! [X10,X5] :
( class_Groups_Ozero(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = X10
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('<stdin>',fact_zero__reorient) ).
fof(c_0_965,axiom,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('<stdin>',fact_i__def) ).
fof(c_0_966,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Oone__class_Oone(X5) != c_Groups_Ozero__class_Ozero(X5) ),
file('<stdin>',fact_one__neq__zero) ).
fof(c_0_967,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Ozero__class_Ozero(X5) != c_Groups_Oone__class_Oone(X5) ),
file('<stdin>',fact_zero__neq__one) ).
fof(c_0_968,axiom,
! [X4] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',fact_rcis__zero__mod) ).
fof(c_0_969,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('<stdin>',fact_real__of__nat__1) ).
fof(c_0_970,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('<stdin>',fact_real__of__nat__zero) ).
fof(c_0_971,axiom,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('<stdin>',fact_complex__Im__one) ).
fof(c_0_972,axiom,
hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('<stdin>',fact_Re_Ozero) ).
fof(c_0_973,axiom,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('<stdin>',fact_complex__Re__one) ).
fof(c_0_974,axiom,
hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('<stdin>',fact_Im_Ozero) ).
fof(c_0_975,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Groups_Oone(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oone) ).
fof(c_0_976,axiom,
! [X103] :
( class_Rings_Ocomm__ring(X103)
=> class_Rings_Oring(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oring) ).
fof(c_0_977,axiom,
! [X103] :
( class_Groups_Ozero(X103)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(c_0_978,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Power_Opower(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Power_Opower) ).
fof(c_0_979,axiom,
! [X103] :
( class_Rings_Ocomm__ring__1(X103)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(c_0_980,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Osgn__if(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Osgn__if) ).
fof(c_0_981,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(c_0_982,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(c_0_983,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(c_0_984,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(c_0_985,axiom,
! [X103] :
( class_Groups_Oab__group__add(X103)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(c_0_986,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(c_0_987,axiom,
! [X103] :
( class_Groups_Ocomm__monoid__add(X103)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(c_0_988,axiom,
! [X103] :
( class_Rings_Ocomm__ring__1(X103)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(c_0_989,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(c_0_990,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(c_0_991,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(c_0_992,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(c_0_993,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(c_0_994,axiom,
! [X103] :
( class_Groups_Oab__group__add(X103)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(c_0_995,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(c_0_996,axiom,
! [X103] :
( class_Fields_Ofield(X103)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(c_0_997,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(c_0_998,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(c_0_999,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(c_0_1000,axiom,
! [X103] :
( class_Groups_Ocomm__monoid__add(X103)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(c_0_1001,axiom,
! [X103] :
( class_Rings_Oidom(X103)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(c_0_1002,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
fof(c_0_1003,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(c_0_1004,axiom,
! [X103] :
( class_Groups_Ocomm__monoid__add(X103)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(c_0_1005,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(c_0_1006,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(c_0_1007,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(c_0_1008,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(c_0_1009,axiom,
! [X103] :
( class_Groups_Ocancel__comm__monoid__add(X103)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(c_0_1010,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(c_0_1011,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(c_0_1012,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(c_0_1013,axiom,
! [X103] :
( class_Rings_Oidom(X103)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(c_0_1014,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(c_0_1015,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(c_0_1016,axiom,
! [X103] :
( class_Rings_Oidom(X103)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(c_0_1017,axiom,
! [X103] :
( class_Groups_Ocancel__comm__monoid__add(X103)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1018,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(c_0_1019,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(c_0_1020,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
fof(c_0_1021,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(c_0_1022,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(c_0_1023,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(c_0_1024,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_1025,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(c_0_1026,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(c_0_1027,axiom,
! [X103] :
( class_Rings_Oidom(X103)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(c_0_1028,axiom,
! [X103] :
( class_Rings_Ocomm__ring(X103)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(c_0_1029,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(c_0_1030,axiom,
! [X103] :
( class_Groups_Ocancel__comm__monoid__add(X103)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(c_0_1031,axiom,
! [X103] :
( class_Rings_Oidom(X103)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X103)) ),
file('<stdin>',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(c_0_1032,axiom,
! [X7] :
( c_Transcendental_Ocos(X7) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
=> c_Transcendental_Osin(X7) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('<stdin>',fact_cos__one__sin__zero) ).
fof(c_0_1033,axiom,
! [X80,X81] :
( c_Nat_OSuc(X81) = c_Nat_OSuc(X80)
<=> X81 = X80 ),
file('<stdin>',fact_nat_Oinject) ).
fof(c_0_1034,axiom,
! [X12,X7] :
( c_Nat_OSuc(X7) = c_Nat_OSuc(X12)
=> X7 = X12 ),
file('<stdin>',fact_Suc__inject) ).
fof(c_0_1035,axiom,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('<stdin>',fact_complex__Im__i) ).
fof(c_0_1036,axiom,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('<stdin>',fact_complex__Re__i) ).
fof(c_0_1037,axiom,
! [X30] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X30),
file('<stdin>',fact_Zero__not__Suc) ).
fof(c_0_1038,axiom,
! [X79] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X79),
file('<stdin>',fact_nat_Osimps_I2_J) ).
fof(c_0_1039,axiom,
! [X30] : c_Nat_OSuc(X30) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_Suc__not__Zero) ).
fof(c_0_1040,axiom,
! [X78] : c_Nat_OSuc(X78) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_nat_Osimps_I3_J) ).
fof(c_0_1041,axiom,
! [X30] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X30),
file('<stdin>',fact_Zero__neq__Suc) ).
fof(c_0_1042,axiom,
! [X30] : c_Nat_OSuc(X30) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_Suc__neq__Zero) ).
fof(c_0_1043,axiom,
c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('<stdin>',fact_ln__one) ).
fof(c_0_1044,axiom,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('<stdin>',fact_sin__zero) ).
fof(c_0_1045,axiom,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('<stdin>',fact_cos__zero) ).
fof(c_0_1046,axiom,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('<stdin>',fact_cis__zero) ).
fof(c_0_1047,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_1048,axiom,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('<stdin>',fact_natceiling__one) ).
fof(c_0_1049,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_natceiling__zero) ).
fof(c_0_1050,axiom,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('<stdin>',fact_natfloor__one) ).
fof(c_0_1051,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('<stdin>',fact_natfloor__zero) ).
fof(c_0_1052,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_1053,axiom,
! [X29] : X29 != c_Nat_OSuc(X29),
file('<stdin>',fact_n__not__Suc__n) ).
fof(c_0_1054,axiom,
! [X29] : c_Nat_OSuc(X29) != X29,
file('<stdin>',fact_Suc__n__not__n) ).
fof(c_0_1055,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_1056,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_1057,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('<stdin>',fact_complex__i__not__one) ).
fof(c_0_1058,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',fact_complex__i__not__zero) ).
fof(c_0_1059,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Oone) ).
fof(c_0_1060,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Oring) ).
fof(c_0_1061,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(c_0_1062,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Power_Opower) ).
fof(c_0_1063,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(c_0_1064,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(c_0_1065,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(c_0_1066,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(c_0_1067,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(c_0_1068,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(c_0_1069,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(c_0_1070,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(c_0_1071,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(c_0_1072,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(c_0_1073,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(c_0_1074,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(c_0_1075,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(c_0_1076,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(c_0_1077,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(c_0_1078,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(c_0_1079,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(c_0_1080,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(c_0_1081,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(c_0_1082,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Ometric__space) ).
fof(c_0_1083,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(c_0_1084,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(c_0_1085,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(c_0_1086,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(c_0_1087,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(c_0_1088,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(c_0_1089,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_1090,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1091,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(c_0_1092,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(c_0_1093,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(c_0_1094,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(c_0_1095,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_1096,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oone) ).
fof(c_0_1097,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oring) ).
fof(c_0_1098,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ozero) ).
fof(c_0_1099,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Power_Opower) ).
fof(c_0_1100,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Fields_Ofield) ).
fof(c_0_1101,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(c_0_1102,axiom,
class_Groups_Osgn__if(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Osgn__if) ).
fof(c_0_1103,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Orderings_Oord) ).
fof(c_0_1104,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(c_0_1105,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Orderings_Oorder) ).
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_RealVector_Oreal__field(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__field) ).
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__ring__abs(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
fof(c_0_1126,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(c_0_1127,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(c_0_1128,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(c_0_1129,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(c_0_1130,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Ometric__space) ).
fof(c_0_1131,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(c_0_1132,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(c_0_1133,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(c_0_1134,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(c_0_1135,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(c_0_1136,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(c_0_1137,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(c_0_1138,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(c_0_1139,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(c_0_1140,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(c_0_1141,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(c_0_1142,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(c_0_1143,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(c_0_1144,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_1145,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1146,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(c_0_1147,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(c_0_1148,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(c_0_1149,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(c_0_1150,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(c_0_1151,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(c_0_1152,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(c_0_1153,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(c_0_1154,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(c_0_1155,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(c_0_1156,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(c_0_1157,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_1158,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_1159,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_1160,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_1161,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('<stdin>',arity_HOL__Obool__Orderings_Oord) ).
fof(c_0_1162,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('<stdin>',arity_HOL__Obool__Orderings_Oorder) ).
fof(c_0_1163,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('<stdin>',arity_HOL__Obool__Orderings_Opreorder) ).
fof(c_0_1164,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oone) ).
fof(c_0_1165,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ozero) ).
fof(c_0_1166,axiom,
class_Power_Opower(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Power_Opower) ).
fof(c_0_1167,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Orderings_Oord) ).
fof(c_0_1168,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Osemiring) ).
fof(c_0_1169,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Orderings_Oorder) ).
fof(c_0_1170,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Omult__zero) ).
fof(c_0_1171,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(c_0_1172,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(c_0_1173,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(c_0_1174,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Orderings_Olinorder) ).
fof(c_0_1175,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Orderings_Opreorder) ).
fof(c_0_1176,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(c_0_1177,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(c_0_1178,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(c_0_1179,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(c_0_1180,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(c_0_1181,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(c_0_1182,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(c_0_1183,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(c_0_1184,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(c_0_1185,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(c_0_1186,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(c_0_1187,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(c_0_1188,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(c_0_1189,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(c_0_1190,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(c_0_1191,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1192,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(c_0_1193,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(c_0_1194,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(c_0_1195,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_1196,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_1197,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_1198,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_1199,axiom,
class_Groups_Oone(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oone) ).
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_Groups_Osgn__if(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Osgn__if) ).
fof(c_0_1205,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Orderings_Oord) ).
fof(c_0_1206,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Osemiring) ).
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_Omult__zero(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Omult__zero) ).
fof(c_0_1209,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ogroup__add) ).
fof(c_0_1210,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Osemiring__0) ).
fof(c_0_1211,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Omonoid__add) ).
fof(c_0_1212,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(c_0_1213,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(c_0_1214,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Orderings_Olinorder) ).
fof(c_0_1215,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Orderings_Opreorder) ).
fof(c_0_1216,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oordered__ring) ).
fof(c_0_1217,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(c_0_1218,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oab__group__add) ).
fof(c_0_1219,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(c_0_1220,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Divides_Osemiring__div) ).
fof(c_0_1221,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(c_0_1222,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(c_0_1223,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(c_0_1224,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(c_0_1225,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(c_0_1226,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(c_0_1227,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(c_0_1228,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(c_0_1229,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(c_0_1230,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(c_0_1231,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(c_0_1232,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(c_0_1233,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(c_0_1234,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(c_0_1235,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(c_0_1236,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(c_0_1237,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(c_0_1238,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(c_0_1239,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(c_0_1240,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_1241,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1242,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(c_0_1243,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(c_0_1244,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
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_Rings_Ocomm__ring(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(c_0_1253,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(c_0_1254,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(c_0_1255,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('<stdin>',arity_Int__Oint__Rings_Oidom) ).
fof(c_0_1256,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(c_0_1257,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('<stdin>',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(c_0_1258,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(c_0_1259,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
fof(c_0_1260,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
fof(c_0_1261,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('<stdin>',arity_RealDef__Oreal__Rings_Oidom) ).
fof(c_0_1262,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(c_0_1263,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(c_0_1264,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(c_0_1265,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('<stdin>',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(c_0_1266,axiom,
c_SEQ_Osubseq(v_ga____),
file('<stdin>',fact_g_I1_J) ).
fof(c_0_1267,axiom,
c_SEQ_Osubseq(v_f____),
file('<stdin>',fact_f_I1_J) ).
fof(c_0_1268,plain,
! [X27,X33,X35] :
( epred1_3(X35,X33,X27)
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
=> ! [X42] :
( ? [X82] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X82))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X82),X33))
& X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X82) )
=> hBOOL(hAPP(X35,X42)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X42] :
( ? [X82] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X33),X82))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X82),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X82) )
=> hBOOL(hAPP(X35,X42)) ) ) ) ),
introduced(definition) ).
fof(c_0_1269,axiom,
! [X14,X7,X26] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X14))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26))),X14)) ),
c_0_0 ).
fof(c_0_1270,axiom,
! [X25,X89,X5,X13] :
( ( class_RealVector_Oreal__normed__vector(X13)
& class_Orderings_Oord(X5) )
=> ( ! [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X89),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,c_Groups_Ominus__class_Ominus(X13,hAPP(X25,X89),hAPP(X25,X8)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
=> ! [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X89),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X8))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X89))))) ) ) ),
c_0_1 ).
fof(c_0_1271,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X22)),X85)),X21)),X52)) ) ),
c_0_2 ).
fof(c_0_1272,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X22)),X85)),X21)),X52)) ) ),
c_0_3 ).
fof(c_0_1273,axiom,
! [X7,X14,X26] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X14))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26)))) ),
c_0_4 ).
fof(c_0_1274,plain,
~ ! [X28] :
( c_SEQ_Osubseq(X28)
=> ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,X28)))) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_1275,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
c_0_6 ).
fof(c_0_1276,axiom,
! [X27,X31,X88,X83,X84] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X84),X83))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X83,X84)),X88)),X31)),X27)) ) ),
c_0_7 ).
fof(c_0_1277,axiom,
! [X27,X31,X88,X83,X84] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X84),X83))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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,X83,X84)),X88)),X31)),X27)) ) ),
c_0_8 ).
fof(c_0_1278,axiom,
! [X40,X25,X41,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( ! [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),X40)) )
=> c_SEQ_OBseq(X5,X25) ) ),
c_0_9 ).
fof(c_0_1279,axiom,
! [X33,X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat,X25,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33)))
=> c_SEQ_OBseq(X5,X25) ) ),
c_0_10 ).
fof(c_0_1280,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X22,X6)),X85)),X52))) ) ),
c_0_11 ).
fof(c_0_1281,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X22,X6)),X85)),X52))) ) ),
c_0_12 ).
fof(c_0_1282,axiom,
! [X1,X2,X5,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X13),X2),X1))
<=> ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(X2,X3)),hAPP(X1,X3))) ) ),
c_0_13 ).
fof(c_0_1283,axiom,
! [X27,X31,X88,X84,X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83),X84))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),hAPP(hAPP(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,X84,X83)),X88)),X27))) ) ),
c_0_14 ).
fof(c_0_1284,axiom,
! [X27,X31,X88,X84,X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83),X84))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),hAPP(hAPP(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,X84,X83)),X88)),X27))) ) ),
c_0_15 ).
fof(c_0_1285,axiom,
! [X22,X6,X2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X2,X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X2,X22),hAPP(X2,X6))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X22,X6))),X6)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X2,X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X2,X22),hAPP(X2,X6))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X22,X6))),X22)),
c_0_16 ).
fof(c_0_1286,axiom,
! [X11,X4,X12,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X7,X4)),c_Groups_Ominus__class_Ominus(X5,X12,X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X7,X4)),X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ominus__class_Ominus(X5,X12,X11))) ),
c_0_17 ).
fof(c_0_1287,axiom,
! [X29,X11] :
( X11 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X66] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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),X11),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X66),X29))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
c_0_18 ).
fof(c_0_1288,axiom,
! [X38,X25,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ( c_SEQ_Oconvergent(X5,X25)
=> ( c_SEQ_Oconvergent(X5,X38)
=> c_SEQ_Oconvergent(X5,c_COMBS(tc_Nat_Onat,X5,X5,c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X5),X25),X38)) ) ) ),
c_0_19 ).
fof(c_0_1289,axiom,
! [X38,X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_Oconvergent(X5,X25)
=> ( c_SEQ_Oconvergent(X5,X38)
=> c_SEQ_Oconvergent(X5,c_COMBS(tc_Nat_Onat,X5,X5,c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(X5),X25),X38)) ) ) ),
c_0_20 ).
fof(c_0_1290,axiom,
! [X26,X15,X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X26)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X4,X15))),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X11,X26))))) ),
c_0_21 ).
fof(c_0_1291,axiom,
! [X9,X25,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_SEQ_Oconvergent(X5,X25)
=> c_SEQ_Oconvergent(X5,c_COMBC(tc_Nat_Onat,X5,X5,c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(X5),X25),X9)) ) ),
c_0_22 ).
fof(c_0_1292,axiom,
! [X9,X25,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ( c_SEQ_Oconvergent(X5,X25)
=> c_SEQ_Oconvergent(X5,c_COMBC(tc_Nat_Onat,X5,X5,c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X5),X25),X9)) ) ),
c_0_23 ).
fof(c_0_1293,axiom,
! [X26,X15,X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X26)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X15))),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X11,X26))))) ),
c_0_24 ).
fof(c_0_1294,axiom,
! [X33,X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X25)
=> c_SEQ_OBseq(X5,c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat,X25,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33))) ) ),
c_0_25 ).
fof(c_0_1295,axiom,
c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
c_0_26 ).
fof(c_0_1296,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
c_0_27 ).
fof(c_0_1297,axiom,
! [X12,X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X7,X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X7),hAPP(c_Complex_ORe,X12)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X7),hAPP(c_Complex_OIm,X12)))))),
c_0_28 ).
fof(c_0_1298,axiom,
! [X102,X26,X15,X11,X4,X5] :
( class_RealVector_Oreal__field(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X26))),X102) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ominus__class_Ominus(X5,X11,X26)),X102))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ominus__class_Ominus(X5,X4,X15)),X102)),X26)) ),
c_0_29 ).
fof(c_0_1299,axiom,
! [X23,X49,X67,X68,X11] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X68)),X67)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X49)),X23)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X67))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X67),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X23),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68),X49)) ) ) ) ),
c_0_30 ).
fof(c_0_1300,axiom,
! [X23,X49,X67,X68,X11] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X68)),X67)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X49)),X23)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X11),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X11),X67))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49),X68)) ) ) ) ),
c_0_31 ).
fof(c_0_1301,axiom,
! [X9,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X9))),c_Groups_Ozero__class_Ozero(X5)))
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
& X9 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
c_0_32 ).
fof(c_0_1302,plain,
! [X12,X7,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X12))),c_Groups_Ozero__class_Ozero(X5))) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_1303,axiom,
! [X29,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X7)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X29))) ),
c_0_34 ).
fof(c_0_1304,axiom,
! [X67,X68,X58,X23,X49,X11] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X49)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X23),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X67))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68),X49)) ) ) ) ) ) ),
c_0_35 ).
fof(c_0_1305,axiom,
! [X7,X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_RealDef_Oreal(tc_Nat_Onat,X7)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X29,X7)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
c_0_36 ).
fof(c_0_1306,axiom,
! [X25,X13] :
( class_RealVector_Oreal__normed__vector(X13)
=> ( ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X8))),X37)) )
<=> ? [X77] :
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X8))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X77)))) ) ),
c_0_37 ).
fof(c_0_1307,axiom,
! [X25,X13] :
( class_RealVector_Oreal__normed__vector(X13)
=> ( ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X8))),X37)) )
<=> ? [X77] :
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,hAPP(X25,X8))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X77)))) ) ),
c_0_38 ).
fof(c_0_1308,axiom,
! [X14] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X14),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X14),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
c_0_39 ).
fof(c_0_1309,axiom,
! [X44,X45,X12,X4,X7,X5] :
( class_Rings_Olinordered__semiring__1(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X45))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X44))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X45),X44) = c_Groups_Oone__class_Oone(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X45),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X44),X12))),X4)) ) ) ) ) ) ),
c_0_40 ).
fof(c_0_1310,axiom,
! [X44,X45,X12,X4,X7,X5] :
( class_Rings_Olinordered__semiring__1__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X45))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X44))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X45),X44) = c_Groups_Oone__class_Oone(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X45),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X44),X12))),X4)) ) ) ) ) ) ),
c_0_41 ).
fof(c_0_1311,axiom,
! [X25,X40,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X40))
=> ( ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),X40))
=> c_SEQ_OBseq(X5,X25) ) ) ),
c_0_42 ).
fof(c_0_1312,axiom,
! [X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X25)
<=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),X37)) ) ) ),
c_0_43 ).
fof(c_0_1313,axiom,
! [X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X25)
<=> ? [X77] :
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X77)))) ) ),
c_0_44 ).
fof(c_0_1314,axiom,
! [X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X25)
<=> ? [X77] :
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X77)))) ) ),
c_0_45 ).
fof(c_0_1315,axiom,
! [X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X53)),X53)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X53),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_46 ).
fof(c_0_1316,axiom,
! [X67,X68,X58] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X67))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
c_0_47 ).
fof(c_0_1317,axiom,
! [X29,X30,X45,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X45)),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X45)),X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,hAPP(hAPP(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,X19)),X45)),X29)) ),
c_0_48 ).
fof(c_0_1318,axiom,
! [X29,X30,X45,X19,X18] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18),X19))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X45)),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X45)),X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(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,X19,X18)),X45)),X30),X29) ),
c_0_49 ).
fof(c_0_1319,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
! [X71,X72] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X71),X72))),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(X5,X71)),c_RealVector_Onorm__class_Onorm(X5,X72))),X37))) ),
c_0_50 ).
fof(c_0_1320,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X71,X72] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X71),X72))),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(X5,X71)),c_RealVector_Onorm__class_Onorm(X5,X72))),X37))) ) ),
c_0_51 ).
fof(c_0_1321,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X71,X72] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X71),X72))),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(X5,X71)),c_RealVector_Onorm__class_Onorm(X5,X72))),X37))) ) ),
c_0_52 ).
fof(c_0_1322,axiom,
! [X67,X68,X58,X23,X49,X11] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X49)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X67),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49),X68)) ) ) ) ) ) ),
c_0_53 ).
fof(c_0_1323,axiom,
! [X12,X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X7),X12) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_ORe,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_OIm,X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_OIm,X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_ORe,X12)))),
c_0_54 ).
fof(c_0_1324,axiom,
! [X10,X25,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ( c_SEQ_Oconvergent(X5,X25)
=> c_SEQ_Oconvergent(X5,c_COMBB(X5,X5,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X25)) ) ),
c_0_55 ).
fof(c_0_1325,axiom,
! [X107,X108,X35,X5,X109,X13] : hAPP(c_COMBS(X13,X109,X5,X35,X108),X107) = hAPP(hAPP(X35,X107),hAPP(X108,X107)),
c_0_56 ).
fof(c_0_1326,axiom,
! [X107,X108,X35,X5,X109,X13] : hAPP(c_COMBC(X13,X109,X5,X35,X108),X107) = hAPP(hAPP(X35,X107),X108),
c_0_57 ).
fof(c_0_1327,axiom,
! [X107,X108,X35,X109,X5,X13] : hAPP(c_COMBB(X13,X5,X109,X35,X108),X107) = hAPP(X35,hAPP(X108,X107)),
c_0_58 ).
fof(c_0_1328,axiom,
! [X9,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X9))))
<=> ( X10 != c_Groups_Ozero__class_Ozero(X5)
| X9 != c_Groups_Ozero__class_Ozero(X5) ) ) ),
c_0_59 ).
fof(c_0_1329,axiom,
! [X25] :
( c_SEQ_Oconvergent(tc_Complex_Ocomplex,X25)
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,X25)) ),
c_0_60 ).
fof(c_0_1330,axiom,
! [X25] :
( c_SEQ_Oconvergent(tc_Complex_Ocomplex,X25)
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,X25)) ),
c_0_61 ).
fof(c_0_1331,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oabs__class_Oabs(X5,X4),c_Groups_Oabs__class_Oabs(X5,X11)))),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)))) ),
c_0_62 ).
fof(c_0_1332,axiom,
! [X4,X11] : hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X11),X4)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X11))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4))),
c_0_63 ).
fof(c_0_1333,axiom,
! [X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X11)))),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)))) ),
c_0_64 ).
fof(c_0_1334,axiom,
! [X86,X6,X10,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X10,X6))),X86))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ominus__class_Ominus(X5,X6,X86)),X10))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X86))) ) ) ),
c_0_65 ).
fof(c_0_1335,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oring(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)
<=> X21 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X22,X6)),X85)),X52) ) ),
c_0_66 ).
fof(c_0_1336,axiom,
! [X52,X22,X21,X85,X6,X5] :
( class_Rings_Oring(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X85)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X85)),X52)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X22)),X85)),X21) = X52 ) ),
c_0_67 ).
fof(c_0_1337,axiom,
! [X27,X31,X88,X84,X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83),X84))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)
<=> X31 = hAPP(hAPP(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,X84,X83)),X88)),X27) ) ),
c_0_68 ).
fof(c_0_1338,axiom,
! [X27,X31,X88,X83,X84] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X84),X83))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X88)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X88)),X27)
<=> hAPP(hAPP(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,X83,X84)),X88)),X31) = X27 ) ),
c_0_69 ).
fof(c_0_1339,axiom,
! [X11,X7,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),X11))
=> ? [X87] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X87))
& ! [X73] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X73))),X87))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),X73))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X73),X11)) ) ) ) ) ),
c_0_70 ).
fof(c_0_1340,axiom,
! [X7,X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_RealDef_Oreal(tc_Nat_Onat,X7)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X29,X7))))),
c_0_71 ).
fof(c_0_1341,axiom,
! [X14,X16] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X16)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X16),X14))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14)))),
c_0_72 ).
fof(c_0_1342,axiom,
! [X7,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ? [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X8)),X12)),X7))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X8))),X12))) ) ) ),
c_0_73 ).
fof(c_0_1343,axiom,
! [X26,X11,X15,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,X4)),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,X11)),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X26))) ) ) ),
c_0_74 ).
fof(c_0_1344,axiom,
! [X67,X68,X58] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X68)),X67)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X67),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X68)) ) ) ),
c_0_75 ).
fof(c_0_1345,axiom,
! [X15,X11,X59,X4,X5] :
( class_Rings_Osemiring(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X59)),X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X59)),X15) ),
c_0_76 ).
fof(c_0_1346,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ) ),
c_0_77 ).
fof(c_0_1347,axiom,
! [X24,X12,X23,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X7)),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X12)),X24))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X24))) ) ) ),
c_0_78 ).
fof(c_0_1348,axiom,
! [X24,X12,X23,X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X7)),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X12)),X24))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X23),X24))) ) ) ),
c_0_79 ).
fof(c_0_1349,axiom,
! [X27,X31,X35] :
( hBOOL(hAPP(X35,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X27)))
<=> ( ( X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X98] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X98)),X31))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),c_Nat_OSuc(X98))))
& hBOOL(hAPP(X35,X98)) ) ) ),
c_0_80 ).
fof(c_0_1350,axiom,
! [X17,X18,X45,X19] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X45)),X17)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X18)),X45)),X17),
c_0_81 ).
fof(c_0_1351,plain,
! [X27,X33,X35] :
( epred1_3(X35,X33,X27)
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
=> ! [X42] :
( ? [X82] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X82))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X82),X33))
& X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X82) )
=> hBOOL(hAPP(X35,X42)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X42] :
( ? [X82] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X33),X82))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X82),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X82) )
=> hBOOL(hAPP(X35,X42)) ) ) ) ),
c_0_1268 ).
fof(c_0_1352,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11)))) ),
c_0_82 ).
fof(c_0_1353,axiom,
! [X12,X7,X5] :
( class_Rings_Olinordered__ring(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X12)))) ),
c_0_83 ).
fof(c_0_1354,axiom,
! [X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)),c_RealVector_Onorm__class_Onorm(X5,X11)))) ),
c_0_84 ).
fof(c_0_1355,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11)))) ),
c_0_85 ).
fof(c_0_1356,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ),
c_0_86 ).
fof(c_0_1357,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ),
c_0_87 ).
fof(c_0_1358,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ) ),
c_0_88 ).
fof(c_0_1359,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ) ),
c_0_89 ).
fof(c_0_1360,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ) ),
c_0_90 ).
fof(c_0_1361,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X37))) ) ),
c_0_91 ).
fof(c_0_1362,axiom,
! [X12,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),c_RealVector_Onorm__class_Onorm(X5,X12)))) ),
c_0_92 ).
fof(c_0_1363,axiom,
! [X12,X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),c_RealVector_Onorm__class_Onorm(X5,X12)))) ),
c_0_93 ).
fof(c_0_1364,axiom,
! [X15,X4,X11,X5] :
( class_Fields_Olinordered__field(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X15),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X15),X11))) ) ) ) ),
c_0_94 ).
fof(c_0_1365,axiom,
! [X11,X4,X12,X7,X5] :
( class_Rings_Oring(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),c_Groups_Ominus__class_Ominus(X5,X12,X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X7,X4)),X11)) ),
c_0_95 ).
fof(c_0_1366,axiom,
! [X15,X11,X4,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X15),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X15),X11))) ) ) ) ),
c_0_96 ).
fof(c_0_1367,axiom,
! [X11,X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_Nat_OSuc(X29))))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ) ),
c_0_97 ).
fof(c_0_1368,axiom,
! [X7,X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X29,X7))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_RealDef_Oreal(tc_Nat_Onat,X7)))),
c_0_98 ).
fof(c_0_1369,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X27)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X31))) ),
c_0_99 ).
fof(c_0_1370,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X27))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X33)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X33)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ) ) ),
c_0_100 ).
fof(c_0_1371,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X27))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X33)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X33)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ) ) ),
c_0_101 ).
fof(c_0_1372,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oabs__class_Oabs(X5,X4),c_Groups_Oabs__class_Oabs(X5,X11))),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)))) ),
c_0_102 ).
fof(c_0_1373,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oabs__class_Oabs(X5,X4),c_Groups_Oabs__class_Oabs(X5,X11))),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X11,X4)))) ),
c_0_103 ).
fof(c_0_1374,axiom,
! [X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X11))),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)))) ),
c_0_104 ).
fof(c_0_1375,axiom,
! [X29,X7,X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X29))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),X29))) ),
c_0_105 ).
fof(c_0_1376,axiom,
! [X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X11))),c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)))) ),
c_0_106 ).
fof(c_0_1377,axiom,
! [X11,X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
c_0_107 ).
fof(c_0_1378,axiom,
! [X11,X4,X15,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ) ),
c_0_108 ).
fof(c_0_1379,axiom,
! [X11,X15,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ) ),
c_0_109 ).
fof(c_0_1380,axiom,
! [X11,X4,X15,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
c_0_110 ).
fof(c_0_1381,axiom,
! [X11,X4,X15,X5] :
( class_Rings_Olinordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
c_0_111 ).
fof(c_0_1382,axiom,
! [X11,X15,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
c_0_112 ).
fof(c_0_1383,axiom,
! [X11,X15,X4,X5] :
( class_Rings_Olinordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
c_0_113 ).
fof(c_0_1384,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X21))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),X22)) ) ) ),
c_0_114 ).
fof(c_0_1385,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X21))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22)) ) ) ),
c_0_115 ).
fof(c_0_1386,axiom,
! [X9,X10,X22,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X22))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X22),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X22),X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10),X9)) ) ) ),
c_0_116 ).
fof(c_0_1387,axiom,
! [X29,X30,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ) ) ),
c_0_117 ).
fof(c_0_1388,axiom,
! [X29,X30,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ) ) ),
c_0_118 ).
fof(c_0_1389,axiom,
! [X9,X10,X22,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X22))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X22),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X22),X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10),X9)) ) ) ),
c_0_119 ).
fof(c_0_1390,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X22),X6)) ) ) ),
c_0_120 ).
fof(c_0_1391,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X22),X6)) ) ) ),
c_0_121 ).
fof(c_0_1392,axiom,
! [X31,X97,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27))
=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X97)),X31))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),c_Nat_OSuc(X97)))) )
<=> X97 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X27) ) ),
c_0_122 ).
fof(c_0_1393,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X22)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X21))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22)) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X22),X6)) ) ) ) ),
c_0_123 ).
fof(c_0_1394,axiom,
! [X22,X21,X6,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X21)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X21))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22)) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X22),X6)) ) ) ) ),
c_0_124 ).
fof(c_0_1395,plain,
! [X7] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X7)),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_1396,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
c_0_126 ).
fof(c_0_1397,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
c_0_127 ).
fof(c_0_1398,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
c_0_128 ).
fof(c_0_1399,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
c_0_129 ).
fof(c_0_1400,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
c_0_130 ).
fof(c_0_1401,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X26))) ) ) ) ) ),
c_0_131 ).
fof(c_0_1402,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Omonoseq(X5,X25)
<=> ( ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,X8)),hAPP(X25,c_Nat_OSuc(X8))))
| ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,c_Nat_OSuc(X8))),hAPP(X25,X8))) ) ) ),
c_0_132 ).
fof(c_0_1403,axiom,
! [X23] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X23))
=> ? [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X8,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X23))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23),c_RealDef_Oreal(tc_Nat_Onat,X8))) ) ),
c_0_133 ).
fof(c_0_1404,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)))) ) ),
c_0_134 ).
fof(c_0_1405,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ),
c_0_135 ).
fof(c_0_1406,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ),
c_0_136 ).
fof(c_0_1407,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X4)),c_RComplete_Onatfloor(X11))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X11)))) ) ),
c_0_137 ).
fof(c_0_1408,axiom,
! [X26,X15,X11,X4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X4,X11)),c_Complex_Ocomplex_OComplex(X15,X26)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X26)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X15))),
c_0_138 ).
fof(c_0_1409,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ) ),
c_0_139 ).
fof(c_0_1410,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ) ),
c_0_140 ).
fof(c_0_1411,axiom,
! [X29,X30,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ) ),
c_0_141 ).
fof(c_0_1412,axiom,
! [X27,X33,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X33)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ) ),
c_0_142 ).
fof(c_0_1413,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ) ),
c_0_143 ).
fof(c_0_1414,axiom,
! [X9,X10,X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X53))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X53),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X53),X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9)) ) ),
c_0_144 ).
fof(c_0_1415,axiom,
! [X9,X10,X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X53))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X53)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9)) ) ),
c_0_145 ).
fof(c_0_1416,axiom,
! [X9,X10,X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X53))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X53)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),X9)) ) ),
c_0_146 ).
fof(c_0_1417,axiom,
! [X11,X4,X15,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X11)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ),
c_0_147 ).
fof(c_0_1418,axiom,
! [X11,X15,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ),
c_0_148 ).
fof(c_0_1419,axiom,
! [X22,X6,X21,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22)) ) ),
c_0_149 ).
fof(c_0_1420,axiom,
! [X22,X21,X6,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X21)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22)) ) ),
c_0_150 ).
fof(c_0_1421,axiom,
! [X11,X4,X15,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X11)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ),
c_0_151 ).
fof(c_0_1422,axiom,
! [X11,X15,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ),
c_0_152 ).
fof(c_0_1423,axiom,
! [X22,X6,X21,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),X22)) ) ),
c_0_153 ).
fof(c_0_1424,axiom,
! [X22,X21,X6,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X21)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),X22)) ) ),
c_0_154 ).
fof(c_0_1425,axiom,
! [X53,X10,X9,X54,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X54),X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X53)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X54),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X9))
<=> ( X54 = X10
| X9 = X53 ) ) ),
c_0_155 ).
fof(c_0_1426,axiom,
! [X52,X21,X22,X6,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( ( X6 != X22
& X21 != X52 )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X52)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X52)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X21)) ) ),
c_0_156 ).
fof(c_0_1427,axiom,
! [X4,X62,X29,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X62))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X62)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ) ) ),
c_0_157 ).
fof(c_0_1428,axiom,
! [X4,X62,X29,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X62))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X62)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ) ) ),
c_0_158 ).
fof(c_0_1429,axiom,
! [X29,X11,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29))) ) ) ) ),
c_0_159 ).
fof(c_0_1430,axiom,
! [X11,X58,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X58))) ) ) ),
c_0_160 ).
fof(c_0_1431,axiom,
! [X83,X84,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X84))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X84,X33)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X83),X33)),X84)) ) ),
c_0_161 ).
fof(c_0_1432,axiom,
! [X11,X58,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X58)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11))) ) ) ),
c_0_162 ).
fof(c_0_1433,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7))),X7)) ),
c_0_163 ).
fof(c_0_1434,axiom,
! [X27,X33,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X33)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ) ),
c_0_164 ).
fof(c_0_1435,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ) ),
c_0_165 ).
fof(c_0_1436,axiom,
! [X33,X27,X35] :
( hBOOL(hAPP(X35,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X27,X33)))
<=> ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [X42,X82] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X82),X33))
=> ( X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X42)),X82)
=> hBOOL(hAPP(X35,X42)) ) ) ) ) ),
c_0_166 ).
fof(c_0_1437,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ),
c_0_167 ).
fof(c_0_1438,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ),
c_0_168 ).
fof(c_0_1439,axiom,
! [X83,X33,X84] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X84,X33)),X83))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X83),X33))) ),
c_0_169 ).
fof(c_0_1440,axiom,
! [X7,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X29)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
=> c_RComplete_Onatceiling(X7) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
c_0_170 ).
fof(c_0_1441,axiom,
! [X22,X6,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X22)),c_Groups_Ozero__class_Ozero(X5)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X6))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X22),c_Groups_Ozero__class_Ozero(X5))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X22)) ) ) ) ),
c_0_171 ).
fof(c_0_1442,axiom,
! [X6,X22] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X22)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
c_0_172 ).
fof(c_0_1443,axiom,
! [X29,X11,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29))) ) ) ),
c_0_173 ).
fof(c_0_1444,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Olinordered__comm__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
c_0_174 ).
fof(c_0_1445,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
c_0_175 ).
fof(c_0_1446,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15))) ) ) ),
c_0_176 ).
fof(c_0_1447,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Oordered__comm__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
c_0_177 ).
fof(c_0_1448,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
c_0_178 ).
fof(c_0_1449,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15))) ) ) ),
c_0_179 ).
fof(c_0_1450,axiom,
! [X6,X22] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X22),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X22)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) ),
c_0_180 ).
fof(c_0_1451,axiom,
! [X29,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X14)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14),c_RealDef_Oreal(tc_Nat_Onat,X29))) ),
c_0_181 ).
fof(c_0_1452,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ! [X73] :
? [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X73),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X8)),X7))) ),
c_0_182 ).
fof(c_0_1453,axiom,
! [X4,X62,X29,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X62))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X62))) ) ) ),
c_0_183 ).
fof(c_0_1454,axiom,
! [X4,X62,X29,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X62))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X62))) ) ) ),
c_0_184 ).
fof(c_0_1455,axiom,
! [X12,X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X7)),X7)) ) ) ) ),
c_0_185 ).
fof(c_0_1456,axiom,
! [X12,X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12)),X7)) ) ) ) ),
c_0_186 ).
fof(c_0_1457,axiom,
! [X15,X4,X11,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
c_0_187 ).
fof(c_0_1458,axiom,
! [X15,X4,X11,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15))) ) ) ),
c_0_188 ).
fof(c_0_1459,axiom,
! [X15,X4,X11,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11))) ) ) ),
c_0_189 ).
fof(c_0_1460,axiom,
! [X15,X4,X11,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15))) ) ) ),
c_0_190 ).
fof(c_0_1461,axiom,
! [X7,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X29)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
=> c_RComplete_Onatfloor(X7) = X29 ) ),
c_0_191 ).
fof(c_0_1462,axiom,
! [X33,X84,X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X83),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X84,X33)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X83),X33)),X84)) ),
c_0_192 ).
fof(c_0_1463,axiom,
! [X12,X29,X50,X5] :
( class_Groups_Omonoid__mult(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X29))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X29),X50)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X50))),X12) ) ),
c_0_193 ).
fof(c_0_1464,axiom,
! [X26,X15,X11,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26))) ) ) ),
c_0_194 ).
fof(c_0_1465,axiom,
! [X26,X15,X11,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26))) ) ) ),
c_0_195 ).
fof(c_0_1466,axiom,
! [X26,X15,X11,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26))) ) ) ),
c_0_196 ).
fof(c_0_1467,axiom,
! [X26,X15,X11,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X26))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26))) ) ) ),
c_0_197 ).
fof(c_0_1468,axiom,
! [X17,X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X17,X29)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X17,X30))) ) ),
c_0_198 ).
fof(c_0_1469,axiom,
! [X11,X56,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),X56))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X56,X11))) ) ),
c_0_199 ).
fof(c_0_1470,axiom,
! [X11,X56,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),X56))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X56,X11)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11))) ) ),
c_0_200 ).
fof(c_0_1471,axiom,
! [X15,X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X15)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X15))) ) ),
c_0_201 ).
fof(c_0_1472,axiom,
! [X34,X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X29)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X30))) ) ),
c_0_202 ).
fof(c_0_1473,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27),X31))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X31)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
c_0_203 ).
fof(c_0_1474,axiom,
! [X46,X47,X51,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),X46)) ),
c_0_204 ).
fof(c_0_1475,plain,
! [X90,X12,X91,X92] :
( X92 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),X12)),X90)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X90),X91)) ) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),X90))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> ( X91 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X92,X91) = X12 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_1476,axiom,
! [X22,X6,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),X22))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,X6,X22)),c_Groups_Ozero__class_Ozero(X5))) ) ),
c_0_206 ).
fof(c_0_1477,axiom,
! [X22,X6,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ominus__class_Ominus(X5,X6,X22)),c_Groups_Ozero__class_Ozero(X5))) ) ),
c_0_207 ).
fof(c_0_1478,axiom,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X8)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
c_0_208 ).
fof(c_0_1479,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)))) ) ),
c_0_209 ).
fof(c_0_1480,axiom,
! [X7,X29,X5] :
( class_Groups_Omonoid__mult(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X29) ) ),
c_0_210 ).
fof(c_0_1481,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
c_0_211 ).
fof(c_0_1482,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
c_0_212 ).
fof(c_0_1483,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
c_0_213 ).
fof(c_0_1484,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Oincseq(X5,X25)
<=> ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,X20)),hAPP(X25,X8))) ) ) ),
c_0_214 ).
fof(c_0_1485,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Odecseq(X5,X25)
<=> ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,X8)),hAPP(X25,X20))) ) ) ),
c_0_215 ).
fof(c_0_1486,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Omonoseq(X5,X25)
<=> ( ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,X20)),hAPP(X25,X8))) )
| ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(X25,X8)),hAPP(X25,X20))) ) ) ) ),
c_0_216 ).
fof(c_0_1487,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29))),c_Groups_Oone__class_Oone(X5))) ) ) ),
c_0_217 ).
fof(c_0_1488,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X18))) ) ),
c_0_218 ).
fof(c_0_1489,axiom,
! [X12,X7,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X14))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X12))) ) ),
c_0_219 ).
fof(c_0_1490,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X18))) ) ),
c_0_220 ).
fof(c_0_1491,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X17))) ) ),
c_0_221 ).
fof(c_0_1492,axiom,
! [X12,X7,X15,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),c_RealVector_Onorm__class_Onorm(X5,X12))))
=> X7 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
c_0_222 ).
fof(c_0_1493,axiom,
! [X29,X23,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X23),c_Groups_Oone__class_Oone(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X23),c_Nat_OSuc(X29))),X23)) ) ) ),
c_0_223 ).
fof(c_0_1494,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X10,X9)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
c_0_224 ).
fof(c_0_1495,axiom,
! [X39,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X33),X39))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X33,X39)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_225 ).
fof(c_0_1496,axiom,
! [X14,X64,X16,X65] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X65),X16))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X64),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X65),X64)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),X14))) ) ),
c_0_226 ).
fof(c_0_1497,axiom,
! [X34,X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X34))) ) ),
c_0_227 ).
fof(c_0_1498,axiom,
! [X34,X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X34))) ) ),
c_0_228 ).
fof(c_0_1499,axiom,
! [X34,X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X34))) ) ),
c_0_229 ).
fof(c_0_1500,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X11))) ) ),
c_0_230 ).
fof(c_0_1501,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15))) ) ),
c_0_231 ).
fof(c_0_1502,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X11))) ) ),
c_0_232 ).
fof(c_0_1503,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15))) ) ),
c_0_233 ).
fof(c_0_1504,axiom,
! [X12,X7] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_OIm,X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_ORe,X12))),
c_0_234 ).
fof(c_0_1505,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
c_0_235 ).
fof(c_0_1506,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X4)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
c_0_236 ).
fof(c_0_1507,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
c_0_237 ).
fof(c_0_1508,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11)) ) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ),
c_0_238 ).
fof(c_0_1509,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
c_0_239 ).
fof(c_0_1510,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X4)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
c_0_240 ).
fof(c_0_1511,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
c_0_241 ).
fof(c_0_1512,axiom,
! [X12,X7,X15] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X12))))
=> X7 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
c_0_242 ).
fof(c_0_1513,axiom,
! [X17,X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X17)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X29,X17))) ),
c_0_243 ).
fof(c_0_1514,axiom,
! [X34,X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X29)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X30))) ),
c_0_244 ).
fof(c_0_1515,axiom,
! [X34,X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X34)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X34))) ),
c_0_245 ).
fof(c_0_1516,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
c_0_246 ).
fof(c_0_1517,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
c_0_247 ).
fof(c_0_1518,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
c_0_248 ).
fof(c_0_1519,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
c_0_249 ).
fof(c_0_1520,axiom,
! [X27,X6,X69,X70,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X70,X69),X6),c_Nat_OSuc(X27)) = hAPP(hAPP(X69,X6),hAPP(hAPP(c_Power_Opower_Opower(X5,X70,X69),X6),X27)),
c_0_250 ).
fof(c_0_1521,axiom,
! [X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X54),c_Groups_Oone__class_Oone(tc_Int_Oint))),X53))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),X53)) ),
c_0_251 ).
fof(c_0_1522,plain,
! [X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4)),c_Groups_Ozero__class_Ozero(X5))) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_1523,axiom,
! [X4,X11,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X4)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11)) ) ) ),
c_0_253 ).
fof(c_0_1524,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11)) ) ) ),
c_0_254 ).
fof(c_0_1525,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29)),X30)) ) ),
c_0_255 ).
fof(c_0_1526,axiom,
! [X17,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X7,X17)),X7)) ) ),
c_0_256 ).
fof(c_0_1527,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)),X30)) ) ),
c_0_257 ).
fof(c_0_1528,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
c_0_258 ).
fof(c_0_1529,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
c_0_259 ).
fof(c_0_1530,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
c_0_260 ).
fof(c_0_1531,axiom,
! [X30,X29,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X30),X17))) ),
c_0_261 ).
fof(c_0_1532,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X18)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X17)) ),
c_0_262 ).
fof(c_0_1533,plain,
! [X29,X17,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X17)),X29))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X29)) ) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_1534,axiom,
! [X29,X17,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X17)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ),
c_0_264 ).
fof(c_0_1535,axiom,
! [X29,X17,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X17)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X29)) ),
c_0_265 ).
fof(c_0_1536,axiom,
! [X12,X7,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X7,X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12)) ),
c_0_266 ).
fof(c_0_1537,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17),X18))) ),
c_0_267 ).
fof(c_0_1538,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18),X17))) ),
c_0_268 ).
fof(c_0_1539,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X17))) ),
c_0_269 ).
fof(c_0_1540,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X18))) ),
c_0_270 ).
fof(c_0_1541,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X17))) ),
c_0_271 ).
fof(c_0_1542,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X17))) ),
c_0_272 ).
fof(c_0_1543,axiom,
! [X14,X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X14),X7)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X14),X12))) ),
c_0_273 ).
fof(c_0_1544,axiom,
! [X46,X47,X51,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X47)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X51),X46)) ),
c_0_274 ).
fof(c_0_1545,axiom,
! [X46,X47,X51,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46))) ),
c_0_275 ).
fof(c_0_1546,axiom,
! [X26,X15,X11,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26)) ),
c_0_276 ).
fof(c_0_1547,axiom,
! [X27,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X10)),X27)))
<=> ( X10 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_277 ).
fof(c_0_1548,axiom,
? [X37] :
! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))),
c_0_278 ).
fof(c_0_1549,axiom,
? [X37] :
! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))),
c_0_279 ).
fof(c_0_1550,axiom,
? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))) ),
c_0_280 ).
fof(c_0_1551,axiom,
? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))) ),
c_0_281 ).
fof(c_0_1552,axiom,
? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))) ),
c_0_282 ).
fof(c_0_1553,axiom,
? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))) ),
c_0_283 ).
fof(c_0_1554,axiom,
! [X27,X31] :
( hBOOL(hAPP(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),X31),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27)) ) ),
c_0_284 ).
fof(c_0_1555,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X30))
=> hBOOL(hAPP(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),X30),X29))) ) ),
c_0_285 ).
fof(c_0_1556,axiom,
! [X22,X6,X35] :
( hBOOL(hAPP(X35,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X22)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6),X22))
=> hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X87] :
( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X87)
=> hBOOL(hAPP(X35,X87)) ) ) ),
c_0_286 ).
fof(c_0_1557,plain,
! [X22,X6,X35] :
( hBOOL(hAPP(X35,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X22)))
<=> ~ ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6),X22))
& ~ hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X87] :
( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X87)
& ~ hBOOL(hAPP(X35,X87)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_1558,axiom,
! [X22,X6,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X22)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X6))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X22)) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X22),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ),
c_0_288 ).
fof(c_0_1559,axiom,
! [X22,X6] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X22)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22),X6))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22)) ) ) ),
c_0_289 ).
fof(c_0_1560,axiom,
! [X6,X22] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
=> ( hBOOL(hAPP(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,X6,X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) ),
c_0_290 ).
fof(c_0_1561,plain,
! [X18,X19] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X18)),X19)),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_1562,plain,
! [X19,X18] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X19)),X19)),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_1563,axiom,
! [X83,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X83,X33)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33),X83)) ) ),
c_0_293 ).
fof(c_0_1564,axiom,
! [X19,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Nat_OSuc(X19))),X29)) ),
c_0_294 ).
fof(c_0_1565,axiom,
! [X6,X22] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X22),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(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,X6,X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
c_0_295 ).
fof(c_0_1566,plain,
! [X1,X2,X5,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X13),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X13),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X13),X1),X2)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_1567,axiom,
! [X4,X29] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X29))),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X4))),
c_0_297 ).
fof(c_0_1568,axiom,
! [X29,X30,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X30),X29))) ) ) ),
c_0_298 ).
fof(c_0_1569,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11))) ) ) ),
c_0_299 ).
fof(c_0_1570,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11)) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5))) ) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11))) ) ),
c_0_300 ).
fof(c_0_1571,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11))) ) ) ),
c_0_301 ).
fof(c_0_1572,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11))) ) ) ),
c_0_302 ).
fof(c_0_1573,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11))) ) ) ),
c_0_303 ).
fof(c_0_1574,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11))) ) ) ),
c_0_304 ).
fof(c_0_1575,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11))) ) ) ),
c_0_305 ).
fof(c_0_1576,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29))) ) ),
c_0_306 ).
fof(c_0_1577,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X30))) ) ),
c_0_307 ).
fof(c_0_1578,axiom,
! [X11,X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> X4 = X11 ) ) ) ) ),
c_0_308 ).
fof(c_0_1579,axiom,
! [X30,X29,X4,X5] :
( class_Fields_Ofield(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) ) ) ),
c_0_309 ).
fof(c_0_1580,axiom,
! [X26,X11,X15,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ominus__class_Ominus(X5,X4,X11)),c_Groups_Ominus__class_Ominus(X5,X15,X26)) ),
c_0_310 ).
fof(c_0_1581,axiom,
! [X29,X4,X11,X5] :
( class_Fields_Ofield(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X11)),X29) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29)) ) ),
c_0_311 ).
fof(c_0_1582,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),X29)) ) ),
c_0_312 ).
fof(c_0_1583,axiom,
! [X29,X30] :
( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29)) ) ),
c_0_313 ).
fof(c_0_1584,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ) ),
c_0_314 ).
fof(c_0_1585,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X15)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X15)) ),
c_0_315 ).
fof(c_0_1586,axiom,
! [X55,X12,X7,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12)),X55) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X7),X55)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X12),X55)) ),
c_0_316 ).
fof(c_0_1587,axiom,
! [X29,X11,X4,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X11)),X29) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29)) ),
c_0_317 ).
fof(c_0_1588,axiom,
! [X29,X11,X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),X29) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X29)) ),
c_0_318 ).
fof(c_0_1589,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Ocomm__semiring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)) ),
c_0_319 ).
fof(c_0_1590,axiom,
! [X11,X56,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X56)),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),X11)) ),
c_0_320 ).
fof(c_0_1591,axiom,
! [X55,X12,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12)),X55) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X55)) ),
c_0_321 ).
fof(c_0_1592,axiom,
! [X11,X30,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X30)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X30) ),
c_0_322 ).
fof(c_0_1593,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)) ),
c_0_323 ).
fof(c_0_1594,axiom,
! [X49,X12,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12)),X49) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X49)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X49)) ),
c_0_324 ).
fof(c_0_1595,axiom,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X30)))),
c_0_325 ).
fof(c_0_1596,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11))) ) ) ),
c_0_326 ).
fof(c_0_1597,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11))) ) ) ),
c_0_327 ).
fof(c_0_1598,axiom,
! [X29,X17,X18] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X29)),X17)) ),
c_0_328 ).
fof(c_0_1599,axiom,
! [X12,X7] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X7),X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_ORe,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_OIm,X12))),
c_0_329 ).
fof(c_0_1600,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
c_0_330 ).
fof(c_0_1601,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
c_0_331 ).
fof(c_0_1602,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27)) ) ),
c_0_332 ).
fof(c_0_1603,axiom,
! [X17,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17))
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17),X30),X17) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
c_0_333 ).
fof(c_0_1604,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X10),X9)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X9)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ),
c_0_334 ).
fof(c_0_1605,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15))) ) ) ),
c_0_335 ).
fof(c_0_1606,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15))) ) ) ),
c_0_336 ).
fof(c_0_1607,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15))) ) ) ),
c_0_337 ).
fof(c_0_1608,axiom,
! [X4,X11,X15,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15))) ) ) ),
c_0_338 ).
fof(c_0_1609,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15))) ) ) ),
c_0_339 ).
fof(c_0_1610,axiom,
! [X11,X4,X5] :
( class_Rings_Oordered__ring__abs(X5)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Ozero__class_Ozero(X5))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Groups_Ozero__class_Ozero(X5))) ) )
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11)) ) ),
c_0_340 ).
fof(c_0_1611,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7)))),
c_0_341 ).
fof(c_0_1612,plain,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),X29)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_1613,plain,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),X29)) ) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_1614,axiom,
! [X29,X30] :
( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29) = X29 )
& ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29)) ) ),
c_0_344 ).
fof(c_0_1615,axiom,
! [X9,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X9)) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
& X9 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
c_0_345 ).
fof(c_0_1616,axiom,
! [X14,X16] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X16),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),c_Groups_Oone__class_Oone(tc_Int_Oint))),X14)) ),
c_0_346 ).
fof(c_0_1617,axiom,
! [X49,X23,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
=> ( X4 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X49))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ),
c_0_347 ).
fof(c_0_1618,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
=> hBOOL(hAPP(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,X7,X12))) ) ),
c_0_348 ).
fof(c_0_1619,axiom,
! [X7,X5] :
( class_Rings_Oring__1(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X7),c_Groups_Oone__class_Oone(X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),c_Groups_Oone__class_Oone(X5))),c_Groups_Ominus__class_Ominus(X5,X7,c_Groups_Oone__class_Oone(X5))) ),
c_0_349 ).
fof(c_0_1620,axiom,
! [X49,X23,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
=> ( X4 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X49))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X23),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X49)) ) ) ),
c_0_350 ).
fof(c_0_1621,axiom,
! [X2] :
( c_SEQ_Osubseq(X2)
<=> ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X8)),hAPP(X2,c_Nat_OSuc(X8)))) ),
c_0_351 ).
fof(c_0_1622,axiom,
! [X29,X30,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X29))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X17),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X17)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29) ) ),
c_0_352 ).
fof(c_0_1623,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
c_0_353 ).
fof(c_0_1624,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7),X12))) ) ),
c_0_354 ).
fof(c_0_1625,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
=> hBOOL(hAPP(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),X7),X12))) ) ),
c_0_355 ).
fof(c_0_1626,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
=> hBOOL(hAPP(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),X7),X12))) ) ),
c_0_356 ).
fof(c_0_1627,axiom,
! [X27,X31] :
( hBOOL(hAPP(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),X31),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27)) ) ),
c_0_357 ).
fof(c_0_1628,axiom,
! [X30,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X30)),X30) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Oone__class_Oone(X5))),X30) ),
c_0_358 ).
fof(c_0_1629,axiom,
! [X16,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),X60)),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X16)),
c_0_359 ).
fof(c_0_1630,axiom,
! [X16,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X61),X60)),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X61),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X60),X16)),
c_0_360 ).
fof(c_0_1631,axiom,
! [X17,X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X17)),
c_0_361 ).
fof(c_0_1632,axiom,
! [X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X53,c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),X53)) ),
c_0_362 ).
fof(c_0_1633,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ),
c_0_363 ).
fof(c_0_1634,axiom,
! [X10,X1,X2,X5,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X13),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(X2,X10)),hAPP(X1,X10))) ) ),
c_0_364 ).
fof(c_0_1635,axiom,
! [X10,X1,X2,X5,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X13),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(X2,X10)),hAPP(X1,X10))) ) ),
c_0_365 ).
fof(c_0_1636,axiom,
! [X30,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)),X30) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X30)) ),
c_0_366 ).
fof(c_0_1637,axiom,
! [X30,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X17),c_Nat_OSuc(X18)) ),
c_0_367 ).
fof(c_0_1638,axiom,
! [X12,X7] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X12)),c_Transcendental_Ocos(X7))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X12)),c_Transcendental_Osin(X7))),
c_0_368 ).
fof(c_0_1639,axiom,
! [X12,X7] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X7)),c_Transcendental_Ocos(X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X7)),c_Transcendental_Osin(X12))),
c_0_369 ).
fof(c_0_1640,axiom,
! [X15,X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),c_Divides_Odiv__class_Odiv(X5,X4,X11)) ) ),
c_0_370 ).
fof(c_0_1641,axiom,
! [X15,X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),c_Divides_Odiv__class_Odiv(X5,X4,X11)) ) ),
c_0_371 ).
fof(c_0_1642,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ominus__class_Ominus(X5,X4,X11)),X15) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X15)) ),
c_0_372 ).
fof(c_0_1643,axiom,
! [X55,X12,X7,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ominus__class_Ominus(X5,X7,X12)),X55) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X7),X55),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X12),X55)) ),
c_0_373 ).
fof(c_0_1644,axiom,
! [X55,X12,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X7,X12)),X55) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X55)) ),
c_0_374 ).
fof(c_0_1645,axiom,
! [X11,X56,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X56)),X11) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),X11)) ),
c_0_375 ).
fof(c_0_1646,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X9))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X10)),c_Transcendental_Oln(X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9)) ) ) ),
c_0_376 ).
fof(c_0_1647,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X9))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X10)),c_Transcendental_Oln(X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),X9)) ) ) ),
c_0_377 ).
fof(c_0_1648,axiom,
! [X11,X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_Nat_OSuc(X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X11))
=> X4 = X11 ) ) ) ),
c_0_378 ).
fof(c_0_1649,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oabs__class_Oabs(X5,X4)),X29))) ),
c_0_379 ).
fof(c_0_1650,axiom,
! [X58,X11,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X58)) ),
c_0_380 ).
fof(c_0_1651,axiom,
! [X12,X7,X57,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),X12)) ),
c_0_381 ).
fof(c_0_1652,axiom,
! [X14,X12,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X12),X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X14)) ),
c_0_382 ).
fof(c_0_1653,axiom,
! [X47,X51,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),X47) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X47)),X51) ),
c_0_383 ).
fof(c_0_1654,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),X11) ),
c_0_384 ).
fof(c_0_1655,axiom,
! [X12,X7] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X7)),c_Transcendental_Ocos(X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X7)),c_Transcendental_Osin(X12))),
c_0_385 ).
fof(c_0_1656,axiom,
! [X19,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X19),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)),X19) ),
c_0_386 ).
fof(c_0_1657,axiom,
! [X19,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)),X19) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X19),X17) ),
c_0_387 ).
fof(c_0_1658,axiom,
! [X12,X7] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X7),X12) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_ORe,X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_OIm,X12))),
c_0_388 ).
fof(c_0_1659,plain,
! [X27,X35] :
( ~ hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X35,X27))
=> ? [X32] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X27))
& ! [X42] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42),X32))
=> ~ hBOOL(hAPP(X35,X42)) )
& hBOOL(hAPP(X35,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_1660,axiom,
! [X27,X10] :
( hBOOL(hAPP(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),X10),X27)))
<=> ( X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)) ) ),
c_0_390 ).
fof(c_0_1661,axiom,
! [X27,X10] :
( hBOOL(hAPP(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),X10),X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))
| X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_391 ).
fof(c_0_1662,axiom,
! [X25] :
( c_SEQ_OBseq(tc_RealDef_Oreal,X25)
=> ( ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(X25,X20)),hAPP(X25,X8))) )
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,X25) ) ),
c_0_392 ).
fof(c_0_1663,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29)))) ) ),
c_0_393 ).
fof(c_0_1664,axiom,
! [X29,X30,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) ),
c_0_394 ).
fof(c_0_1665,axiom,
! [X49,X50,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X50)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X49)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X49)) ),
c_0_395 ).
fof(c_0_1666,axiom,
! [X4,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4))
=> ? [X3] :
( hBOOL(hAPP(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),X29) = X4
& ! [X73] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X73))
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X73),X29) = X4 )
=> X73 = X3 ) ) ) ),
c_0_396 ).
fof(c_0_1667,axiom,
! [X9,X10] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X10 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X9 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
c_0_397 ).
fof(c_0_1668,axiom,
! [X26,X15,X11,X4,X23,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X23 != c_Groups_Ozero__class_Ozero(X5)
=> ( ( X4 = X11
& X15 != X26 )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X15)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X26)) ) ) ),
c_0_398 ).
fof(c_0_1669,axiom,
! [X29,X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)),c_Nat_OSuc(X30))),
c_0_399 ).
fof(c_0_1670,axiom,
! [X29,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19))
=> hBOOL(hAPP(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),X19),X29))) ),
c_0_400 ).
fof(c_0_1671,axiom,
! [X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),X53))
| X54 = X53 ) ),
c_0_401 ).
fof(c_0_1672,axiom,
! [X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54),X53)) ),
c_0_402 ).
fof(c_0_1673,axiom,
! [X29,X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29)),X30)),
c_0_403 ).
fof(c_0_1674,axiom,
! [X29,X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)),X30)),
c_0_404 ).
fof(c_0_1675,axiom,
! [X6,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6),c_RComplete_Onatfloor(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X6)),X10)) ) ),
c_0_405 ).
fof(c_0_1676,axiom,
! [X16,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X61,X60)),X16) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X16)),
c_0_406 ).
fof(c_0_1677,axiom,
! [X17,X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)),X17) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X17)),
c_0_407 ).
fof(c_0_1678,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ),
c_0_408 ).
fof(c_0_1679,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ),
c_0_409 ).
fof(c_0_1680,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29))) ) ),
c_0_410 ).
fof(c_0_1681,axiom,
! [X2] :
( c_SEQ_Osubseq(X2)
<=> ! [X20,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X20)),hAPP(X2,X8))) ) ),
c_0_411 ).
fof(c_0_1682,axiom,
! [X29,X4,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Oone__class_Oone(X5)),X4)),X29) ),
c_0_412 ).
fof(c_0_1683,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X7),c_RealDef_Oreal(tc_Nat_Onat,X12))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X7),X12) ) ),
c_0_413 ).
fof(c_0_1684,axiom,
! [X7,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4)),X7))
=> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,X4))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X7),X4) ),
c_0_414 ).
fof(c_0_1685,axiom,
! [X7,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4)),X7))
=> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,X4))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X7),X4) ),
c_0_415 ).
fof(c_0_1686,axiom,
! [X35,X27,X31] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
=> hBOOL(hAPP(hAPP(X35,X27),X31)) )
=> ( ( X31 = X27
=> hBOOL(hAPP(hAPP(X35,X27),X31)) )
=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31))
=> hBOOL(hAPP(hAPP(X35,X27),X31)) )
=> hBOOL(hAPP(hAPP(X35,X27),X31)) ) ) ),
c_0_416 ).
fof(c_0_1687,axiom,
! [X25,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X25)
=> ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X25,X8))),X37)) ) ) ),
c_0_417 ).
fof(c_0_1688,axiom,
! [X60,X61,X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),X60)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X61)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X60)),
c_0_418 ).
fof(c_0_1689,axiom,
! [X14,X12,X7] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X12)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X14)),
c_0_419 ).
fof(c_0_1690,axiom,
! [X29,X30,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X29)),
c_0_420 ).
fof(c_0_1691,axiom,
! [X29,X7] : hBOOL(hAPP(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X7)),X29))),
c_0_421 ).
fof(c_0_1692,axiom,
! [X30,X19] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X19)))),
c_0_422 ).
fof(c_0_1693,axiom,
! [X30,X19] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X30)))),
c_0_423 ).
fof(c_0_1694,axiom,
! [X4,X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X30)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Oone__class_Oone(X5))),X30) ),
c_0_424 ).
fof(c_0_1695,axiom,
! [X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X4),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Divides_Odiv__class_Odiv(X5,X4,X11)),c_Groups_Oone__class_Oone(X5)) ) ),
c_0_425 ).
fof(c_0_1696,axiom,
! [X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Divides_Odiv__class_Odiv(X5,X4,X11)),c_Groups_Oone__class_Oone(X5)) ) ),
c_0_426 ).
fof(c_0_1697,axiom,
! [X11,X4,X15] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15))
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X15)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11),X15) ),
c_0_427 ).
fof(c_0_1698,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
=> c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X7),X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(X7),c_Transcendental_Oln(X12)) ) ),
c_0_428 ).
fof(c_0_1699,axiom,
! [X30,X29,X5] :
( class_Power_Opower(X5)
=> ( ( X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X30),X29) = c_Groups_Oone__class_Oone(X5) )
& ( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X30),X29) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X30),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X30),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
c_0_429 ).
fof(c_0_1700,axiom,
! [X9,X10,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X9))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X10),X9) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
& X9 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ) ),
c_0_430 ).
fof(c_0_1701,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
=> c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(X7)),c_Transcendental_Oln(X12)) ) ),
c_0_431 ).
fof(c_0_1702,axiom,
! [X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14))) ),
c_0_432 ).
fof(c_0_1703,axiom,
! [X29,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),c_RealDef_Oreal(tc_Nat_Onat,X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X7)),X29)) ) ),
c_0_433 ).
fof(c_0_1704,axiom,
! [X6,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X10)),X6))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_RealDef_Oreal(tc_Nat_Onat,X6))) ) ),
c_0_434 ).
fof(c_0_1705,axiom,
! [X33,X27,X35] :
( hBOOL(hAPP(X35,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X27,X33)))
<=> ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X35,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& epred1_3(X35,X33,X27) ) ),
inference(apply_def,[status(thm)],[c_0_435,c_0_1268,theory(equality,[symmetry])]) ).
fof(c_0_1706,axiom,
! [X7] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X7)),c_Transcendental_Ocos(X7))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X7)),c_Transcendental_Osin(X7))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_436 ).
fof(c_0_1707,plain,
! [X10] :
( ~ hBOOL(hAPP(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),X10),X10)))
<=> X10 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_1708,axiom,
! [X12,X7,X57,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),c_Groups_Ominus__class_Ominus(X5,X7,X12)) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X57),X12)) ),
c_0_438 ).
fof(c_0_1709,axiom,
! [X58,X11,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ominus__class_Ominus(X5,X11,X58)) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X58)) ),
c_0_439 ).
fof(c_0_1710,axiom,
! [X29,X30,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X29)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) ),
c_0_440 ).
fof(c_0_1711,axiom,
! [X19,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17),X18) ),
c_0_441 ).
fof(c_0_1712,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X7,X12))) ) ),
c_0_442 ).
fof(c_0_1713,axiom,
! [X4,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4))
=> ? [X74] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X74))
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X74),X29) = X4 ) ) ),
c_0_443 ).
fof(c_0_1714,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X15)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),X15) ),
c_0_444 ).
fof(c_0_1715,axiom,
! [X29,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) ),
c_0_445 ).
fof(c_0_1716,axiom,
! [X47,X51,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X51)),X47) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X51),X47)) ),
c_0_446 ).
fof(c_0_1717,axiom,
! [X46,X47,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X47)),X46) ),
c_0_447 ).
fof(c_0_1718,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oab__semigroup__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)) ),
c_0_448 ).
fof(c_0_1719,axiom,
! [X26,X15,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)),X26) ),
c_0_449 ).
fof(c_0_1720,axiom,
! [X15,X11,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15)) ),
c_0_450 ).
fof(c_0_1721,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Oab__semigroup__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X15)) ),
c_0_451 ).
fof(c_0_1722,axiom,
! [X12,X7] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X7)),c_Transcendental_Ocos(X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X7)),c_Transcendental_Osin(X12))),
c_0_452 ).
fof(c_0_1723,axiom,
! [X12,X7] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X12)),c_Transcendental_Osin(X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X12)),c_Transcendental_Ocos(X7))),
c_0_453 ).
fof(c_0_1724,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Osgn__class_Osgn(X5,X6)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
c_0_454 ).
fof(c_0_1725,axiom,
! [X19,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X18),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)) ),
c_0_455 ).
fof(c_0_1726,axiom,
! [X19,X18,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X18))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X18),X17) ),
c_0_456 ).
fof(c_0_1727,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X27)),c_RealDef_Oreal(tc_Nat_Onat,X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27),X31)) ),
c_0_457 ).
fof(c_0_1728,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X27)),c_RealDef_Oreal(tc_Nat_Onat,X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31)) ),
c_0_458 ).
fof(c_0_1729,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11)) ),
c_0_459 ).
fof(c_0_1730,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X27))
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X33) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X33)
<=> X31 = X27 ) ) ),
c_0_460 ).
fof(c_0_1731,axiom,
! [X29,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))
=> hBOOL(hAPP(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),X7),X29))) ),
c_0_461 ).
fof(c_0_1732,axiom,
! [X29,X30,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X30)),X29) ),
c_0_462 ).
fof(c_0_1733,axiom,
! [X49,X50,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X50)),X49) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X49)) ),
c_0_463 ).
fof(c_0_1734,axiom,
! [X50,X30] :
( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X50),X30) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X50),X30) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X50),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
c_0_464 ).
fof(c_0_1735,axiom,
! [X12,X7] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X7)),c_Transcendental_Ocos(X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X7)),c_Transcendental_Osin(X12))),
c_0_465 ).
fof(c_0_1736,axiom,
! [X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14)),X14) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_466 ).
fof(c_0_1737,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X7))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7))),
c_0_467 ).
fof(c_0_1738,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X7))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7))),
c_0_468 ).
fof(c_0_1739,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
c_0_469 ).
fof(c_0_1740,axiom,
! [X12,X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X7))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X12)),X7) = c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X7)) ) ),
c_0_470 ).
fof(c_0_1741,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5)))) ),
c_0_471 ).
fof(c_0_1742,axiom,
! [X52,X21,X22,X6,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X6,X22) = c_Groups_Ominus__class_Ominus(X5,X21,X52)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X6),X22))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X21),X52)) ) ) ),
c_0_472 ).
fof(c_0_1743,axiom,
! [X52,X21,X22,X6,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X6,X22) = c_Groups_Ominus__class_Ominus(X5,X21,X52)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X6),X22))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X21),X52)) ) ) ),
c_0_473 ).
fof(c_0_1744,axiom,
! [X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X30) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5))),X30) ),
c_0_474 ).
fof(c_0_1745,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X10)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
c_0_475 ).
fof(c_0_1746,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10)) ) ),
c_0_476 ).
fof(c_0_1747,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X7)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7)) ) ),
c_0_477 ).
fof(c_0_1748,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10)) ) ),
c_0_478 ).
fof(c_0_1749,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X7)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7)) ) ),
c_0_479 ).
fof(c_0_1750,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7)))),
c_0_480 ).
fof(c_0_1751,axiom,
! [X29,X4,X23] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X23,X4)),X29) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X23),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X4)),
c_0_481 ).
fof(c_0_1752,axiom,
! [X60,X61,X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X61,X60)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X60)),
c_0_482 ).
fof(c_0_1753,axiom,
! [X29,X30,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X29)),
c_0_483 ).
fof(c_0_1754,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X4)),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11)) ) ),
c_0_484 ).
fof(c_0_1755,axiom,
! [X14,X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14))) ),
c_0_485 ).
fof(c_0_1756,axiom,
! [X12,X14,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14))) ),
c_0_486 ).
fof(c_0_1757,axiom,
! [X12,X14,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14))) ),
c_0_487 ).
fof(c_0_1758,axiom,
! [X14,X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14))) ),
c_0_488 ).
fof(c_0_1759,axiom,
! [X30,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X30))) ),
c_0_489 ).
fof(c_0_1760,axiom,
! [X30,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X18))) ),
c_0_490 ).
fof(c_0_1761,axiom,
! [X30,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X18))) ),
c_0_491 ).
fof(c_0_1762,axiom,
! [X30,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X30))) ),
c_0_492 ).
fof(c_0_1763,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X7)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ),
c_0_493 ).
fof(c_0_1764,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)),X29) = X30 ),
c_0_494 ).
fof(c_0_1765,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Osgn__class_Osgn(X5,X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
c_0_495 ).
fof(c_0_1766,axiom,
! [X4,X23] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X23)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X4),X23),
c_0_496 ).
fof(c_0_1767,axiom,
! [X63,X60,X61] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),X60)),X63) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X63)),
c_0_497 ).
fof(c_0_1768,axiom,
! [X63,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X60)),X63) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X63)),
c_0_498 ).
fof(c_0_1769,axiom,
! [X63,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X61),X60)),X63) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X60),X63)),
c_0_499 ).
fof(c_0_1770,axiom,
! [X17,X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X17)),
c_0_500 ).
fof(c_0_1771,axiom,
! [X14,X12,X7] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X12)),X14) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X14)),
c_0_501 ).
fof(c_0_1772,axiom,
! [X17,X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X17)),
c_0_502 ).
fof(c_0_1773,axiom,
! [X23] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X23))
=> ? [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X8)),X23))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X8)))) ) ),
c_0_503 ).
fof(c_0_1774,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7))),X7)) ),
c_0_504 ).
fof(c_0_1775,axiom,
! [X4,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X7)),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),c_RComplete_Onatfloor(X4))) ),
c_0_505 ).
fof(c_0_1776,axiom,
! [X14,X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X14)) ) ) ),
c_0_506 ).
fof(c_0_1777,axiom,
! [X14,X7,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X14),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X14),X7)) ) ) ),
c_0_507 ).
fof(c_0_1778,axiom,
! [X14,X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X14)) ) ) ),
c_0_508 ).
fof(c_0_1779,axiom,
! [X14,X7,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X14),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X14),X7)) ) ) ),
c_0_509 ).
fof(c_0_1780,axiom,
! [X14,X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X14)) ) ) ),
c_0_510 ).
fof(c_0_1781,axiom,
! [X14,X7,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X14),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X14),X7)) ) ) ),
c_0_511 ).
fof(c_0_1782,axiom,
! [X14,X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X14)) ) ) ),
c_0_512 ).
fof(c_0_1783,axiom,
! [X14,X7,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X14),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X14),X7)) ) ) ),
c_0_513 ).
fof(c_0_1784,axiom,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X8))),v_r)),
c_0_514 ).
fof(c_0_1785,axiom,
! [X27,X31,X6,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),X6))
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X31) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X27)
<=> X31 = X27 ) ) ),
c_0_515 ).
fof(c_0_1786,axiom,
! [X29,X30,X34,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17),X34))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X29)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ) ),
c_0_516 ).
fof(c_0_1787,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19)),X17)) ) ),
c_0_517 ).
fof(c_0_1788,axiom,
! [X4,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),c_RealDef_Oreal(tc_Nat_Onat,X4))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X7)),X4) ),
c_0_518 ).
fof(c_0_1789,axiom,
! [X4,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),c_RealDef_Oreal(tc_Nat_Onat,X4))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X7)),X4) ),
c_0_519 ).
fof(c_0_1790,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),c_RealDef_Oreal(tc_Nat_Onat,X29)) ),
c_0_520 ).
fof(c_0_1791,axiom,
! [X17,X29,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X30),X29),c_Nat_OSuc(X17)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),X17),
c_0_521 ).
fof(c_0_1792,axiom,
! [X29,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X7),X29)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_Transcendental_Oln(X7)) ),
c_0_522 ).
fof(c_0_1793,axiom,
! [X26,X15,X11,X4] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X4,X11),c_Complex_Ocomplex_OComplex(X15,X26)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4,X15),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X11,X26)),
c_0_523 ).
fof(c_0_1794,axiom,
! [X11,X4,X15,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X15 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)) = c_Divides_Odiv__class_Odiv(X5,X4,X11) ) ),
c_0_524 ).
fof(c_0_1795,axiom,
! [X11,X4,X15,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X15 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X15)) = c_Divides_Odiv__class_Odiv(X5,X4,X11) ) ),
c_0_525 ).
fof(c_0_1796,axiom,
! [X11,X4,X15,X5] :
( class_Divides_Osemiring__div(X5)
=> ( ( X15 = c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)) = c_Groups_Ozero__class_Ozero(X5) )
& ( X15 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X11)) = c_Divides_Odiv__class_Odiv(X5,X4,X11) ) ) ),
c_0_526 ).
fof(c_0_1797,axiom,
! [X6,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X6)),c_Groups_Ozero__class_Ozero(X5)))
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_527 ).
fof(c_0_1798,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),c_Nat_OSuc(X27)))
<=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X82] :
( X31 = c_Nat_OSuc(X82)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X82),X27)) ) ) ),
c_0_528 ).
fof(c_0_1799,axiom,
! [X49,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X49)),X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Nat_OSuc(X49)) ),
c_0_529 ).
fof(c_0_1800,axiom,
! [X29,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)),X4) ),
c_0_530 ).
fof(c_0_1801,plain,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Ozero__class_Ozero(X5))) ),
inference(fof_simplification,[status(thm)],[c_0_531]) ).
fof(c_0_1802,axiom,
! [X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4))) ),
c_0_532 ).
fof(c_0_1803,axiom,
! [X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Oone__class_Oone(X5)))) ),
c_0_533 ).
fof(c_0_1804,axiom,
! [X26,X15,X11,X4] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X4,X11)),c_Complex_Ocomplex_OComplex(X15,X26)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X11),X26)),
c_0_534 ).
fof(c_0_1805,axiom,
! [X11,X75,X4,X76] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X76,X4)),c_Complex_Orcis(X75,X11)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X76),X75),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X11)),
c_0_535 ).
fof(c_0_1806,axiom,
! [X46,X47,X48,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X46)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X46)) ),
c_0_536 ).
fof(c_0_1807,axiom,
! [X26,X15,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X26)) ),
c_0_537 ).
fof(c_0_1808,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X19),X17)) ) ),
c_0_538 ).
fof(c_0_1809,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X17)) ) ),
c_0_539 ).
fof(c_0_1810,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X17)) ) ),
c_0_540 ).
fof(c_0_1811,axiom,
! [X33,X83] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X83,X33) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( X33 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X83))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X83),X33)) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X83),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X33),X83)) ) ) ),
c_0_541 ).
fof(c_0_1812,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X11))
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
c_0_542 ).
fof(c_0_1813,axiom,
! [X17,X18,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18),X17) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X17),X18),
c_0_543 ).
fof(c_0_1814,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X10)) ) ),
c_0_544 ).
fof(c_0_1815,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X10)) ) ),
c_0_545 ).
fof(c_0_1816,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X10)) ) ),
c_0_546 ).
fof(c_0_1817,axiom,
! [X4,X29] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X4)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),X29)),
c_0_547 ).
fof(c_0_1818,axiom,
! [X4,X29] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X4)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),X29)),
c_0_548 ).
fof(c_0_1819,axiom,
! [X11,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X11),X4))
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X11) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
c_0_549 ).
fof(c_0_1820,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X10)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_550 ).
fof(c_0_1821,plain,
! [X9,X10,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_551]) ).
fof(c_0_1822,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X7)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
c_0_552 ).
fof(c_0_1823,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X7)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
c_0_553 ).
fof(c_0_1824,axiom,
! [X15,X11,X4] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X15)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4,X11),X15),
c_0_554 ).
fof(c_0_1825,axiom,
! [X17,X18,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18),X17) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X17)),
c_0_555 ).
fof(c_0_1826,plain,
! [X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X7)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(fof_simplification,[status(thm)],[c_0_556]) ).
fof(c_0_1827,axiom,
! [X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27)) ),
c_0_557 ).
fof(c_0_1828,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X9))
=> ( c_Transcendental_Oln(X10) = c_Transcendental_Oln(X9)
<=> X10 = X9 ) ) ),
c_0_558 ).
fof(c_0_1829,axiom,
! [X4,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),c_RealDef_Oreal(tc_Nat_Onat,X4)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X7)),X4)) ),
c_0_559 ).
fof(c_0_1830,axiom,
! [X29,X30,X17] :
( ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X29)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X29)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) ) ),
c_0_560 ).
fof(c_0_1831,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X30),X29) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) ),
c_0_561 ).
fof(c_0_1832,axiom,
! [X27,X31,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)
<=> X31 = X27 ) ),
c_0_562 ).
fof(c_0_1833,axiom,
! [X29,X30,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),
c_0_563 ).
fof(c_0_1834,axiom,
! [X29,X17,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X17)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),
c_0_564 ).
fof(c_0_1835,axiom,
! [X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X12)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_Transcendental_Ocos(c_Transcendental_Oarccos(X12)) = X12 ),
c_0_565 ).
fof(c_0_1836,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X30),X29) = X30 ),
c_0_566 ).
fof(c_0_1837,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29),X29) = X30 ),
c_0_567 ).
fof(c_0_1838,axiom,
! [X29,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4))
=> ? [X74] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X74))
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X74),c_Nat_OSuc(X29)) = X4 ) ),
c_0_568 ).
fof(c_0_1839,plain,
! [X27,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X27)),X31)) ),
inference(fof_simplification,[status(thm)],[c_0_569]) ).
fof(c_0_1840,axiom,
! [X29,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X29))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X19)) = X19 ),
c_0_570 ).
fof(c_0_1841,axiom,
! [X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X27)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
<=> X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_571 ).
fof(c_0_1842,axiom,
! [X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X53)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> X53 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
c_0_572 ).
fof(c_0_1843,axiom,
! [X11,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ominus__class_Ominus(X5,X4,X11)),X11) = X4 ),
c_0_573 ).
fof(c_0_1844,plain,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X29)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(fof_simplification,[status(thm)],[c_0_574]) ).
fof(c_0_1845,axiom,
! [X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X29 ),
c_0_575 ).
fof(c_0_1846,axiom,
! [X14,X12,X7] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7),X14)),
c_0_576 ).
fof(c_0_1847,axiom,
! [X14,X12,X7] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X14)),
c_0_577 ).
fof(c_0_1848,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) = X30 ),
c_0_578 ).
fof(c_0_1849,plain,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> X10 = X9 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_579]) ).
fof(c_0_1850,axiom,
! [X9,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( X10 = X9
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10)) ) ) ),
c_0_580 ).
fof(c_0_1851,axiom,
! [X10,X9,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
<=> X10 = X9 ) ) ),
c_0_581 ).
fof(c_0_1852,axiom,
! [X12,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> X7 = X12 ) ) ),
c_0_582 ).
fof(c_0_1853,axiom,
! [X7,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> X7 = X12 ) ) ),
c_0_583 ).
fof(c_0_1854,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
<=> ? [X32] : X27 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32)) ),
c_0_584 ).
fof(c_0_1855,plain,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_585]) ).
fof(c_0_1856,plain,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X9),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_586]) ).
fof(c_0_1857,plain,
! [X7,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12)) ) ),
inference(fof_simplification,[status(thm)],[c_0_587]) ).
fof(c_0_1858,plain,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X9),X10))
| X10 = X9 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_588]) ).
fof(c_0_1859,plain,
! [X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ),
inference(fof_simplification,[status(thm)],[c_0_589]) ).
fof(c_0_1860,plain,
! [X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ),
inference(fof_simplification,[status(thm)],[c_0_590]) ).
fof(c_0_1861,plain,
! [X11,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4)) ) ),
inference(fof_simplification,[status(thm)],[c_0_591]) ).
fof(c_0_1862,plain,
! [X4,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ),
inference(fof_simplification,[status(thm)],[c_0_592]) ).
fof(c_0_1863,plain,
! [X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ),
inference(fof_simplification,[status(thm)],[c_0_593]) ).
fof(c_0_1864,axiom,
! [X6,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oabs__class_Oabs(X5,X6)))
<=> X6 != c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_594 ).
fof(c_0_1865,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),c_Nat_OSuc(X31)))
<=> X27 = X31 ) ),
c_0_595 ).
fof(c_0_1866,plain,
! [X27,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),c_Nat_OSuc(X31))) ),
inference(fof_simplification,[status(thm)],[c_0_596]) ).
fof(c_0_1867,axiom,
! [X6,X69,X70,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X70,X69),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X70,
c_0_597 ).
fof(c_0_1868,axiom,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X30))),
c_0_598 ).
fof(c_0_1869,axiom,
! [X30,X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X30))),
c_0_599 ).
fof(c_0_1870,axiom,
! [X30,X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29))),
c_0_600 ).
fof(c_0_1871,axiom,
! [X11,X4,X5] :
( ( class_Fields_Ofield__inverse__zero(X5)
& class_RealVector_Oreal__normed__field(X5) )
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X11)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)),c_RealVector_Onorm__class_Onorm(X5,X11)) ),
c_0_601 ).
fof(c_0_1872,axiom,
! [X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X29 ),
c_0_602 ).
fof(c_0_1873,axiom,
! [X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
=> X29 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
c_0_603 ).
fof(c_0_1874,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X27)),c_Nat_OSuc(X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27),X31)) ),
c_0_604 ).
fof(c_0_1875,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X31)),c_Nat_OSuc(X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ),
c_0_605 ).
fof(c_0_1876,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X30)),c_Nat_OSuc(X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ),
c_0_606 ).
fof(c_0_1877,axiom,
! [X12,X7,X5] :
( class_RealVector_Oreal__normed__div__algebra(X5)
=> c_Groups_Osgn__class_Osgn(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Osgn__class_Osgn(X5,X7)),c_Groups_Osgn__class_Osgn(X5,X12)) ),
c_0_607 ).
fof(c_0_1878,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Osgn__class_Osgn(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Osgn__class_Osgn(X5,X4)),c_Groups_Osgn__class_Osgn(X5,X11)) ),
c_0_608 ).
fof(c_0_1879,axiom,
! [X11,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X11)) ),
c_0_609 ).
fof(c_0_1880,axiom,
! [X4,X11,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X11)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)),c_RealVector_Onorm__class_Onorm(X5,X11)) ) ),
c_0_610 ).
fof(c_0_1881,axiom,
! [X33,X84,X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83),X84))
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X84,X83) = X33
<=> X84 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X83) ) ),
c_0_611 ).
fof(c_0_1882,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X10)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
c_0_612 ).
fof(c_0_1883,axiom,
! [X11,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)) = c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X11,X4)) ),
c_0_613 ).
fof(c_0_1884,axiom,
! [X11,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X11)) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X11,X4)) ),
c_0_614 ).
fof(c_0_1885,axiom,
! [X12,X7,X5] :
( class_RealVector_Oreal__normed__div__algebra(X5)
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),c_RealVector_Onorm__class_Onorm(X5,X12)) ),
c_0_615 ).
fof(c_0_1886,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10)) ),
c_0_616 ).
fof(c_0_1887,axiom,
! [X29,X4] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),X29) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),X4)),
c_0_617 ).
fof(c_0_1888,axiom,
! [X16,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14),X16))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16),X14))
=> X14 = X16 ) ),
c_0_618 ).
fof(c_0_1889,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> X30 = X29 ) ),
c_0_619 ).
fof(c_0_1890,axiom,
! [X16,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X16))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16),X14))
=> X14 = X16 ) ),
c_0_620 ).
fof(c_0_1891,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X7))) ),
c_0_621 ).
fof(c_0_1892,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X7))) ),
c_0_622 ).
fof(c_0_1893,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X7)),X7)) ),
c_0_623 ).
fof(c_0_1894,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X5,X10)))
<=> X10 != c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_624 ).
fof(c_0_1895,axiom,
! [X31,X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X27)),X31)) ),
c_0_625 ).
fof(c_0_1896,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X31)),X27))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27)) ),
c_0_626 ).
fof(c_0_1897,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X30)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ),
c_0_627 ).
fof(c_0_1898,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X30)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ),
c_0_628 ).
fof(c_0_1899,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X30)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ),
c_0_629 ).
fof(c_0_1900,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X30)),c_Nat_OSuc(X29))) ),
c_0_630 ).
fof(c_0_1901,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X7)),c_RComplete_Onatceiling(X12))) ),
c_0_631 ).
fof(c_0_1902,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X7)),c_RComplete_Onatfloor(X12))) ),
c_0_632 ).
fof(c_0_1903,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
=> ( X7 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X7 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
c_0_633 ).
fof(c_0_1904,axiom,
! [X29,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oabs__class_Oabs(X5,X4)),X29) ),
c_0_634 ).
fof(c_0_1905,axiom,
! [X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X53))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X53)) ),
c_0_635 ).
fof(c_0_1906,plain,
! [X29,X30] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29)) = X30 ),
inference(fof_simplification,[status(thm)],[c_0_636]) ).
fof(c_0_1907,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> ( c_Nat_OSuc(X30) != X29
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X30)),X29)) ) ),
c_0_637 ).
fof(c_0_1908,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X7))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
c_0_638 ).
fof(c_0_1909,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(X7))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
c_0_639 ).
fof(c_0_1910,plain,
! [X10,X9,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X9),X10))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> X10 = X9 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_640]) ).
fof(c_0_1911,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oord(X5)
=> ( X4 = X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X15)) ) ) ),
c_0_641 ).
fof(c_0_1912,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 = X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X4)) ) ) ),
c_0_642 ).
fof(c_0_1913,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oord(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11))
=> ( X11 = X15
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X15)) ) ) ),
c_0_643 ).
fof(c_0_1914,axiom,
! [X15,X4,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4))
=> ( X11 = X15
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X4)) ) ) ),
c_0_644 ).
fof(c_0_1915,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oord(X5)
=> ( X4 = X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X15)) ) ) ),
c_0_645 ).
fof(c_0_1916,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 = X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X4)) ) ) ),
c_0_646 ).
fof(c_0_1917,axiom,
! [X15,X11,X4,X5] :
( class_Orderings_Oord(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( X11 = X15
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X15)) ) ) ),
c_0_647 ).
fof(c_0_1918,axiom,
! [X15,X4,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> ( X11 = X15
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X4)) ) ) ),
c_0_648 ).
fof(c_0_1919,axiom,
! [X29,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Nat_OSuc(X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X29),
c_0_649 ).
fof(c_0_1920,axiom,
! [X29,X7,X5] :
( class_RealVector_Oreal__normed__div__algebra(X5)
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),X29) ),
c_0_650 ).
fof(c_0_1921,axiom,
! [X9,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
& X10 != X9 ) ) ),
c_0_651 ).
fof(c_0_1922,axiom,
! [X9,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
| X10 = X9 ) ) ),
c_0_652 ).
fof(c_0_1923,plain,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
<=> X10 = X9 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_653]) ).
fof(c_0_1924,axiom,
! [X11,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 != X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
c_0_654 ).
fof(c_0_1925,axiom,
! [X11,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 != X11
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4)) ) ) ),
c_0_655 ).
fof(c_0_1926,axiom,
! [X12,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
| X7 = X12 ) ) ),
c_0_656 ).
fof(c_0_1927,axiom,
! [X11,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X11))
=> ( X4 != X11
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X4),X11)) ) ) ),
c_0_657 ).
fof(c_0_1928,axiom,
! [X4,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X4))
=> ( X4 != X11
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X11),X4)) ) ) ),
c_0_658 ).
fof(c_0_1929,plain,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),c_Nat_OSuc(X29)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> X30 = c_Nat_OSuc(X29) ) ),
inference(fof_simplification,[status(thm)],[c_0_659]) ).
fof(c_0_1930,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),c_Nat_OSuc(X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
| X31 = c_Nat_OSuc(X27) ) ),
c_0_660 ).
fof(c_0_1931,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X30)),X29)) ),
c_0_661 ).
fof(c_0_1932,axiom,
! [X49,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Nat_OSuc(X49)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X49)) ),
c_0_662 ).
fof(c_0_1933,axiom,
! [X49,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X49)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Nat_OSuc(X49)) ),
c_0_663 ).
fof(c_0_1934,axiom,
! [X29,X4,X5] :
( class_Power_Opower(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X29)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29)) ),
c_0_664 ).
fof(c_0_1935,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),X27) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X31 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X27 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
c_0_665 ).
fof(c_0_1936,axiom,
! [X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12)) ) ),
c_0_666 ).
fof(c_0_1937,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),c_Nat_OSuc(X27)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
| X31 = X27 ) ),
c_0_667 ).
fof(c_0_1938,plain,
! [X31,X27] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),c_Nat_OSuc(X31)))
<=> X27 = X31 ) ),
inference(fof_simplification,[status(thm)],[c_0_668]) ).
fof(c_0_1939,plain,
! [X30,X29] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),c_Nat_OSuc(X30)))
=> X30 = X29 ) ),
inference(fof_simplification,[status(thm)],[c_0_669]) ).
fof(c_0_1940,plain,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),c_Nat_OSuc(X29)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> X30 = X29 ) ),
inference(fof_simplification,[status(thm)],[c_0_670]) ).
fof(c_0_1941,axiom,
! [X29,X30] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),c_RealDef_Oreal(tc_Nat_Onat,X29)),
c_0_671 ).
fof(c_0_1942,axiom,
! [X29,X30] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),c_RealDef_Oreal(tc_Nat_Onat,X29)),
c_0_672 ).
fof(c_0_1943,axiom,
! [X12,X7] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X7)),hAPP(c_Complex_OIm,X12)),
c_0_673 ).
fof(c_0_1944,axiom,
! [X12,X7] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X7),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X7)),hAPP(c_Complex_ORe,X12)),
c_0_674 ).
fof(c_0_1945,axiom,
! [X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
=> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_675 ).
fof(c_0_1946,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),c_Nat_OSuc(X27)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ),
c_0_676 ).
fof(c_0_1947,axiom,
! [X12,X7] : hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X7,X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X7),hAPP(c_Complex_OIm,X12)),
c_0_677 ).
fof(c_0_1948,axiom,
! [X12,X7] : hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X7,X12)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X7),hAPP(c_Complex_ORe,X12)),
c_0_678 ).
fof(c_0_1949,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X7)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7))),
c_0_679 ).
fof(c_0_1950,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),c_Nat_OSuc(X29))) ),
c_0_680 ).
fof(c_0_1951,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),c_Nat_OSuc(X29))) ),
c_0_681 ).
fof(c_0_1952,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),c_Nat_OSuc(X29))) ),
c_0_682 ).
fof(c_0_1953,axiom,
! [X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_683 ).
fof(c_0_1954,axiom,
! [X54,X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X53),X54))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53),X54))
& X53 != X54 ) ),
c_0_684 ).
fof(c_0_1955,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
& X31 != X27 ) ),
c_0_685 ).
fof(c_0_1956,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
| X31 = X27 ) ),
c_0_686 ).
fof(c_0_1957,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> ( X30 != X29
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29)) ) ),
c_0_687 ).
fof(c_0_1958,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),X9))
| X10 = X9 ) ),
c_0_688 ).
fof(c_0_1959,axiom,
! [X9,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9))
& X10 != X9 ) ),
c_0_689 ).
fof(c_0_1960,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),X12)) ),
c_0_690 ).
fof(c_0_1961,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ),
c_0_691 ).
fof(c_0_1962,axiom,
! [X29,X30] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
| X30 = X29 )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ),
c_0_692 ).
fof(c_0_1963,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X30)),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)),
c_0_693 ).
fof(c_0_1964,axiom,
! [X29,X30] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),X29) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X29)),
c_0_694 ).
fof(c_0_1965,axiom,
! [X29,X30] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),X29),
c_0_695 ).
fof(c_0_1966,plain,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(X5))) ),
inference(fof_simplification,[status(thm)],[c_0_696]) ).
fof(c_0_1967,plain,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(X5))) ),
inference(fof_simplification,[status(thm)],[c_0_697]) ).
fof(c_0_1968,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Groups_Osgn__class_Osgn(X5,X6) = c_Groups_Oone__class_Oone(X5)
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
c_0_698 ).
fof(c_0_1969,axiom,
! [X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> c_Groups_Osgn__class_Osgn(X5,X4) = c_Groups_Oone__class_Oone(X5) ) ),
c_0_699 ).
fof(c_0_1970,axiom,
! [X39,X33] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X39))
<=> ? [X8] : X39 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X8) ),
c_0_700 ).
fof(c_0_1971,axiom,
! [X27,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27))
<=> ? [X32] : X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32) ),
c_0_701 ).
fof(c_0_1972,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> c_Groups_Oabs__class_Oabs(X5,X4) = X4 ) ),
c_0_702 ).
fof(c_0_1973,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> c_Groups_Oabs__class_Oabs(X5,X4) = X4 ) ),
c_0_703 ).
fof(c_0_1974,axiom,
! [X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X4)),c_Groups_Oabs__class_Oabs(X5,X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4) ),
c_0_704 ).
fof(c_0_1975,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),c_Nat_OSuc(X29)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)),
c_0_705 ).
fof(c_0_1976,axiom,
! [X7,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12),X7))
=> c_Nat__Transfer_Otsub(X7,X12) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X12) ),
c_0_706 ).
fof(c_0_1977,plain,
! [X7,X12] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12),X7))
=> c_Nat__Transfer_Otsub(X7,X12) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X12) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12),X7))
=> c_Nat__Transfer_Otsub(X7,X12) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[c_0_707]) ).
fof(c_0_1978,axiom,
! [X27,X31,X33] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X33)),X27)
<=> X31 = X27 ),
c_0_708 ).
fof(c_0_1979,axiom,
! [X52,X21,X22,X6,X5] :
( class_Groups_Oab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X6,X22) = c_Groups_Ominus__class_Ominus(X5,X21,X52)
=> ( X6 = X22
<=> X21 = X52 ) ) ),
c_0_709 ).
fof(c_0_1980,axiom,
! [X29,X7] :
( X7 = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X7),X29)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X7)),X29) ),
c_0_710 ).
fof(c_0_1981,axiom,
! [X29,X30] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X29)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X30) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
c_0_711 ).
fof(c_0_1982,axiom,
! [X29,X30] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X30 = X29 ) ),
c_0_712 ).
fof(c_0_1983,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_713 ).
fof(c_0_1984,axiom,
! [X27,X31] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X27) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ),
c_0_714 ).
fof(c_0_1985,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_715 ).
fof(c_0_1986,plain,
! [X12,X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X7 != X12
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_716]) ).
fof(c_0_1987,axiom,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( X10 != X9
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X9),X10)) ) ) ),
c_0_717 ).
fof(c_0_1988,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
| X7 = X12
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ),
c_0_718 ).
fof(c_0_1989,plain,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( X7 != X12
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_719]) ).
fof(c_0_1990,plain,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> ( X7 != X12
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_720]) ).
fof(c_0_1991,axiom,
! [X15,X4,X11,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4)
=> X11 = X15 ) ),
c_0_721 ).
fof(c_0_1992,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Ocancel__ab__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)
=> X11 = X15 ) ),
c_0_722 ).
fof(c_0_1993,axiom,
! [X15,X11,X4,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15)
=> X11 = X15 ) ),
c_0_723 ).
fof(c_0_1994,axiom,
! [X21,X6,X22,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X6)
<=> X22 = X21 ) ),
c_0_724 ).
fof(c_0_1995,axiom,
! [X21,X22,X6,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X22) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21)
<=> X22 = X21 ) ),
c_0_725 ).
fof(c_0_1996,axiom,
! [X11,X4] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),c_Complex_Ocis(X11)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4,X11)),
c_0_726 ).
fof(c_0_1997,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X12),X7)) ) ),
c_0_727 ).
fof(c_0_1998,plain,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7)) ) ),
inference(fof_simplification,[status(thm)],[c_0_728]) ).
fof(c_0_1999,plain,
! [X7,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12)) ) ),
inference(fof_simplification,[status(thm)],[c_0_729]) ).
fof(c_0_2000,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7)) ) ),
c_0_730 ).
fof(c_0_2001,plain,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7)) ) ),
inference(fof_simplification,[status(thm)],[c_0_731]) ).
fof(c_0_2002,axiom,
! [X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X4),X11) = X4 ) ),
c_0_732 ).
fof(c_0_2003,axiom,
! [X4,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11),X11) = X4 ) ),
c_0_733 ).
fof(c_0_2004,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oabs__class_Oabs(X5,X4))) ),
c_0_734 ).
fof(c_0_2005,axiom,
! [X11,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11),X11) = X4 ),
c_0_735 ).
fof(c_0_2006,axiom,
! [X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_736 ).
fof(c_0_2007,axiom,
! [X11,X4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X4)),c_Complex_Ocis(X11)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X11)),
c_0_737 ).
fof(c_0_2008,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X29)))),
c_0_738 ).
fof(c_0_2009,axiom,
! [X11,X4] : c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X4),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X4)),c_Complex_Oexpi(X11)),
c_0_739 ).
fof(c_0_2010,plain,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X29)),X29)),
inference(fof_simplification,[status(thm)],[c_0_740]) ).
fof(c_0_2011,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X7),X12))
| X7 = X12
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X12),X7)) ),
c_0_741 ).
fof(c_0_2012,axiom,
! [X27,X31] :
( X31 != X27
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X27))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27),X31)) ) ),
c_0_742 ).
fof(c_0_2013,plain,
! [X12,X7] :
( X7 != X12
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12),X7)) ) ),
inference(fof_simplification,[status(thm)],[c_0_743]) ).
fof(c_0_2014,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X7))
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X7) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
c_0_744 ).
fof(c_0_2015,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X10))
=> ( c_Transcendental_Oln(X10) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X10 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
c_0_745 ).
fof(c_0_2016,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X30)),X29) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)),
c_0_746 ).
fof(c_0_2017,axiom,
! [X16,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16),X14)) ),
c_0_747 ).
fof(c_0_2018,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30)) ),
c_0_748 ).
fof(c_0_2019,axiom,
! [X16,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16),X14)) ),
c_0_749 ).
fof(c_0_2020,axiom,
! [X27,X31,X33] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)
<=> ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X31 = X27 ) ),
c_0_750 ).
fof(c_0_2021,axiom,
! [X22,X6,X21] :
( X21 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X22)
<=> X6 = X22 ) ),
c_0_751 ).
fof(c_0_2022,axiom,
! [X22,X6,X21] :
( X21 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X21)
<=> X6 = X22 ) ),
c_0_752 ).
fof(c_0_2023,axiom,
! [X27,X33,X31] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X33)
<=> ( X31 = X27
| X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_753 ).
fof(c_0_2024,axiom,
! [X27,X31,X33] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X27)
<=> ( X31 = X27
| X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_754 ).
fof(c_0_2025,axiom,
! [X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27))
<=> ? [X20] : X27 = c_Nat_OSuc(X20) ),
c_0_755 ).
fof(c_0_2026,axiom,
! [X14] : hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X14)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X14)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14)),
c_0_756 ).
fof(c_0_2027,axiom,
! [X14] : hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X14)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X14)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14)),
c_0_757 ).
fof(c_0_2028,axiom,
! [X22,X6,X21,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X21 != c_Groups_Ozero__class_Ozero(X5)
=> ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X22),X21)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21) = X22 ) ) ),
c_0_758 ).
fof(c_0_2029,axiom,
! [X6,X22,X21,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X21 != c_Groups_Ozero__class_Ozero(X5)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X22),X21) = X6
<=> X22 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21) ) ) ),
c_0_759 ).
fof(c_0_2030,axiom,
! [X4,X11,X15,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X15 != c_Groups_Ozero__class_Ozero(X5)
=> ( X11 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X15) = X4 ) ) ),
c_0_760 ).
fof(c_0_2031,axiom,
! [X11,X4,X15,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X15 != c_Groups_Ozero__class_Ozero(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X15) = X11
=> X4 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X15) ) ) ),
c_0_761 ).
fof(c_0_2032,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X5,X7))) ),
c_0_762 ).
fof(c_0_2033,axiom,
! [X27,X31,X33] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X27)
<=> X31 = X27 ),
c_0_763 ).
fof(c_0_2034,axiom,
! [X27,X33,X31] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X33)
<=> X31 = X27 ),
c_0_764 ).
fof(c_0_2035,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Nat_OSuc(X29)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)),
c_0_765 ).
fof(c_0_2036,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X7)))),
c_0_766 ).
fof(c_0_2037,axiom,
! [X30,X29] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X30)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_767 ).
fof(c_0_2038,axiom,
! [X27] :
( X27 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27)) ),
c_0_768 ).
fof(c_0_2039,axiom,
! [X29,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29),X29) = X30,
c_0_769 ).
fof(c_0_2040,axiom,
! [X30,X29] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X30),X29) = X30,
c_0_770 ).
fof(c_0_2041,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),c_Groups_Oabs__class_Oabs(X5,X4))) ),
c_0_771 ).
fof(c_0_2042,axiom,
! [X12,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> X7 != X12 ) ),
c_0_772 ).
fof(c_0_2043,axiom,
! [X12,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> X7 != X12 ) ),
c_0_773 ).
fof(c_0_2044,axiom,
! [X12,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> X12 != X7 ) ),
c_0_774 ).
fof(c_0_2045,axiom,
! [X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Osgn__class_Osgn(X5,X7)),c_Groups_Oabs__class_Oabs(X5,X7)) = X7 ),
c_0_775 ).
fof(c_0_2046,plain,
! [X7,X5] :
( class_Orderings_Opreorder(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_776]) ).
fof(c_0_2047,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_777 ).
fof(c_0_2048,axiom,
! [X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> c_RComplete_Onatfloor(X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_778 ).
fof(c_0_2049,axiom,
! [X27,X2] :
( c_SEQ_Osubseq(X2)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27),hAPP(X2,X27))) ),
c_0_779 ).
fof(c_0_2050,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X29))),
c_0_780 ).
fof(c_0_2051,axiom,
! [X27] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_781 ).
fof(c_0_2052,plain,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[c_0_782]) ).
fof(c_0_2053,plain,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[c_0_783]) ).
fof(c_0_2054,plain,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[c_0_784]) ).
fof(c_0_2055,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
c_0_785 ).
fof(c_0_2056,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oone__class_Oone(X5))) ),
c_0_786 ).
fof(c_0_2057,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oone__class_Oone(X5))) ),
c_0_787 ).
fof(c_0_2058,axiom,
! [X29,X30] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X29))
=> X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_788 ).
fof(c_0_2059,axiom,
! [X21,X5] :
( class_RealVector_Ometric__space(X5)
=> c_SEQ_Oconvergent(X5,c_COMBK(X5,tc_Nat_Onat,X21)) ),
c_0_789 ).
fof(c_0_2060,axiom,
! [X27,X6,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Omult__zero(X5)
& class_Rings_Ono__zero__divisors(X5)
& class_Rings_Ozero__neq__one(X5) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X27) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X6 = c_Groups_Ozero__class_Ozero(X5)
& X27 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
c_0_790 ).
fof(c_0_2061,axiom,
! [X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X30))
=> X30 != X29 ),
c_0_791 ).
fof(c_0_2062,axiom,
! [X36,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24),X36))
=> X24 != X36 ),
c_0_792 ).
fof(c_0_2063,axiom,
! [X105,X106,X13,X5] : hAPP(c_COMBK(X5,X13,X106),X105) = X106,
c_0_793 ).
fof(c_0_2064,axiom,
! [X95,X96,X101,X5] : c_Complex_Ocomplex_Ocomplex__case(X5,X101,c_Complex_Ocomplex_OComplex(X96,X95)) = hAPP(hAPP(X101,X96),X95),
c_0_794 ).
fof(c_0_2065,axiom,
! [X95,X96,X101,X5] : c_Complex_Ocomplex_Ocomplex__rec(X5,X101,c_Complex_Ocomplex_OComplex(X96,X95)) = hAPP(hAPP(X101,X96),X95),
c_0_795 ).
fof(c_0_2066,plain,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X29)),
inference(fof_simplification,[status(thm)],[c_0_796]) ).
fof(c_0_2067,plain,
! [X29] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),X29)),
inference(fof_simplification,[status(thm)],[c_0_797]) ).
fof(c_0_2068,axiom,
! [X29,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X30),c_Nat_OSuc(X29)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),
c_0_798 ).
fof(c_0_2069,axiom,
! [X29] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X29)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X29)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
c_0_799 ).
fof(c_0_2070,axiom,
! [X11,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X4) ),
c_0_800 ).
fof(c_0_2071,axiom,
! [X15,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X15),X4) ),
c_0_801 ).
fof(c_0_2072,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X30)),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Nat_OSuc(X29)),
c_0_802 ).
fof(c_0_2073,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(X7)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
c_0_803 ).
fof(c_0_2074,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(X7)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
c_0_804 ).
fof(c_0_2075,axiom,
! [X11,X4,X5] :
( class_Rings_Ono__zero__divisors(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11) = c_Groups_Ozero__class_Ozero(X5)
=> ( X4 = c_Groups_Ozero__class_Ozero(X5)
| X11 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
c_0_805 ).
fof(c_0_2076,axiom,
! [X11,X4,X5] :
( class_Rings_Ono__zero__divisors(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X11) != c_Groups_Ozero__class_Ozero(X5) ) ) ),
c_0_806 ).
fof(c_0_2077,axiom,
! [X22,X6,X5] :
( class_Rings_Oring__no__zero__divisors(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X22) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X6 = c_Groups_Ozero__class_Ozero(X5)
| X22 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
c_0_807 ).
fof(c_0_2078,axiom,
! [X6,X22,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X22 != c_Groups_Ozero__class_Ozero(X5)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X22) = c_Groups_Oone__class_Oone(X5)
<=> X6 = X22 ) ) ),
c_0_808 ).
fof(c_0_2079,axiom,
! [X22,X6,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X6,X22) = c_Groups_Ozero__class_Ozero(X5)
<=> X6 = X22 ) ),
c_0_809 ).
fof(c_0_2080,axiom,
! [X22,X6,X5] :
( class_Groups_Oab__group__add(X5)
=> ( X6 = X22
<=> c_Groups_Ominus__class_Ominus(X5,X6,X22) = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_810 ).
fof(c_0_2081,axiom,
! [X29,X4,X5] :
( class_Rings_Oring__1__no__zero__divisors(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X29) != c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_811 ).
fof(c_0_2082,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6) = c_Groups_Ozero__class_Ozero(X5)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_812 ).
fof(c_0_2083,axiom,
! [X6,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_813 ).
fof(c_0_2084,axiom,
! [X27,X31] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X27) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X31 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X27 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
c_0_814 ).
fof(c_0_2085,axiom,
! [X27,X31] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X27)
<=> ( ( X31 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X27 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
c_0_815 ).
fof(c_0_2086,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(X29))),
c_0_816 ).
fof(c_0_2087,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(X7))),
c_0_817 ).
fof(c_0_2088,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X7))),
c_0_818 ).
fof(c_0_2089,axiom,
! [X17,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),c_Groups_Osgn__class_Osgn(X5,X17)) ),
c_0_819 ).
fof(c_0_2090,axiom,
! [X6,X22,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X22 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X6)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_820 ).
fof(c_0_2091,axiom,
! [X31,X10] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X10),X31) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X10 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
c_0_821 ).
fof(c_0_2092,axiom,
hBOOL(hAPP(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_822 ).
fof(c_0_2093,axiom,
hBOOL(hAPP(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_823 ).
fof(c_0_2094,axiom,
hBOOL(hAPP(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_824 ).
fof(c_0_2095,axiom,
! [X12,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( X7 = X12
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X12)) ) ),
c_0_825 ).
fof(c_0_2096,axiom,
! [X27,X31] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X27) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X31 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X27 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
c_0_826 ).
fof(c_0_2097,axiom,
! [X16,X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),X14),
c_0_827 ).
fof(c_0_2098,axiom,
! [X16,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X14),
c_0_828 ).
fof(c_0_2099,axiom,
! [X16,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X14),
c_0_829 ).
fof(c_0_2100,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X30),
c_0_830 ).
fof(c_0_2101,axiom,
! [X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X30),
c_0_831 ).
fof(c_0_2102,axiom,
! [X29] :
( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)) ),
c_0_832 ).
fof(c_0_2103,axiom,
! [X4,X23] : hAPP(c_Complex_ORe,c_Complex_Orcis(X23,X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),c_Transcendental_Ocos(X4)),
c_0_833 ).
fof(c_0_2104,axiom,
! [X4,X23] : hAPP(c_Complex_OIm,c_Complex_Orcis(X23,X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),c_Transcendental_Osin(X4)),
c_0_834 ).
fof(c_0_2105,axiom,
! [X7,X5] :
( class_Orderings_Opreorder(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X7),X7)) ),
c_0_835 ).
fof(c_0_2106,axiom,
! [X29,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Osemiring__0(X5) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),c_Nat_OSuc(X29)) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_836 ).
fof(c_0_2107,axiom,
! [X29,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Osemiring__0(X5) )
=> ( ( X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),X29) = c_Groups_Oone__class_Oone(X5) )
& ( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),X29) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
c_0_837 ).
fof(c_0_2108,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),c_Nat_OSuc(X29))),
c_0_838 ).
fof(c_0_2109,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)),
c_0_839 ).
fof(c_0_2110,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)),
c_0_840 ).
fof(c_0_2111,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
c_0_841 ).
fof(c_0_2112,axiom,
! [X27,X31] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X27) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_842 ).
fof(c_0_2113,axiom,
! [X29,X30] :
( X30 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)
=> ( X29 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_843 ).
fof(c_0_2114,axiom,
! [X7] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X7) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X7),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7)),
c_0_844 ).
fof(c_0_2115,axiom,
! [X9,X10] :
( X10 = X9
<=> ( hAPP(c_Complex_ORe,X10) = hAPP(c_Complex_ORe,X9)
& hAPP(c_Complex_OIm,X10) = hAPP(c_Complex_OIm,X9) ) ),
c_0_845 ).
fof(c_0_2116,axiom,
! [X12,X7] :
( hAPP(c_Complex_ORe,X7) = hAPP(c_Complex_ORe,X12)
=> ( hAPP(c_Complex_OIm,X7) = hAPP(c_Complex_OIm,X12)
=> X7 = X12 ) ),
c_0_846 ).
fof(c_0_2117,axiom,
! [X12] :
( X12 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_847 ).
fof(c_0_2118,axiom,
! [X27,X31] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X27) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X31 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X27 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
c_0_848 ).
fof(c_0_2119,axiom,
! [X27,X31] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X27)
<=> ( X31 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X27 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
c_0_849 ).
fof(c_0_2120,axiom,
! [X27,X31] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X27) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
c_0_850 ).
fof(c_0_2121,axiom,
! [X29,X30] :
( X30 = X29
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X29)) ),
c_0_851 ).
fof(c_0_2122,axiom,
! [X5] :
( class_Power_Opower(X5)
=> c_Power_Opower__class_Opower(X5) = c_Power_Opower_Opower(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Otimes__class_Otimes(X5)) ),
c_0_852 ).
fof(c_0_2123,axiom,
! [X29,X30] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29) = X30
=> X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_853 ).
fof(c_0_2124,axiom,
! [X29] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X29) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_854 ).
fof(c_0_2125,axiom,
! [X16] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16),X16)),
c_0_855 ).
fof(c_0_2126,axiom,
! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X29)),
c_0_856 ).
fof(c_0_2127,axiom,
! [X16] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16),X16)),
c_0_857 ).
fof(c_0_2128,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_858 ).
fof(c_0_2129,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),c_Groups_Ozero__class_Ozero(X5)),X12) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_859 ).
fof(c_0_2130,axiom,
! [X29,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oone__class_Oone(X5)),X29) = c_Groups_Oone__class_Oone(X5) ),
c_0_860 ).
fof(c_0_2131,axiom,
! [X4,X5] :
( class_Rings_Omult__zero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_861 ).
fof(c_0_2132,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X12) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_862 ).
fof(c_0_2133,axiom,
! [X11,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X11) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_863 ).
fof(c_0_2134,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_864 ).
fof(c_0_2135,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
c_0_865 ).
fof(c_0_2136,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
c_0_866 ).
fof(c_0_2137,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
c_0_867 ).
fof(c_0_2138,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = X4 ),
c_0_868 ).
fof(c_0_2139,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = X4 ),
c_0_869 ).
fof(c_0_2140,axiom,
! [X4,X5] :
( class_Groups_Omonoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X4) = X4 ),
c_0_870 ).
fof(c_0_2141,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> ( ( X4 = c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X4) = c_Groups_Ozero__class_Ozero(X5) )
& ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X4) = c_Groups_Oone__class_Oone(X5) ) ) ),
c_0_871 ).
fof(c_0_2142,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Odiv(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_872 ).
fof(c_0_2143,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Odiv(X5,c_Groups_Ozero__class_Ozero(X5),X4) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_873 ).
fof(c_0_2144,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,X4,X4) = c_Groups_Oone__class_Oone(X5) ) ),
c_0_874 ).
fof(c_0_2145,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_875 ).
fof(c_0_2146,axiom,
! [X4,X5] :
( class_Rings_Omult__zero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_876 ).
fof(c_0_2147,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_877 ).
fof(c_0_2148,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_878 ).
fof(c_0_2149,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_879 ).
fof(c_0_2150,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),X4) = c_Groups_Oone__class_Oone(X5) ) ),
c_0_880 ).
fof(c_0_2151,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Odiv(X5,X4,c_Groups_Oone__class_Oone(X5)) = X4 ),
c_0_881 ).
fof(c_0_2152,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
c_0_882 ).
fof(c_0_2153,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
c_0_883 ).
fof(c_0_2154,axiom,
! [X4,X5] :
( class_Power_Opower(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5) ),
c_0_884 ).
fof(c_0_2155,axiom,
! [X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5) ),
c_0_885 ).
fof(c_0_2156,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
c_0_886 ).
fof(c_0_2157,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
c_0_887 ).
fof(c_0_2158,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
c_0_888 ).
fof(c_0_2159,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = X4 ),
c_0_889 ).
fof(c_0_2160,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = X4 ),
c_0_890 ).
fof(c_0_2161,axiom,
! [X4,X5] :
( class_Groups_Omonoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = X4 ),
c_0_891 ).
fof(c_0_2162,axiom,
! [X30] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X30,
c_0_892 ).
fof(c_0_2163,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X4,X4) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_893 ).
fof(c_0_2164,axiom,
! [X4] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X4),c_Transcendental_Osin(X4))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_894 ).
fof(c_0_2165,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4 ),
c_0_895 ).
fof(c_0_2166,axiom,
! [X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X7 ),
c_0_896 ).
fof(c_0_2167,axiom,
! [X29] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X29),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X29,
c_0_897 ).
fof(c_0_2168,axiom,
! [X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Osgn__class_Osgn(X5,c_Groups_Osgn__class_Osgn(X5,X4)) = c_Groups_Osgn__class_Osgn(X5,X4) ),
c_0_898 ).
fof(c_0_2169,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Oabs__class_Oabs(X5,X4)) = c_Groups_Oabs__class_Oabs(X5,X4) ),
c_0_899 ).
fof(c_0_2170,axiom,
! [X14] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X14),hAPP(c_Complex_OIm,X14)) = X14,
c_0_900 ).
fof(c_0_2171,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4)) = c_RealVector_Onorm__class_Onorm(X5,X4) ),
c_0_901 ).
fof(c_0_2172,axiom,
! [X4] :
( X4 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X4) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
c_0_902 ).
fof(c_0_2173,axiom,
! [X11] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_903 ).
fof(c_0_2174,axiom,
! [X29] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_904 ).
fof(c_0_2175,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( ( X7 = c_Groups_Ozero__class_Ozero(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Osgn__class_Osgn(X5,X7)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X7 != c_Groups_Ozero__class_Ozero(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Osgn__class_Osgn(X5,X7)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
c_0_905 ).
fof(c_0_2176,axiom,
! [X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X30,
c_0_906 ).
fof(c_0_2177,axiom,
! [X29] : c_Nat_OSuc(X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X29),
c_0_907 ).
fof(c_0_2178,axiom,
! [X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_908 ).
fof(c_0_2179,axiom,
! [X29] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_909 ).
fof(c_0_2180,axiom,
! [X25] :
( c_SEQ_OBseq(tc_RealDef_Oreal,X25)
=> ( c_SEQ_Omonoseq(tc_RealDef_Oreal,X25)
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,X25) ) ),
c_0_910 ).
fof(c_0_2181,axiom,
! [X29] : c_Nat_OSuc(X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
c_0_911 ).
fof(c_0_2182,axiom,
! [X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14) = X14,
c_0_912 ).
fof(c_0_2183,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14) = X14,
c_0_913 ).
fof(c_0_2184,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X14) = X14,
c_0_914 ).
fof(c_0_2185,axiom,
! [X29] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X29) = X29,
c_0_915 ).
fof(c_0_2186,axiom,
! [X29] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29) = X29,
c_0_916 ).
fof(c_0_2187,axiom,
! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_917 ).
fof(c_0_2188,axiom,
! [X4,X23] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X23,X4)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23),
c_0_918 ).
fof(c_0_2189,axiom,
! [X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X14,
c_0_919 ).
fof(c_0_2190,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X14,
c_0_920 ).
fof(c_0_2191,axiom,
! [X29] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X29,
c_0_921 ).
fof(c_0_2192,axiom,
! [X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X30,
c_0_922 ).
fof(c_0_2193,axiom,
! [X7] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X7)) = c_RealDef_Oreal(tc_Nat_Onat,X7),
c_0_923 ).
fof(c_0_2194,axiom,
! [X93,X94,X95,X96] :
( c_Complex_Ocomplex_OComplex(X96,X95) = c_Complex_Ocomplex_OComplex(X94,X93)
<=> ( X96 = X94
& X95 = X93 ) ),
c_0_924 ).
fof(c_0_2195,axiom,
! [X43,X5] :
( class_Groups_Ozero(X5)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X5,X43) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X43 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ),
c_0_925 ).
fof(c_0_2196,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Odecseq(X5,X25)
=> c_SEQ_Omonoseq(X5,X25) ) ),
c_0_926 ).
fof(c_0_2197,axiom,
! [X25,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Oincseq(X5,X25)
=> c_SEQ_Omonoseq(X5,X25) ) ),
c_0_927 ).
fof(c_0_2198,axiom,
! [X31,X27] :
( c_RealDef_Oreal(tc_Nat_Onat,X27) = c_RealDef_Oreal(tc_Nat_Onat,X31)
<=> X27 = X31 ),
c_0_928 ).
fof(c_0_2199,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Groups_Osgn__class_Osgn(X5,X10) = c_Groups_Ozero__class_Ozero(X5)
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_929 ).
fof(c_0_2200,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Groups_Osgn__class_Osgn(X5,X6) = c_Groups_Ozero__class_Ozero(X5)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_930 ).
fof(c_0_2201,axiom,
! [X6,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Groups_Oabs__class_Oabs(X5,X6) = c_Groups_Ozero__class_Ozero(X5)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_931 ).
fof(c_0_2202,axiom,
! [X99,X100] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X100,X99)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_932 ).
fof(c_0_2203,axiom,
! [X12,X7] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X7,X12)) = X7,
c_0_933 ).
fof(c_0_2204,axiom,
! [X12,X7] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X7,X12)) = X12,
c_0_934 ).
fof(c_0_2205,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_RealVector_Onorm__class_Onorm(X5,X10) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_935 ).
fof(c_0_2206,axiom,
! [X104,X103] :
( class_Orderings_Oord(X103)
=> class_Orderings_Oord(tc_fun(X104,X103)) ),
c_0_936 ).
fof(c_0_2207,axiom,
! [X104,X103] :
( class_Orderings_Oorder(X103)
=> class_Orderings_Oorder(tc_fun(X104,X103)) ),
c_0_937 ).
fof(c_0_2208,axiom,
! [X104,X103] :
( class_Orderings_Opreorder(X103)
=> class_Orderings_Opreorder(tc_fun(X104,X103)) ),
c_0_938 ).
fof(c_0_2209,axiom,
! [X99,X100] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(X100,X99)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_939 ).
fof(c_0_2210,axiom,
! [X7] :
( c_Transcendental_Osin(X7) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X7)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
c_0_940 ).
fof(c_0_2211,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> c_Groups_Osgn__class_Osgn(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(X5) ),
c_0_941 ).
fof(c_0_2212,axiom,
! [X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Groups_Osgn__class_Osgn(X5,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_942 ).
fof(c_0_2213,axiom,
! [X5] :
( class_Groups_Osgn__if(X5)
=> c_Groups_Osgn__class_Osgn(X5,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_943 ).
fof(c_0_2214,axiom,
! [X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(X5) ),
c_0_944 ).
fof(c_0_2215,axiom,
! [X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
c_0_945 ).
fof(c_0_2216,axiom,
! [X27] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X27)),
c_0_946 ).
fof(c_0_2217,axiom,
! [X4] : c_Complex_Ocis(X4) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X4),c_Transcendental_Osin(X4)),
c_0_947 ).
fof(c_0_2218,axiom,
! [X22,X6] :
( c_Complex_Ocomplex_OComplex(X6,X22) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
<=> ( X6 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
& X22 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
c_0_948 ).
fof(c_0_2219,axiom,
! [X22,X6] :
( c_Complex_Ocomplex_OComplex(X6,X22) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
<=> ( X6 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X22 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
c_0_949 ).
fof(c_0_2220,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
c_0_950 ).
fof(c_0_2221,axiom,
! [X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_951 ).
fof(c_0_2222,axiom,
! [X29] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X29)) = X29,
c_0_952 ).
fof(c_0_2223,axiom,
! [X29] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X29)) = X29,
c_0_953 ).
fof(c_0_2224,axiom,
! [X27] :
( c_RealDef_Oreal(tc_Nat_Onat,X27) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_954 ).
fof(c_0_2225,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_955 ).
fof(c_0_2226,axiom,
! [X9,X10] :
( c_Complex_Ocomplex_OComplex(X10,X9) = c_Complex_Oii
<=> ( X10 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X9 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
c_0_956 ).
fof(c_0_2227,axiom,
! [X23] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X23) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23),
c_0_957 ).
fof(c_0_2228,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
c_0_958 ).
fof(c_0_2229,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
c_0_959 ).
fof(c_0_2230,axiom,
! [X4] : hAPP(c_Complex_ORe,c_Complex_Ocis(X4)) = c_Transcendental_Ocos(X4),
c_0_960 ).
fof(c_0_2231,axiom,
! [X4] : hAPP(c_Complex_OIm,c_Complex_Ocis(X4)) = c_Transcendental_Osin(X4),
c_0_961 ).
fof(c_0_2232,axiom,
! [X4] : c_Complex_Ocis(X4) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4),
c_0_962 ).
fof(c_0_2233,axiom,
! [X10,X5] :
( class_Groups_Oone(X5)
=> ( c_Groups_Oone__class_Oone(X5) = X10
<=> X10 = c_Groups_Oone__class_Oone(X5) ) ),
c_0_963 ).
fof(c_0_2234,axiom,
! [X10,X5] :
( class_Groups_Ozero(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = X10
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
c_0_964 ).
fof(c_0_2235,axiom,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
c_0_965 ).
fof(c_0_2236,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Oone__class_Oone(X5) != c_Groups_Ozero__class_Ozero(X5) ),
c_0_966 ).
fof(c_0_2237,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Ozero__class_Ozero(X5) != c_Groups_Oone__class_Oone(X5) ),
c_0_967 ).
fof(c_0_2238,axiom,
! [X4] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_968 ).
fof(c_0_2239,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_969 ).
fof(c_0_2240,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_970 ).
fof(c_0_2241,axiom,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_971 ).
fof(c_0_2242,axiom,
hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_972 ).
fof(c_0_2243,axiom,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_973 ).
fof(c_0_2244,axiom,
hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_974 ).
fof(c_0_2245,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Groups_Oone(tc_Polynomial_Opoly(X103)) ),
c_0_975 ).
fof(c_0_2246,axiom,
! [X103] :
( class_Rings_Ocomm__ring(X103)
=> class_Rings_Oring(tc_Polynomial_Opoly(X103)) ),
c_0_976 ).
fof(c_0_2247,axiom,
! [X103] :
( class_Groups_Ozero(X103)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X103)) ),
c_0_977 ).
fof(c_0_2248,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Power_Opower(tc_Polynomial_Opoly(X103)) ),
c_0_978 ).
fof(c_0_2249,axiom,
! [X103] :
( class_Rings_Ocomm__ring__1(X103)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X103)) ),
c_0_979 ).
fof(c_0_2250,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Osgn__if(tc_Polynomial_Opoly(X103)) ),
c_0_980 ).
fof(c_0_2251,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X103)) ),
c_0_981 ).
fof(c_0_2252,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X103)) ),
c_0_982 ).
fof(c_0_2253,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X103)) ),
c_0_983 ).
fof(c_0_2254,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X103)) ),
c_0_984 ).
fof(c_0_2255,axiom,
! [X103] :
( class_Groups_Oab__group__add(X103)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X103)) ),
c_0_985 ).
fof(c_0_2256,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X103)) ),
c_0_986 ).
fof(c_0_2257,axiom,
! [X103] :
( class_Groups_Ocomm__monoid__add(X103)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X103)) ),
c_0_987 ).
fof(c_0_2258,axiom,
! [X103] :
( class_Rings_Ocomm__ring__1(X103)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X103)) ),
c_0_988 ).
fof(c_0_2259,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X103)) ),
c_0_989 ).
fof(c_0_2260,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X103)) ),
c_0_990 ).
fof(c_0_2261,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X103)) ),
c_0_991 ).
fof(c_0_2262,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X103)) ),
c_0_992 ).
fof(c_0_2263,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X103)) ),
c_0_993 ).
fof(c_0_2264,axiom,
! [X103] :
( class_Groups_Oab__group__add(X103)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X103)) ),
c_0_994 ).
fof(c_0_2265,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X103)) ),
c_0_995 ).
fof(c_0_2266,axiom,
! [X103] :
( class_Fields_Ofield(X103)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X103)) ),
c_0_996 ).
fof(c_0_2267,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X103)) ),
c_0_997 ).
fof(c_0_2268,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X103)) ),
c_0_998 ).
fof(c_0_2269,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X103)) ),
c_0_999 ).
fof(c_0_2270,axiom,
! [X103] :
( class_Groups_Ocomm__monoid__add(X103)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X103)) ),
c_0_1000 ).
fof(c_0_2271,axiom,
! [X103] :
( class_Rings_Oidom(X103)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X103)) ),
c_0_1001 ).
fof(c_0_2272,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X103)) ),
c_0_1002 ).
fof(c_0_2273,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X103)) ),
c_0_1003 ).
fof(c_0_2274,axiom,
! [X103] :
( class_Groups_Ocomm__monoid__add(X103)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X103)) ),
c_0_1004 ).
fof(c_0_2275,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__1(X103)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X103)) ),
c_0_1005 ).
fof(c_0_2276,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X103)) ),
c_0_1006 ).
fof(c_0_2277,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X103)) ),
c_0_1007 ).
fof(c_0_2278,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X103)) ),
c_0_1008 ).
fof(c_0_2279,axiom,
! [X103] :
( class_Groups_Ocancel__comm__monoid__add(X103)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X103)) ),
c_0_1009 ).
fof(c_0_2280,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X103)) ),
c_0_1010 ).
fof(c_0_2281,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X103)) ),
c_0_1011 ).
fof(c_0_2282,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X103)) ),
c_0_1012 ).
fof(c_0_2283,axiom,
! [X103] :
( class_Rings_Oidom(X103)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X103)) ),
c_0_1013 ).
fof(c_0_2284,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X103)) ),
c_0_1014 ).
fof(c_0_2285,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X103)) ),
c_0_1015 ).
fof(c_0_2286,axiom,
! [X103] :
( class_Rings_Oidom(X103)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X103)) ),
c_0_1016 ).
fof(c_0_2287,axiom,
! [X103] :
( class_Groups_Ocancel__comm__monoid__add(X103)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X103)) ),
c_0_1017 ).
fof(c_0_2288,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X103)) ),
c_0_1018 ).
fof(c_0_2289,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X103)) ),
c_0_1019 ).
fof(c_0_2290,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X103)) ),
c_0_1020 ).
fof(c_0_2291,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X103)) ),
c_0_1021 ).
fof(c_0_2292,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X103)) ),
c_0_1022 ).
fof(c_0_2293,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X103)) ),
c_0_1023 ).
fof(c_0_2294,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X103)) ),
c_0_1024 ).
fof(c_0_2295,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X103)) ),
c_0_1025 ).
fof(c_0_2296,axiom,
! [X103] :
( class_Rings_Olinordered__idom(X103)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X103)) ),
c_0_1026 ).
fof(c_0_2297,axiom,
! [X103] :
( class_Rings_Oidom(X103)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X103)) ),
c_0_1027 ).
fof(c_0_2298,axiom,
! [X103] :
( class_Rings_Ocomm__ring(X103)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X103)) ),
c_0_1028 ).
fof(c_0_2299,axiom,
! [X103] :
( class_Rings_Ocomm__semiring__0(X103)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X103)) ),
c_0_1029 ).
fof(c_0_2300,axiom,
! [X103] :
( class_Groups_Ocancel__comm__monoid__add(X103)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X103)) ),
c_0_1030 ).
fof(c_0_2301,axiom,
! [X103] :
( class_Rings_Oidom(X103)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X103)) ),
c_0_1031 ).
fof(c_0_2302,axiom,
! [X7] :
( c_Transcendental_Ocos(X7) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
=> c_Transcendental_Osin(X7) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_1032 ).
fof(c_0_2303,axiom,
! [X80,X81] :
( c_Nat_OSuc(X81) = c_Nat_OSuc(X80)
<=> X81 = X80 ),
c_0_1033 ).
fof(c_0_2304,axiom,
! [X12,X7] :
( c_Nat_OSuc(X7) = c_Nat_OSuc(X12)
=> X7 = X12 ),
c_0_1034 ).
fof(c_0_2305,axiom,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_1035 ).
fof(c_0_2306,axiom,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_1036 ).
fof(c_0_2307,axiom,
! [X30] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X30),
c_0_1037 ).
fof(c_0_2308,axiom,
! [X79] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X79),
c_0_1038 ).
fof(c_0_2309,axiom,
! [X30] : c_Nat_OSuc(X30) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_1039 ).
fof(c_0_2310,axiom,
! [X78] : c_Nat_OSuc(X78) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_1040 ).
fof(c_0_2311,axiom,
! [X30] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X30),
c_0_1041 ).
fof(c_0_2312,axiom,
! [X30] : c_Nat_OSuc(X30) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_1042 ).
fof(c_0_2313,axiom,
c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_1043 ).
fof(c_0_2314,axiom,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_1044 ).
fof(c_0_2315,axiom,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_1045 ).
fof(c_0_2316,axiom,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_1046 ).
fof(c_0_2317,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_1047 ).
fof(c_0_2318,axiom,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
c_0_1048 ).
fof(c_0_2319,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_1049 ).
fof(c_0_2320,axiom,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
c_0_1050 ).
fof(c_0_2321,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_1051 ).
fof(c_0_2322,axiom,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_1052 ).
fof(c_0_2323,axiom,
! [X29] : X29 != c_Nat_OSuc(X29),
c_0_1053 ).
fof(c_0_2324,axiom,
! [X29] : c_Nat_OSuc(X29) != X29,
c_0_1054 ).
fof(c_0_2325,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
c_0_1055 ).
fof(c_0_2326,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_1056 ).
fof(c_0_2327,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_1057 ).
fof(c_0_2328,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_1058 ).
fof(c_0_2329,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
c_0_1059 ).
fof(c_0_2330,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
c_0_1060 ).
fof(c_0_2331,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
c_0_1061 ).
fof(c_0_2332,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_1062 ).
fof(c_0_2333,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
c_0_1063 ).
fof(c_0_2334,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
c_0_1064 ).
fof(c_0_2335,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
c_0_1065 ).
fof(c_0_2336,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
c_0_1066 ).
fof(c_0_2337,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
c_0_1067 ).
fof(c_0_2338,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
c_0_1068 ).
fof(c_0_2339,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
c_0_1069 ).
fof(c_0_2340,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_1070 ).
fof(c_0_2341,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
c_0_1071 ).
fof(c_0_2342,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_1072 ).
fof(c_0_2343,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
c_0_1073 ).
fof(c_0_2344,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_1074 ).
fof(c_0_2345,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
c_0_1075 ).
fof(c_0_2346,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
c_0_1076 ).
fof(c_0_2347,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_1077 ).
fof(c_0_2348,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_1078 ).
fof(c_0_2349,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_1079 ).
fof(c_0_2350,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_1080 ).
fof(c_0_2351,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_1081 ).
fof(c_0_2352,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
c_0_1082 ).
fof(c_0_2353,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_1083 ).
fof(c_0_2354,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
c_0_1084 ).
fof(c_0_2355,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_1085 ).
fof(c_0_2356,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_1086 ).
fof(c_0_2357,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
c_0_1087 ).
fof(c_0_2358,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
c_0_1088 ).
fof(c_0_2359,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_1089 ).
fof(c_0_2360,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_1090 ).
fof(c_0_2361,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_1091 ).
fof(c_0_2362,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
c_0_1092 ).
fof(c_0_2363,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
c_0_1093 ).
fof(c_0_2364,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
c_0_1094 ).
fof(c_0_2365,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
c_0_1095 ).
fof(c_0_2366,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
c_0_1096 ).
fof(c_0_2367,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
c_0_1097 ).
fof(c_0_2368,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
c_0_1098 ).
fof(c_0_2369,axiom,
class_Power_Opower(tc_RealDef_Oreal),
c_0_1099 ).
fof(c_0_2370,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
c_0_1100 ).
fof(c_0_2371,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
c_0_1101 ).
fof(c_0_2372,axiom,
class_Groups_Osgn__if(tc_RealDef_Oreal),
c_0_1102 ).
fof(c_0_2373,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
c_0_1103 ).
fof(c_0_2374,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
c_0_1104 ).
fof(c_0_2375,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
c_0_1105 ).
fof(c_0_2376,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
c_0_1106 ).
fof(c_0_2377,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
c_0_1107 ).
fof(c_0_2378,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
c_0_1108 ).
fof(c_0_2379,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
c_0_1109 ).
fof(c_0_2380,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
c_0_1110 ).
fof(c_0_2381,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
c_0_1111 ).
fof(c_0_2382,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
c_0_1112 ).
fof(c_0_2383,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
c_0_1113 ).
fof(c_0_2384,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
c_0_1114 ).
fof(c_0_2385,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
c_0_1115 ).
fof(c_0_2386,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
c_0_1116 ).
fof(c_0_2387,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
c_0_1117 ).
fof(c_0_2388,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
c_0_1118 ).
fof(c_0_2389,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
c_0_1119 ).
fof(c_0_2390,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
c_0_1120 ).
fof(c_0_2391,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
c_0_1121 ).
fof(c_0_2392,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
c_0_1122 ).
fof(c_0_2393,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
c_0_1123 ).
fof(c_0_2394,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
c_0_1124 ).
fof(c_0_2395,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
c_0_1125 ).
fof(c_0_2396,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
c_0_1126 ).
fof(c_0_2397,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
c_0_1127 ).
fof(c_0_2398,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
c_0_1128 ).
fof(c_0_2399,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
c_0_1129 ).
fof(c_0_2400,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
c_0_1130 ).
fof(c_0_2401,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
c_0_1131 ).
fof(c_0_2402,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
c_0_1132 ).
fof(c_0_2403,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
c_0_1133 ).
fof(c_0_2404,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
c_0_1134 ).
fof(c_0_2405,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
c_0_1135 ).
fof(c_0_2406,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
c_0_1136 ).
fof(c_0_2407,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
c_0_1137 ).
fof(c_0_2408,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
c_0_1138 ).
fof(c_0_2409,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
c_0_1139 ).
fof(c_0_2410,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
c_0_1140 ).
fof(c_0_2411,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
c_0_1141 ).
fof(c_0_2412,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
c_0_1142 ).
fof(c_0_2413,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
c_0_1143 ).
fof(c_0_2414,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
c_0_1144 ).
fof(c_0_2415,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_1145 ).
fof(c_0_2416,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
c_0_1146 ).
fof(c_0_2417,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
c_0_1147 ).
fof(c_0_2418,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
c_0_1148 ).
fof(c_0_2419,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
c_0_1149 ).
fof(c_0_2420,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
c_0_1150 ).
fof(c_0_2421,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
c_0_1151 ).
fof(c_0_2422,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
c_0_1152 ).
fof(c_0_2423,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
c_0_1153 ).
fof(c_0_2424,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
c_0_1154 ).
fof(c_0_2425,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
c_0_1155 ).
fof(c_0_2426,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
c_0_1156 ).
fof(c_0_2427,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
c_0_1157 ).
fof(c_0_2428,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
c_0_1158 ).
fof(c_0_2429,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_1159 ).
fof(c_0_2430,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
c_0_1160 ).
fof(c_0_2431,axiom,
class_Orderings_Oord(tc_HOL_Obool),
c_0_1161 ).
fof(c_0_2432,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
c_0_1162 ).
fof(c_0_2433,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
c_0_1163 ).
fof(c_0_2434,axiom,
class_Groups_Oone(tc_Nat_Onat),
c_0_1164 ).
fof(c_0_2435,axiom,
class_Groups_Ozero(tc_Nat_Onat),
c_0_1165 ).
fof(c_0_2436,axiom,
class_Power_Opower(tc_Nat_Onat),
c_0_1166 ).
fof(c_0_2437,axiom,
class_Orderings_Oord(tc_Nat_Onat),
c_0_1167 ).
fof(c_0_2438,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
c_0_1168 ).
fof(c_0_2439,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
c_0_1169 ).
fof(c_0_2440,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
c_0_1170 ).
fof(c_0_2441,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
c_0_1171 ).
fof(c_0_2442,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
c_0_1172 ).
fof(c_0_2443,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
c_0_1173 ).
fof(c_0_2444,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
c_0_1174 ).
fof(c_0_2445,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
c_0_1175 ).
fof(c_0_2446,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
c_0_1176 ).
fof(c_0_2447,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
c_0_1177 ).
fof(c_0_2448,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
c_0_1178 ).
fof(c_0_2449,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
c_0_1179 ).
fof(c_0_2450,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
c_0_1180 ).
fof(c_0_2451,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
c_0_1181 ).
fof(c_0_2452,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
c_0_1182 ).
fof(c_0_2453,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
c_0_1183 ).
fof(c_0_2454,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
c_0_1184 ).
fof(c_0_2455,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
c_0_1185 ).
fof(c_0_2456,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
c_0_1186 ).
fof(c_0_2457,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
c_0_1187 ).
fof(c_0_2458,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
c_0_1188 ).
fof(c_0_2459,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
c_0_1189 ).
fof(c_0_2460,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
c_0_1190 ).
fof(c_0_2461,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
c_0_1191 ).
fof(c_0_2462,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
c_0_1192 ).
fof(c_0_2463,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
c_0_1193 ).
fof(c_0_2464,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
c_0_1194 ).
fof(c_0_2465,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
c_0_1195 ).
fof(c_0_2466,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
c_0_1196 ).
fof(c_0_2467,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
c_0_1197 ).
fof(c_0_2468,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
c_0_1198 ).
fof(c_0_2469,axiom,
class_Groups_Oone(tc_Int_Oint),
c_0_1199 ).
fof(c_0_2470,axiom,
class_Rings_Oring(tc_Int_Oint),
c_0_1200 ).
fof(c_0_2471,axiom,
class_Groups_Ozero(tc_Int_Oint),
c_0_1201 ).
fof(c_0_2472,axiom,
class_Power_Opower(tc_Int_Oint),
c_0_1202 ).
fof(c_0_2473,axiom,
class_Rings_Oring__1(tc_Int_Oint),
c_0_1203 ).
fof(c_0_2474,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
c_0_1204 ).
fof(c_0_2475,axiom,
class_Orderings_Oord(tc_Int_Oint),
c_0_1205 ).
fof(c_0_2476,axiom,
class_Rings_Osemiring(tc_Int_Oint),
c_0_1206 ).
fof(c_0_2477,axiom,
class_Orderings_Oorder(tc_Int_Oint),
c_0_1207 ).
fof(c_0_2478,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
c_0_1208 ).
fof(c_0_2479,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
c_0_1209 ).
fof(c_0_2480,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
c_0_1210 ).
fof(c_0_2481,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
c_0_1211 ).
fof(c_0_2482,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
c_0_1212 ).
fof(c_0_2483,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
c_0_1213 ).
fof(c_0_2484,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
c_0_1214 ).
fof(c_0_2485,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
c_0_1215 ).
fof(c_0_2486,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
c_0_1216 ).
fof(c_0_2487,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
c_0_1217 ).
fof(c_0_2488,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
c_0_1218 ).
fof(c_0_2489,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
c_0_1219 ).
fof(c_0_2490,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
c_0_1220 ).
fof(c_0_2491,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
c_0_1221 ).
fof(c_0_2492,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
c_0_1222 ).
fof(c_0_2493,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
c_0_1223 ).
fof(c_0_2494,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
c_0_1224 ).
fof(c_0_2495,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
c_0_1225 ).
fof(c_0_2496,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
c_0_1226 ).
fof(c_0_2497,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
c_0_1227 ).
fof(c_0_2498,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
c_0_1228 ).
fof(c_0_2499,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
c_0_1229 ).
fof(c_0_2500,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
c_0_1230 ).
fof(c_0_2501,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
c_0_1231 ).
fof(c_0_2502,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
c_0_1232 ).
fof(c_0_2503,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
c_0_1233 ).
fof(c_0_2504,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
c_0_1234 ).
fof(c_0_2505,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
c_0_1235 ).
fof(c_0_2506,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
c_0_1236 ).
fof(c_0_2507,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
c_0_1237 ).
fof(c_0_2508,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
c_0_1238 ).
fof(c_0_2509,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
c_0_1239 ).
fof(c_0_2510,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
c_0_1240 ).
fof(c_0_2511,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
c_0_1241 ).
fof(c_0_2512,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
c_0_1242 ).
fof(c_0_2513,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
c_0_1243 ).
fof(c_0_2514,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
c_0_1244 ).
fof(c_0_2515,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
c_0_1245 ).
fof(c_0_2516,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
c_0_1246 ).
fof(c_0_2517,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
c_0_1247 ).
fof(c_0_2518,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
c_0_1248 ).
fof(c_0_2519,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
c_0_1249 ).
fof(c_0_2520,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
c_0_1250 ).
fof(c_0_2521,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
c_0_1251 ).
fof(c_0_2522,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
c_0_1252 ).
fof(c_0_2523,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
c_0_1253 ).
fof(c_0_2524,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
c_0_1254 ).
fof(c_0_2525,axiom,
class_Rings_Oidom(tc_Int_Oint),
c_0_1255 ).
fof(c_0_2526,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
c_0_1256 ).
fof(c_0_2527,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
c_0_1257 ).
fof(c_0_2528,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
c_0_1258 ).
fof(c_0_2529,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
c_0_1259 ).
fof(c_0_2530,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
c_0_1260 ).
fof(c_0_2531,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
c_0_1261 ).
fof(c_0_2532,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
c_0_1262 ).
fof(c_0_2533,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_1263 ).
fof(c_0_2534,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_1264 ).
fof(c_0_2535,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
c_0_1265 ).
fof(c_0_2536,axiom,
c_SEQ_Osubseq(v_ga____),
c_0_1266 ).
fof(c_0_2537,axiom,
c_SEQ_Osubseq(v_f____),
c_0_1267 ).
fof(c_0_2538,plain,
! [X27,X28,X29] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X28,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X28,X27))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X29))),X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1269])]) ).
fof(c_0_2539,plain,
! [X90,X91,X92,X93,X95] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X92,X91),esk67_4(X90,X91,X92,X93)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X92,X91),X95))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X93,hAPP(X90,X95))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X93,hAPP(X90,X91)))))
| ~ class_RealVector_Oreal__normed__vector(X93)
| ~ class_Orderings_Oord(X92) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X93,c_Groups_Ominus__class_Ominus(X93,hAPP(X90,X91),hAPP(X90,esk67_4(X90,X91,X92,X93))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X92,X91),X95))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X93,hAPP(X90,X95))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X93,hAPP(X90,X91)))))
| ~ class_RealVector_Oreal__normed__vector(X93)
| ~ class_Orderings_Oord(X92) ) ),
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_1270])])])])]) ).
fof(c_0_2540,plain,
! [X86,X87,X88,X89,X90,X91] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X90,X87)),X89)),X88)),X86))
| ~ class_Rings_Oordered__ring(X91) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X90,X87)),X89)),X88)),X86))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)))
| ~ class_Rings_Oordered__ring(X91) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1271])])]) ).
fof(c_0_2541,plain,
! [X86,X87,X88,X89,X90,X91] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X90,X87)),X89)),X88)),X86))
| ~ class_Rings_Oordered__ring(X91) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X90,X87)),X89)),X88)),X86))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)))
| ~ class_Rings_Oordered__ring(X91) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1272])])]) ).
fof(c_0_2542,plain,
! [X27,X28,X29] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X28),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X27,X28))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X29)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1273])]) ).
fof(c_0_2543,plain,
( c_SEQ_Osubseq(esk9_0)
& c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,esk9_0)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1274])])]) ).
fof(c_0_2544,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
c_0_1275 ).
fof(c_0_2545,plain,
! [X89,X90,X91,X92,X93] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X89)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X92,X93)),X91)),X90)),X89))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X92,X93)),X91)),X90)),X89))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X89)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1276])])]) ).
fof(c_0_2546,plain,
! [X89,X90,X91,X92,X93] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X89)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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,X92,X93)),X91)),X90)),X89))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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,X92,X93)),X91)),X90)),X89))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X89)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1277])])]) ).
fof(c_0_2547,plain,
! [X42,X43,X44,X45] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),esk20_4(X42,X43,X44,X45)))
| c_SEQ_OBseq(X45,X43)
| ~ class_RealVector_Oreal__normed__vector(X45) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X45,hAPP(X43,esk20_4(X42,X43,X44,X45)))),X42))
| c_SEQ_OBseq(X45,X43)
| ~ class_RealVector_Oreal__normed__vector(X45) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1278])])])]) ).
fof(c_0_2548,plain,
! [X34,X35,X36] :
( ~ class_RealVector_Oreal__normed__vector(X36)
| ~ c_SEQ_OBseq(X36,c_COMBB(tc_Nat_Onat,X36,tc_Nat_Onat,X35,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34)))
| c_SEQ_OBseq(X36,X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1279])]) ).
fof(c_0_2549,plain,
! [X86,X87,X88,X89,X90,X91] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X91,X88),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X87,X90)),X89)),X86)))
| ~ class_Rings_Oordered__ring(X91) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X91,X88),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X87,X90)),X89)),X86)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)))
| ~ class_Rings_Oordered__ring(X91) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1280])])]) ).
fof(c_0_2550,plain,
! [X86,X87,X88,X89,X90,X91] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X91,X88),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X87,X90)),X89)),X86)))
| ~ class_Rings_Oordered__ring(X91) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X91,X88),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X87,X90)),X89)),X86)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)))
| ~ class_Rings_Oordered__ring(X91) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1281])])]) ).
fof(c_0_2551,plain,
! [X14,X15,X16,X17,X18] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,X17),X15),X14))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X17,hAPP(X15,X18)),hAPP(X14,X18)))
| ~ class_Orderings_Oord(X17) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X17,hAPP(X15,esk2_4(X14,X15,X16,X17))),hAPP(X14,esk2_4(X14,X15,X16,X17))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,X17),X15),X14))
| ~ class_Orderings_Oord(X17) ) ),
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_1282])])])])]) ).
fof(c_0_2552,plain,
! [X89,X90,X91,X92,X93] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X89)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X90),hAPP(hAPP(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,X92,X93)),X91)),X89)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X90),hAPP(hAPP(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,X92,X93)),X91)),X89)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X89)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1283])])]) ).
fof(c_0_2553,plain,
! [X89,X90,X91,X92,X93] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X89)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X90),hAPP(hAPP(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,X92,X93)),X91)),X89)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X90),hAPP(hAPP(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,X92,X93)),X91)),X89)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X89)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1284])])]) ).
fof(c_0_2554,plain,
! [X23,X24,X25] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X25,X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X25,X23),hAPP(X25,X24))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X23,X24))),X24)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X25,X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X25,X23),hAPP(X25,X24))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X23,X24))),X23)),
inference(variable_rename,[status(thm)],[c_0_1285]) ).
fof(c_0_2555,plain,
! [X13,X14,X15,X16,X17] :
( ~ class_RealVector_Oreal__normed__algebra(X17)
| c_Groups_Ominus__class_Ominus(X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X16),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X14),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),c_Groups_Ominus__class_Ominus(X17,X16,X14)),c_Groups_Ominus__class_Ominus(X17,X15,X13))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),c_Groups_Ominus__class_Ominus(X17,X16,X14)),X13))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X14),c_Groups_Ominus__class_Ominus(X17,X15,X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1286])]) ).
fof(c_0_2556,plain,
! [X67,X68] :
( X68 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X67 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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),X68),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk24_2(X67,X68)),X67))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1287])])]) ).
fof(c_0_2557,plain,
! [X39,X40,X41] :
( ~ class_RealVector_Oreal__normed__algebra(X41)
| ~ c_SEQ_Oconvergent(X41,X40)
| ~ c_SEQ_Oconvergent(X41,X39)
| c_SEQ_Oconvergent(X41,c_COMBS(tc_Nat_Onat,X41,X41,c_COMBB(X41,tc_fun(X41,X41),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X41),X40),X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1288])]) ).
fof(c_0_2558,plain,
! [X39,X40,X41] :
( ~ class_RealVector_Oreal__normed__vector(X41)
| ~ c_SEQ_Oconvergent(X41,X40)
| ~ c_SEQ_Oconvergent(X41,X39)
| c_SEQ_Oconvergent(X41,c_COMBS(tc_Nat_Onat,X41,X41,c_COMBB(X41,tc_fun(X41,X41),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(X41),X40),X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1289])]) ).
fof(c_0_2559,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Groups_Oordered__ab__group__add__abs(X31)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Oabs__class_Oabs(X31,c_Groups_Ominus__class_Ominus(X31,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X30),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X28),X27)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),c_Groups_Oabs__class_Oabs(X31,c_Groups_Ominus__class_Ominus(X31,X30,X28))),c_Groups_Oabs__class_Oabs(X31,c_Groups_Ominus__class_Ominus(X31,X29,X27))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1290])]) ).
fof(c_0_2560,plain,
! [X26,X27,X28] :
( ~ class_RealVector_Oreal__normed__field(X28)
| ~ c_SEQ_Oconvergent(X28,X27)
| c_SEQ_Oconvergent(X28,c_COMBC(tc_Nat_Onat,X28,X28,c_COMBB(X28,tc_fun(X28,X28),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(X28),X27),X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1291])]) ).
fof(c_0_2561,plain,
! [X26,X27,X28] :
( ~ class_RealVector_Oreal__normed__algebra(X28)
| ~ c_SEQ_Oconvergent(X28,X27)
| c_SEQ_Oconvergent(X28,c_COMBC(tc_Nat_Onat,X28,X28,c_COMBB(X28,tc_fun(X28,X28),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X28),X27),X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1292])]) ).
fof(c_0_2562,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_RealVector_Oreal__normed__vector(X31)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X31,c_Groups_Ominus__class_Ominus(X31,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X30),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X28),X27)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X31,c_Groups_Ominus__class_Ominus(X31,X30,X28))),c_RealVector_Onorm__class_Onorm(X31,c_Groups_Ominus__class_Ominus(X31,X29,X27))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1293])]) ).
fof(c_0_2563,plain,
! [X34,X35,X36] :
( ~ class_RealVector_Oreal__normed__vector(X36)
| ~ c_SEQ_OBseq(X36,X35)
| c_SEQ_OBseq(X36,c_COMBB(tc_Nat_Onat,X36,tc_Nat_Onat,X35,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1294])]) ).
fof(c_0_2564,axiom,
c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
c_0_1295 ).
fof(c_0_2565,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
c_0_1296 ).
fof(c_0_2566,plain,
! [X13,X14] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,X13))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X14),hAPP(c_Complex_ORe,X13)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X14),hAPP(c_Complex_OIm,X13)))))),
inference(variable_rename,[status(thm)],[c_0_1297]) ).
fof(c_0_2567,plain,
! [X103,X104,X105,X106,X107,X108] :
( ~ class_RealVector_Oreal__field(X108)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X108),c_Groups_Ominus__class_Ominus(X108,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X108),X107),X106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X108),X105),X104))),X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X108),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X108),X107),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X108),c_Groups_Ominus__class_Ominus(X108,X106,X104)),X103))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X108),c_Groups_Ominus__class_Ominus(X108,X107,X105)),X103)),X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1298])]) ).
fof(c_0_2568,plain,
! [X69,X70,X71,X72,X73] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X73),X72)),X71)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X73),X70)),X69)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X71),X73))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X69),X73))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X72),X70)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1299])]) ).
fof(c_0_2569,plain,
! [X69,X70,X71,X72,X73] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X73),X72)),X71)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X73),X70)),X69)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X73),X69))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X73),X71))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X70),X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1300])]) ).
fof(c_0_2570,plain,
! [X11,X12,X13] :
( ( X12 = c_Groups_Ozero__class_Ozero(X13)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X11),X11))),c_Groups_Ozero__class_Ozero(X13)))
| ~ class_Rings_Olinordered__ring__strict(X13) )
& ( X11 = c_Groups_Ozero__class_Ozero(X13)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X11),X11))),c_Groups_Ozero__class_Ozero(X13)))
| ~ class_Rings_Olinordered__ring__strict(X13) )
& ( X12 != c_Groups_Ozero__class_Ozero(X13)
| X11 != c_Groups_Ozero__class_Ozero(X13)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X11),X11))),c_Groups_Ozero__class_Ozero(X13)))
| ~ class_Rings_Olinordered__ring__strict(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1301])])]) ).
fof(c_0_2571,plain,
! [X13,X14,X15] :
( ~ class_Rings_Olinordered__ring(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X13),X13))),c_Groups_Ozero__class_Ozero(X15))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1302])]) ).
fof(c_0_2572,plain,
! [X30,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),X31)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X31),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1303])]) ).
fof(c_0_2573,plain,
! [X69,X70,X71,X72,X73,X74] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X74),X73)),X72) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X70)),X69)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X70)),X69)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X72),X74))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X69))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X71),X74))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X70),X73)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1304])]) ).
fof(c_0_2574,plain,
! [X30,X31] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X31)),c_RealDef_Oreal(tc_Nat_Onat,X30)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X30)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[c_0_1305]) ).
fof(c_0_2575,plain,
! [X78,X79,X80,X83,X84,X87] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X80))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,esk43_3(X78,X79,X80)))),X80))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,X83))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk44_2(X78,X79)))))
| ~ class_RealVector_Oreal__normed__vector(X79) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk46_2(X78,X79)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,esk45_3(X78,X79,X84)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X84))))
| ~ class_RealVector_Oreal__normed__vector(X79) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,X87))),esk46_2(X78,X79)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,esk45_3(X78,X79,X84)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X84))))
| ~ class_RealVector_Oreal__normed__vector(X79) ) ),
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_1306])])])])]) ).
fof(c_0_2576,plain,
! [X78,X79,X80,X83,X84,X87] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X80))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,esk39_3(X78,X79,X80)))),X80))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,X83))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk40_2(X78,X79)))))
| ~ class_RealVector_Oreal__normed__vector(X79) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk42_2(X78,X79)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,esk41_3(X78,X79,X84)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X84))))
| ~ class_RealVector_Oreal__normed__vector(X79) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,X87))),esk42_2(X78,X79)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,esk41_3(X78,X79,X84)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X84))))
| ~ class_RealVector_Oreal__normed__vector(X79) ) ),
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_1307])])])])]) ).
fof(c_0_2577,plain,
! [X15] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X15) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X15),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X15,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X15),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X15,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1308])]) ).
fof(c_0_2578,plain,
! [X46,X47,X48,X49,X50,X51] :
( ~ class_Rings_Olinordered__semiring__1(X51)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X51,X50),X49))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X51,X48),X49))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X51,c_Groups_Ozero__class_Ozero(X51)),X47))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X51,c_Groups_Ozero__class_Ozero(X51)),X46))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X51),X47),X46) != c_Groups_Oone__class_Oone(X51)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X51,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X47),X50)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X46),X48))),X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1309])]) ).
fof(c_0_2579,plain,
! [X46,X47,X48,X49,X50,X51] :
( ~ class_Rings_Olinordered__semiring__1__strict(X51)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X51,X50),X49))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X51,X48),X49))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X51,c_Groups_Ozero__class_Ozero(X51)),X47))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X51,c_Groups_Ozero__class_Ozero(X51)),X46))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X51),X47),X46) != c_Groups_Oone__class_Oone(X51)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X51,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X47),X50)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X51),X46),X48))),X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1310])]) ).
fof(c_0_2580,plain,
! [X41,X42,X43] :
( ~ class_RealVector_Oreal__normed__vector(X43)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X42))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X43,hAPP(X41,esk19_3(X41,X42,X43)))),X42))
| c_SEQ_OBseq(X43,X41) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1311])])]) ).
fof(c_0_2581,plain,
! [X38,X39,X41,X42] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk13_2(X38,X39)))
| ~ c_SEQ_OBseq(X39,X38)
| ~ class_RealVector_Oreal__normed__vector(X39) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X39,hAPP(X38,X41))),esk13_2(X38,X39)))
| ~ c_SEQ_OBseq(X39,X38)
| ~ class_RealVector_Oreal__normed__vector(X39) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X42))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X39,hAPP(X38,esk14_3(X38,X39,X42)))),X42))
| c_SEQ_OBseq(X39,X38)
| ~ class_RealVector_Oreal__normed__vector(X39) ) ),
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_1312])])])])]) ).
fof(c_0_2582,plain,
! [X78,X79,X81,X82] :
( ( ~ c_SEQ_OBseq(X79,X78)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,X81))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk56_2(X78,X79)))))
| ~ class_RealVector_Oreal__normed__vector(X79) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,esk57_3(X78,X79,X82)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X82))))
| c_SEQ_OBseq(X79,X78)
| ~ class_RealVector_Oreal__normed__vector(X79) ) ),
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_1313])])])])]) ).
fof(c_0_2583,plain,
! [X78,X79,X81,X82] :
( ( ~ c_SEQ_OBseq(X79,X78)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,X81))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk54_2(X78,X79)))))
| ~ class_RealVector_Oreal__normed__vector(X79) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X79,hAPP(X78,esk55_3(X78,X79,X82)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X82))))
| c_SEQ_OBseq(X79,X78)
| ~ class_RealVector_Oreal__normed__vector(X79) ) ),
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_1314])])])])]) ).
fof(c_0_2584,plain,
! [X54,X55] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X54)),X54)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X54),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X55),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X55)),X55)),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_1315])])])]) ).
fof(c_0_2585,plain,
! [X69,X70,X71] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X70)),X69)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X69))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X70),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1316])]) ).
fof(c_0_2586,plain,
! [X46,X47,X48,X49,X50] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X49))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X48)),X47),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X48)),X46)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X47,hAPP(hAPP(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,X50)),X48)),X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1317])]) ).
fof(c_0_2587,plain,
! [X46,X47,X48,X49,X50] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X49))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X48)),X47),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X48)),X46)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(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,X50)),X48)),X47),X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1318])]) ).
fof(c_0_2588,plain,
! [X73,X75,X76] :
( ~ class_RealVector_Oreal__normed__algebra(X73)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X73,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X73),X75),X76))),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(X73,X75)),c_RealVector_Onorm__class_Onorm(X73,X76))),esk62_1(X73)))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1319])])])]) ).
fof(c_0_2589,plain,
! [X73,X75,X76] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk36_1(X73)))
| ~ class_RealVector_Oreal__normed__algebra(X73) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X73,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X73),X75),X76))),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(X73,X75)),c_RealVector_Onorm__class_Onorm(X73,X76))),esk36_1(X73))))
| ~ class_RealVector_Oreal__normed__algebra(X73) ) ),
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_1320])])])])]) ).
fof(c_0_2590,plain,
! [X73,X75,X76] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk29_1(X73)))
| ~ class_RealVector_Oreal__normed__algebra(X73) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X73,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X73),X75),X76))),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(X73,X75)),c_RealVector_Onorm__class_Onorm(X73,X76))),esk29_1(X73))))
| ~ class_RealVector_Oreal__normed__algebra(X73) ) ),
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_1321])])])])]) ).
fof(c_0_2591,plain,
! [X69,X70,X71,X72,X73,X74] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X74),X73)),X72) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X70)),X69)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X70)),X69)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X69),X71))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X72))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X71),X74))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X73),X70)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1322])]) ).
fof(c_0_2592,plain,
! [X13,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X14),X13) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X14)),hAPP(c_Complex_ORe,X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X14)),hAPP(c_Complex_OIm,X13))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X14)),hAPP(c_Complex_OIm,X13))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X14)),hAPP(c_Complex_ORe,X13)))),
inference(variable_rename,[status(thm)],[c_0_1323]) ).
fof(c_0_2593,plain,
! [X26,X27,X28] :
( ~ class_RealVector_Oreal__normed__algebra(X28)
| ~ c_SEQ_Oconvergent(X28,X27)
| c_SEQ_Oconvergent(X28,c_COMBB(X28,X28,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(X28),X26),X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1324])]) ).
fof(c_0_2594,plain,
! [X110,X111,X112,X113,X114,X115] : hAPP(c_COMBS(X115,X114,X113,X112,X111),X110) = hAPP(hAPP(X112,X110),hAPP(X111,X110)),
inference(variable_rename,[status(thm)],[c_0_1325]) ).
fof(c_0_2595,plain,
! [X110,X111,X112,X113,X114,X115] : hAPP(c_COMBC(X115,X114,X113,X112,X111),X110) = hAPP(hAPP(X112,X110),X111),
inference(variable_rename,[status(thm)],[c_0_1326]) ).
fof(c_0_2596,plain,
! [X110,X111,X112,X113,X114,X115] : hAPP(c_COMBB(X115,X114,X113,X112,X111),X110) = hAPP(X112,hAPP(X111,X110)),
inference(variable_rename,[status(thm)],[c_0_1327]) ).
fof(c_0_2597,plain,
! [X11,X12,X13] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,c_Groups_Ozero__class_Ozero(X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X11),X11))))
| X12 != c_Groups_Ozero__class_Ozero(X13)
| X11 != c_Groups_Ozero__class_Ozero(X13)
| ~ class_Rings_Olinordered__ring__strict(X13) )
& ( X12 = c_Groups_Ozero__class_Ozero(X13)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,c_Groups_Ozero__class_Ozero(X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X11),X11))))
| ~ class_Rings_Olinordered__ring__strict(X13) )
& ( X11 = c_Groups_Ozero__class_Ozero(X13)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,c_Groups_Ozero__class_Ozero(X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X11),X11))))
| ~ class_Rings_Olinordered__ring__strict(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1328])])]) ).
fof(c_0_2598,plain,
! [X26] :
( ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,X26)
| c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1329])]) ).
fof(c_0_2599,plain,
! [X26] :
( ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,X26)
| c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1330])]) ).
fof(c_0_2600,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__ab__group__add__abs(X14)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Oabs__class_Oabs(X14,c_Groups_Ominus__class_Ominus(X14,c_Groups_Oabs__class_Oabs(X14,X13),c_Groups_Oabs__class_Oabs(X14,X12)))),c_Groups_Oabs__class_Oabs(X14,c_Groups_Ominus__class_Ominus(X14,X13,X12)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1331])]) ).
fof(c_0_2601,plain,
! [X12,X13] : hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X13),X12)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X13))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X12))),
inference(variable_rename,[status(thm)],[c_0_1332]) ).
fof(c_0_2602,plain,
! [X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__vector(X14)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,X13),c_RealVector_Onorm__class_Onorm(X14,X12)))),c_RealVector_Onorm__class_Onorm(X14,c_Groups_Ominus__class_Ominus(X14,X13,X12)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1333])]) ).
fof(c_0_2603,plain,
! [X87,X88,X89,X90] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X90,c_Groups_Ominus__class_Ominus(X90,X88,X87)),X89))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X90,c_Groups_Oabs__class_Oabs(X90,c_Groups_Ominus__class_Ominus(X90,X89,X88))),X87))
| ~ class_Rings_Olinordered__idom(X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X90,X89),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X90),X88),X87)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X90,c_Groups_Oabs__class_Oabs(X90,c_Groups_Ominus__class_Ominus(X90,X89,X88))),X87))
| ~ class_Rings_Olinordered__idom(X90) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X90,c_Groups_Ominus__class_Ominus(X90,X88,X87)),X89))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X90,X89),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X90),X88),X87)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X90,c_Groups_Oabs__class_Oabs(X90,c_Groups_Ominus__class_Ominus(X90,X89,X88))),X87))
| ~ class_Rings_Olinordered__idom(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1334])])]) ).
fof(c_0_2604,plain,
! [X86,X87,X88,X89,X90,X91] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)
| X88 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X87,X90)),X89)),X86)
| ~ class_Rings_Oring(X91) )
& ( X88 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X87,X90)),X89)),X86)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)
| ~ class_Rings_Oring(X91) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1335])])]) ).
fof(c_0_2605,plain,
! [X86,X87,X88,X89,X90,X91] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X90,X87)),X89)),X88) = X86
| ~ class_Rings_Oring(X91) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),c_Groups_Ominus__class_Ominus(X91,X90,X87)),X89)),X88) != X86
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X90),X89)),X88) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X91),X87),X89)),X86)
| ~ class_Rings_Oring(X91) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1336])])]) ).
fof(c_0_2606,plain,
! [X89,X90,X91,X92,X93] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X90) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X89)
| X90 = hAPP(hAPP(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,X92,X93)),X91)),X89)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) )
& ( X90 != hAPP(hAPP(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,X92,X93)),X91)),X89)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X89)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1337])])]) ).
fof(c_0_2607,plain,
! [X89,X90,X91,X92,X93] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X90) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X89)
| hAPP(hAPP(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,X92,X93)),X91)),X90) = X89
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) )
& ( hAPP(hAPP(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,X92,X93)),X91)),X90) != X89
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X91)),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X91)),X89)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X93),X92)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1338])])]) ).
fof(c_0_2608,plain,
! [X88,X89,X90,X92] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk68_3(X88,X89,X90)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X89),X88))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X90),X89)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X90),X92))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X89,X92))),esk68_3(X88,X89,X90)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X89),X88))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X90),X89)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X92),X88))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X89,X92))),esk68_3(X88,X89,X90)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X89),X88))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X90),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_1339])])])])]) ).
fof(c_0_2609,plain,
! [X30,X31] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X31)),c_RealDef_Oreal(tc_Nat_Onat,X30)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X30))))),
inference(variable_rename,[status(thm)],[c_0_1340]) ).
fof(c_0_2610,plain,
! [X17,X18] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X18),X17))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X17)))),
inference(variable_rename,[status(thm)],[c_0_1341]) ).
fof(c_0_2611,plain,
! [X13,X14] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk59_2(X13,X14))),X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X14)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk59_2(X13,X14)))),X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X14)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1342])])])]) ).
fof(c_0_2612,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__idom(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,c_Groups_Oabs__class_Oabs(X31,X30)),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,c_Groups_Oabs__class_Oabs(X31,X28)),X27))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),c_Groups_Oabs__class_Oabs(X31,X30)),c_Groups_Oabs__class_Oabs(X31,X28))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31),X29),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1343])]) ).
fof(c_0_2613,plain,
! [X69,X70,X71] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X70)),X69)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X69),X71))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X70)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1344])]) ).
fof(c_0_2614,plain,
! [X60,X61,X62,X63,X64] :
( ~ class_Rings_Osemiring(X64)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X64),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X64),X63),X62)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X64),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X64),X61),X62)),X60)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X64),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X64),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X64),X63),X61)),X62)),X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1345])]) ).
fof(c_0_2615,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__semidom(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Ozero__class_Ozero(X32)),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,X31),c_Groups_Oone__class_Oone(X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),X31),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30))),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1346])]) ).
fof(c_0_2616,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_RealVector_Oreal__normed__algebra(X29)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X29,X28)),X27))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X29,X26)),X25))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),X28),X26))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X25))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1347])]) ).
fof(c_0_2617,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_RealVector_Oreal__normed__vector(X29)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X29,X28)),X27))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X29,X26)),X25))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X29,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29),X28),X26))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X27),X25))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1348])]) ).
fof(c_0_2618,plain,
! [X99,X100,X101,X103,X104,X105,X106] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),esk71_3(X99,X100,X101))),X100))
| X99 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X101,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X100,X99))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),c_Nat_OSuc(esk71_3(X99,X100,X101)))))
| X99 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X101,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X100,X99))) )
& ( hBOOL(hAPP(X101,esk71_3(X99,X100,X101)))
| X99 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X101,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X100,X99))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),esk71_3(X99,X100,X101))),X100))
| hBOOL(hAPP(X101,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X101,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X100,X99))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),c_Nat_OSuc(esk71_3(X99,X100,X101)))))
| hBOOL(hAPP(X101,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X101,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X100,X99))) )
& ( hBOOL(hAPP(X101,esk71_3(X99,X100,X101)))
| hBOOL(hAPP(X101,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X101,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X100,X99))) )
& ( X103 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X105,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X105,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X104,X103))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X106)),X104))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),c_Nat_OSuc(X106))))
| ~ hBOOL(hAPP(X105,X106))
| hBOOL(hAPP(X105,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X104,X103))) ) ),
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_1349])])])])])]) ).
fof(c_0_2619,plain,
! [X46,X47,X48,X49] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),X48)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X47),X48)),X46)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X47)),X48)),X46),
inference(variable_rename,[status(thm)],[c_0_1350]) ).
fof(c_0_2620,plain,
! [X83,X84,X85,X86,X87,X88,X89,X90,X91,X92] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X87),X84))
| X83 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X86)),X87)
| hBOOL(hAPP(X85,X86))
| ~ epred1_3(X85,X84,X83) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X84),X89))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X89),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X83 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X88)),X89)
| hBOOL(hAPP(X85,X88))
| ~ epred1_3(X85,X84,X83) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),esk75_3(X90,X91,X92)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X90,X91,X92)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
| epred1_3(X92,X91,X90) )
& ( X90 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),esk74_3(X90,X91,X92))),esk75_3(X90,X91,X92))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
| epred1_3(X92,X91,X90) )
& ( ~ hBOOL(hAPP(X92,esk74_3(X90,X91,X92)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X90,X91,X92)))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),esk75_3(X90,X91,X92)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X90,X91,X92)))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X90,X91,X92)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X90,X91,X92)))
| epred1_3(X92,X91,X90) )
& ( X90 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),esk74_3(X90,X91,X92))),esk75_3(X90,X91,X92))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X90,X91,X92)))
| epred1_3(X92,X91,X90) )
& ( ~ hBOOL(hAPP(X92,esk74_3(X90,X91,X92)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X90,X91,X92)))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X90,X91,X92)),X91))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),esk75_3(X90,X91,X92)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X90,X91,X92)),X91))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X90,X91,X92)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X90,X91,X92)),X91))
| epred1_3(X92,X91,X90) )
& ( X90 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),esk74_3(X90,X91,X92))),esk75_3(X90,X91,X92))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X90,X91,X92)),X91))
| epred1_3(X92,X91,X90) )
& ( ~ hBOOL(hAPP(X92,esk74_3(X90,X91,X92)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X90,X91,X92)),X91))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X90 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),esk72_3(X90,X91,X92))),esk73_3(X90,X91,X92))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),esk75_3(X90,X91,X92)))
| X90 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),esk72_3(X90,X91,X92))),esk73_3(X90,X91,X92))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X90,X91,X92)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X90 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),esk72_3(X90,X91,X92))),esk73_3(X90,X91,X92))
| epred1_3(X92,X91,X90) )
& ( X90 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),esk74_3(X90,X91,X92))),esk75_3(X90,X91,X92))
| X90 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),esk72_3(X90,X91,X92))),esk73_3(X90,X91,X92))
| epred1_3(X92,X91,X90) )
& ( ~ hBOOL(hAPP(X92,esk74_3(X90,X91,X92)))
| X90 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),esk72_3(X90,X91,X92))),esk73_3(X90,X91,X92))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X92,esk72_3(X90,X91,X92)))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X91),esk75_3(X90,X91,X92)))
| ~ hBOOL(hAPP(X92,esk72_3(X90,X91,X92)))
| epred1_3(X92,X91,X90) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X90,X91,X92)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X92,esk72_3(X90,X91,X92)))
| epred1_3(X92,X91,X90) )
& ( X90 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),esk74_3(X90,X91,X92))),esk75_3(X90,X91,X92))
| ~ hBOOL(hAPP(X92,esk72_3(X90,X91,X92)))
| epred1_3(X92,X91,X90) )
& ( ~ hBOOL(hAPP(X92,esk74_3(X90,X91,X92)))
| ~ hBOOL(hAPP(X92,esk72_3(X90,X91,X92)))
| epred1_3(X92,X91,X90) ) ),
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_1351])])])])])]) ).
fof(c_0_2621,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__ab__group__add__abs(X14)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Oabs__class_Oabs(X14,c_Groups_Ominus__class_Ominus(X14,X13,X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),c_Groups_Oabs__class_Oabs(X14,X13)),c_Groups_Oabs__class_Oabs(X14,X12)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1352])]) ).
fof(c_0_2622,plain,
! [X13,X14,X15] :
( ~ class_Rings_Olinordered__ring(X15)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X13),X13)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1353])]) ).
fof(c_0_2623,plain,
! [X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__vector(X14)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,c_Groups_Ominus__class_Ominus(X14,X13,X12))),hAPP(hAPP(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_1354])]) ).
fof(c_0_2624,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__ab__group__add__abs(X14)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Oabs__class_Oabs(X14,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),c_Groups_Oabs__class_Oabs(X14,X13)),c_Groups_Oabs__class_Oabs(X14,X12)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1355])]) ).
fof(c_0_2625,plain,
! [X38,X39,X41] :
( ~ class_RealVector_Oreal__normed__algebra(X39)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X39,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X39),X38),X41))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X39,X41)),esk63_2(X38,X39)))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1356])])])]) ).
fof(c_0_2626,plain,
! [X38,X39,X41] :
( ~ class_RealVector_Oreal__normed__algebra(X39)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X39,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X39),X41),X38))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X39,X41)),esk61_2(X38,X39)))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1357])])])]) ).
fof(c_0_2627,plain,
! [X38,X39,X41] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk38_2(X38,X39)))
| ~ class_RealVector_Oreal__normed__algebra(X39) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X39,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X39),X41),X38))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X39,X41)),esk38_2(X38,X39))))
| ~ class_RealVector_Oreal__normed__algebra(X39) ) ),
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_1358])])])])]) ).
fof(c_0_2628,plain,
! [X38,X39,X41] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk37_2(X38,X39)))
| ~ class_RealVector_Oreal__normed__algebra(X39) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X39,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X39),X38),X41))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X39,X41)),esk37_2(X38,X39))))
| ~ class_RealVector_Oreal__normed__algebra(X39) ) ),
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_1359])])])])]) ).
fof(c_0_2629,plain,
! [X38,X39,X41] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk31_2(X38,X39)))
| ~ class_RealVector_Oreal__normed__algebra(X39) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X39,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X39),X41),X38))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X39,X41)),esk31_2(X38,X39))))
| ~ class_RealVector_Oreal__normed__algebra(X39) ) ),
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_1360])])])])]) ).
fof(c_0_2630,plain,
! [X38,X39,X41] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk30_2(X38,X39)))
| ~ class_RealVector_Oreal__normed__algebra(X39) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X39,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X39),X38),X41))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X39,X41)),esk30_2(X38,X39))))
| ~ class_RealVector_Oreal__normed__algebra(X39) ) ),
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_1361])])])])]) ).
fof(c_0_2631,plain,
! [X13,X14,X15] :
( ~ class_RealVector_Oreal__normed__algebra(X15)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X13))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X15,X14)),c_RealVector_Onorm__class_Onorm(X15,X13)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1362])]) ).
fof(c_0_2632,plain,
! [X13,X14,X15] :
( ~ class_RealVector_Oreal__normed__vector(X15)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),X13))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X15,X14)),c_RealVector_Onorm__class_Onorm(X15,X13)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1363])]) ).
fof(c_0_2633,plain,
! [X16,X17,X18,X19] :
( ~ class_Fields_Olinordered__field(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X16))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X18)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X16),X17)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X16),X18))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1364])]) ).
fof(c_0_2634,plain,
! [X13,X14,X15,X16,X17] :
( ~ class_Rings_Oring(X17)
| c_Groups_Ominus__class_Ominus(X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X16),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X14),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X16),c_Groups_Ominus__class_Ominus(X17,X15,X13))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),c_Groups_Ominus__class_Ominus(X17,X16,X14)),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1365])]) ).
fof(c_0_2635,plain,
! [X16,X17,X18,X19] :
( ~ class_Fields_Olinordered__field__inverse__zero(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X16),c_Groups_Ozero__class_Ozero(X19)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X16),X18)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X16),X17))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1366])]) ).
fof(c_0_2636,plain,
! [X30,X31,X32,X33] :
( ~ class_Rings_Olinordered__semidom(X33)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,hAPP(hAPP(c_Power_Opower__class_Opower(X33),X32),c_Nat_OSuc(X31))),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X30),c_Nat_OSuc(X31))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,c_Groups_Ozero__class_Ozero(X33)),X30))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,X32),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1367])]) ).
fof(c_0_2637,plain,
! [X30,X31] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X30))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X31)),c_RealDef_Oreal(tc_Nat_Onat,X30)))),
inference(variable_rename,[status(thm)],[c_0_1368]) ).
fof(c_0_2638,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X33)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X32))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X35)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X34)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1369])])])]) ).
fof(c_0_2639,plain,
! [X34,X35,X36] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X36)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X36)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X35)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X36)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X36)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X35)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1370])])]) ).
fof(c_0_2640,plain,
! [X34,X35,X36] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X36)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X36)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X35)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X36)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X36)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X35)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1371])])]) ).
fof(c_0_2641,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__ab__group__add__abs(X14)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ominus__class_Ominus(X14,c_Groups_Oabs__class_Oabs(X14,X13),c_Groups_Oabs__class_Oabs(X14,X12))),c_Groups_Oabs__class_Oabs(X14,c_Groups_Ominus__class_Ominus(X14,X13,X12)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1372])]) ).
fof(c_0_2642,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__ab__group__add__abs(X14)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ominus__class_Ominus(X14,c_Groups_Oabs__class_Oabs(X14,X13),c_Groups_Oabs__class_Oabs(X14,X12))),c_Groups_Oabs__class_Oabs(X14,c_Groups_Ominus__class_Ominus(X14,X12,X13)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1373])]) ).
fof(c_0_2643,plain,
! [X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__vector(X14)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,X13),c_RealVector_Onorm__class_Onorm(X14,X12))),c_RealVector_Onorm__class_Onorm(X14,c_Groups_Ominus__class_Ominus(X14,X13,X12)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1374])]) ).
fof(c_0_2644,plain,
! [X30,X31,X32] :
( ~ class_RealVector_Oreal__normed__algebra__1(X32)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X32,hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X32,X31)),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1375])]) ).
fof(c_0_2645,plain,
! [X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__vector(X14)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,X13),c_RealVector_Onorm__class_Onorm(X14,X12))),c_RealVector_Onorm__class_Onorm(X14,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1376])]) ).
fof(c_0_2646,plain,
! [X30,X31,X32,X33] :
( ~ class_Rings_Olinordered__semidom(X33)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X33,hAPP(hAPP(c_Power_Opower__class_Opower(X33),X32),X31)),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X30),X31)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,c_Groups_Ozero__class_Ozero(X33)),X30))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X33,X32),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1377])]) ).
fof(c_0_2647,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__semiring__strict(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19)),X18))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1378])]) ).
fof(c_0_2648,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__semiring__strict(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X17)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19)),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1379])]) ).
fof(c_0_2649,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__semiring__strict(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X18))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1380])]) ).
fof(c_0_2650,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__semiring(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X18))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1381])]) ).
fof(c_0_2651,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__semiring__strict(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X17)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1382])]) ).
fof(c_0_2652,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__semiring(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X17)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1383])]) ).
fof(c_0_2653,plain,
! [X23,X24,X25,X26] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,X24),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Ozero__class_Ozero(X26)),X25))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,X24),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Ozero__class_Ozero(X26)),X25))
| ~ class_Rings_Olinordered__ring__strict(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1384])])]) ).
fof(c_0_2654,plain,
! [X23,X24,X25,X26] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X24),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Ozero__class_Ozero(X26)),X25))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X24),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Ozero__class_Ozero(X26)),X25))
| ~ class_Rings_Olinordered__ring__strict(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1385])])]) ).
fof(c_0_2655,plain,
! [X23,X24,X25,X26] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X23)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Oone__class_Oone(X26)),X25))
| ~ class_Rings_Olinordered__semidom(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X23)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Oone__class_Oone(X26)),X25))
| ~ class_Rings_Olinordered__semidom(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1386])])]) ).
fof(c_0_2656,plain,
! [X31,X32,X33,X34] :
( ~ class_Rings_Olinordered__semidom(X34)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X34,c_Groups_Oone__class_Oone(X34)),X33))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X34,hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),X32)),hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),X31)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1387])]) ).
fof(c_0_2657,plain,
! [X31,X32,X33,X34] :
( ~ class_Rings_Olinordered__semidom(X34)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X34,c_Groups_Oone__class_Oone(X34)),X33))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X34,hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),X32)),hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),X31)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1388])]) ).
fof(c_0_2658,plain,
! [X23,X24,X25,X26] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X23)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Oone__class_Oone(X26)),X25))
| ~ class_Rings_Olinordered__semidom(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X23)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Oone__class_Oone(X26)),X25))
| ~ class_Rings_Olinordered__semidom(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1389])])]) ).
fof(c_0_2659,plain,
! [X23,X24,X25,X26] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,X23),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),c_Groups_Ozero__class_Ozero(X26)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,X23),X24))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),c_Groups_Ozero__class_Ozero(X26)))
| ~ class_Rings_Olinordered__ring__strict(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1390])])]) ).
fof(c_0_2660,plain,
! [X23,X24,X25,X26] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X23),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),c_Groups_Ozero__class_Ozero(X26)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X23),X24))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),c_Groups_Ozero__class_Ozero(X26)))
| ~ class_Rings_Olinordered__ring__strict(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1391])])]) ).
fof(c_0_2661,plain,
! [X98,X99,X100] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X99)),X98))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),c_Nat_OSuc(X99))))
| X99 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X98,X100)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X100)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X99)),X98))
| X99 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X98,X100)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X100)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),c_Nat_OSuc(X99))))
| X99 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X98,X100)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X100)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1392])])]) ).
fof(c_0_2662,plain,
! [X23,X24,X25,X26] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),c_Groups_Ozero__class_Ozero(X26)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Ozero__class_Ozero(X26)),X25))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X23),X24))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Ozero__class_Ozero(X26)),X25))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),c_Groups_Ozero__class_Ozero(X26)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X24),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X23),X24))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X24),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Ozero__class_Ozero(X26)),X25))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X24),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),c_Groups_Ozero__class_Ozero(X26)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X23),X24))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X23)))
| ~ class_Rings_Olinordered__ring__strict(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1393])])]) ).
fof(c_0_2663,plain,
! [X23,X24,X25,X26] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X24),c_Groups_Ozero__class_Ozero(X26)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Ozero__class_Ozero(X26)),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X23),X24)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X23),X25))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Ozero__class_Ozero(X26)),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X23),X24)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X24),c_Groups_Ozero__class_Ozero(X26)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X23),X24)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X23),X25))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X23),X24)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,c_Groups_Ozero__class_Ozero(X26)),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X23),X24)))
| ~ class_Rings_Olinordered__ring__strict(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X24),c_Groups_Ozero__class_Ozero(X26)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X23),X25))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X23),X24)))
| ~ class_Rings_Olinordered__ring__strict(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1394])])]) ).
fof(c_0_2664,plain,
! [X8] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X8)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X8)),
inference(variable_rename,[status(thm)],[c_0_1395]) ).
fof(c_0_2665,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring__strict(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,X30),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,X28),X27))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,c_Groups_Ozero__class_Ozero(X31)),X30))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31)),X28))
| hBOOL(hAPP(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),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1396])]) ).
fof(c_0_2666,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring__strict(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,X30),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,X28),X27))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31)),X30))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,c_Groups_Ozero__class_Ozero(X31)),X28))
| hBOOL(hAPP(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),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1397])]) ).
fof(c_0_2667,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring__strict(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,X30),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,X28),X27))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31)),X30))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31)),X28))
| hBOOL(hAPP(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),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1398])]) ).
fof(c_0_2668,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Rings_Olinordered__semiring__strict(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,X30),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,X28),X27))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,c_Groups_Ozero__class_Ozero(X31)),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31)),X28))
| hBOOL(hAPP(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),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1399])]) ).
fof(c_0_2669,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Rings_Oordered__semiring(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,X30),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,X28),X27))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31)),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31)),X28))
| hBOOL(hAPP(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),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1400])]) ).
fof(c_0_2670,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Rings_Oordered__semiring(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,X30),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,X28),X27))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31)),X30))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,c_Groups_Ozero__class_Ozero(X31)),X28))
| hBOOL(hAPP(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),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1401])]) ).
fof(c_0_2671,plain,
! [X26,X27,X28,X29] :
( ( ~ c_SEQ_Omonoseq(X27,X26)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,X28)),hAPP(X26,c_Nat_OSuc(X28))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,c_Nat_OSuc(X29))),hAPP(X26,X29)))
| ~ class_Orderings_Oorder(X27) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,esk51_2(X26,X27))),hAPP(X26,c_Nat_OSuc(esk51_2(X26,X27)))))
| c_SEQ_Omonoseq(X27,X26)
| ~ class_Orderings_Oorder(X27) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,c_Nat_OSuc(esk52_2(X26,X27)))),hAPP(X26,esk52_2(X26,X27))))
| c_SEQ_Omonoseq(X27,X26)
| ~ class_Orderings_Oorder(X27) ) ),
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_1402])])])])]) ).
fof(c_0_2672,plain,
! [X24] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk66_1(X24),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X24)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24),c_RealDef_Oreal(tc_Nat_Onat,esk66_1(X24))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X24)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1403])])])]) ).
fof(c_0_2673,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__semidom(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Oone__class_Oone(X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),X31),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1404])]) ).
fof(c_0_2674,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X36)),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X36)),X34)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38),X37))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X37))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1405])])])]) ).
fof(c_0_2675,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X36)),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X36)),X34)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38),X37))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X37))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1406])])])]) ).
fof(c_0_2676,plain,
! [X12,X13] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X13)),c_RComplete_Onatfloor(X12))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),X12)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1407])]) ).
fof(c_0_2677,plain,
! [X27,X28,X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X30,X29)),c_Complex_Ocomplex_OComplex(X28,X27)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X29),X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X29),X28))),
inference(variable_rename,[status(thm)],[c_0_1408]) ).
fof(c_0_2678,plain,
! [X34,X35,X36] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1409])])]) ).
fof(c_0_2679,plain,
! [X34,X35,X36] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1410])])]) ).
fof(c_0_2680,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X33),X32)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X33),X31)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1411])]) ).
fof(c_0_2681,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X35)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X34)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X38))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),X38))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39),X37))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),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_1412])])])])]) ).
fof(c_0_2682,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X39))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X37))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38),X37))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X37))) ) ),
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_1413])])])])]) ).
fof(c_0_2683,plain,
! [X54,X55,X56] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X56),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X56),X54)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X55),X54))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X56)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X55),X54))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X56),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X56),X54)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X56)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1414])])]) ).
fof(c_0_2684,plain,
! [X54,X55,X56] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X55),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X54),X56)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X55),X54))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X56)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X55),X54))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X55),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X54),X56)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X56)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1415])])]) ).
fof(c_0_2685,plain,
! [X54,X55,X56] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X55),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X54),X56)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X55),X54))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X56)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X55),X54))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X55),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X54),X56)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X56)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1416])])]) ).
fof(c_0_2686,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1417])]) ).
fof(c_0_2687,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X16),X17)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1418])]) ).
fof(c_0_2688,plain,
! [X23,X24,X25,X26] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X23)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X24),X23))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X24),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X23)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1419])])]) ).
fof(c_0_2689,plain,
! [X23,X24,X25,X26] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X23),X24)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),X23))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,X25),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X26,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X23),X24)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1420])])]) ).
fof(c_0_2690,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1421])]) ).
fof(c_0_2691,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X16),X17)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1422])]) ).
fof(c_0_2692,plain,
! [X23,X24,X25,X26] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X23)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,X24),X23))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,X24),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X23)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1423])])]) ).
fof(c_0_2693,plain,
! [X23,X24,X25,X26] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X23),X24)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,X25),X23))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,X25),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X26,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X23),X24)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1424])])]) ).
fof(c_0_2694,plain,
! [X55,X56,X57,X58,X59] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X59),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X58),X57)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X56),X55)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X59),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X58),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X56),X57))
| X58 = X56
| X57 = X55
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X59) )
& ( X58 != X56
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X59),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X58),X57)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X56),X55)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X59),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X58),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X56),X57))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X59) )
& ( X57 != X55
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X59),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X58),X57)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X56),X55)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X59),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X58),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X56),X57))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X59) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1425])])]) ).
fof(c_0_2695,plain,
! [X53,X54,X55,X56,X57] :
( ( X56 = X55
| X54 = X53
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X54)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X55),X53)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X55),X54))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X57) )
& ( X56 != X55
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X54)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X55),X53)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X55),X54))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X57) )
& ( X54 != X53
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X54)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X55),X53)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X56),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X57),X55),X54))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1426])])]) ).
fof(c_0_2696,plain,
! [X63,X64,X65,X66] :
( ~ class_Rings_Olinordered__semidom(X66)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X65),X64))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X66,c_Groups_Ozero__class_Ozero(X66)),X63))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X66,X63),c_Groups_Oone__class_Oone(X66)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X66,hAPP(hAPP(c_Power_Opower__class_Opower(X66),X63),X64)),hAPP(hAPP(c_Power_Opower__class_Opower(X66),X63),X65))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1427])]) ).
fof(c_0_2697,plain,
! [X63,X64,X65,X66] :
( ~ class_Rings_Olinordered__semidom(X66)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65),X64))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X66,c_Groups_Ozero__class_Ozero(X66)),X63))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X66,X63),c_Groups_Oone__class_Oone(X66)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X66,hAPP(hAPP(c_Power_Opower__class_Opower(X66),X63),X64)),hAPP(hAPP(c_Power_Opower__class_Opower(X66),X63),X65))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1428])]) ).
fof(c_0_2698,plain,
! [X30,X31,X32,X33] :
( ~ class_Rings_Olinordered__semidom(X33)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X33,X32),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,c_Groups_Ozero__class_Ozero(X33)),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X33,hAPP(hAPP(c_Power_Opower__class_Opower(X33),X32),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X31),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1429])]) ).
fof(c_0_2699,plain,
! [X59,X60,X61] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X60),X59))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X61,X59)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X61,X60))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1430])]) ).
fof(c_0_2700,plain,
! [X85,X86,X87] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X85),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X86,X87)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),X87)),X86))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X87),X86)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),X87)),X86))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X85),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X86,X87)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X87),X86)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1431])])]) ).
fof(c_0_2701,plain,
! [X59,X60,X61] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X60),X59))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X61,X60)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X61,X59))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1432])]) ).
fof(c_0_2702,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X8))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X8))),X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1433])]) ).
fof(c_0_2703,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X35))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X35))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X38))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39),X37))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),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_1434])])])])]) ).
fof(c_0_2704,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X39))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38),X37))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X37))) ) ),
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_1435])])])])]) ).
fof(c_0_2705,plain,
! [X83,X84,X85,X86,X87,X88,X89,X90] :
( ( X83 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X85,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X85,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X84,X83))) )
& ( X83 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X87),X83))
| X84 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X83),X86)),X87)
| hBOOL(hAPP(X85,X86))
| ~ hBOOL(hAPP(X85,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X84,X83))) )
& ( X88 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X88 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X90,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X89,X88))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk70_3(X88,X89,X90)),X88))
| X88 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X90,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X89,X88))) )
& ( X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X88),esk69_3(X88,X89,X90))),esk70_3(X88,X89,X90))
| X88 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X90,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X89,X88))) )
& ( ~ hBOOL(hAPP(X90,esk69_3(X88,X89,X90)))
| X88 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X90,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X89,X88))) )
& ( X88 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X90,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X90,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X89,X88))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk70_3(X88,X89,X90)),X88))
| ~ hBOOL(hAPP(X90,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X90,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X89,X88))) )
& ( X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X88),esk69_3(X88,X89,X90))),esk70_3(X88,X89,X90))
| ~ hBOOL(hAPP(X90,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X90,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X89,X88))) )
& ( ~ hBOOL(hAPP(X90,esk69_3(X88,X89,X90)))
| ~ hBOOL(hAPP(X90,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X90,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X89,X88))) ) ),
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_1436])])])])])]) ).
fof(c_0_2706,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X34)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38),X37))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X38)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X37))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1437])])])]) ).
fof(c_0_2707,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X34)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38),X37))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X38)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X37))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1438])])])]) ).
fof(c_0_2708,plain,
! [X85,X86,X87,X88,X89,X90] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X87,X86)),X85))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),X86))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X88),X89)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X90,X89)),X88)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1439])])])]) ).
fof(c_0_2709,plain,
! [X30,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X31)),X30))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X31)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| c_RComplete_Onatceiling(X30) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1440])]) ).
fof(c_0_2710,plain,
! [X23,X24,X25] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X24),c_Groups_Ozero__class_Ozero(X25)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)),c_Groups_Ozero__class_Ozero(X25)))
| ~ class_Rings_Olinordered__ring__strict(X25) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)),c_Groups_Ozero__class_Ozero(X25)))
| ~ class_Rings_Olinordered__ring__strict(X25) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X24),c_Groups_Ozero__class_Ozero(X25)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X23),c_Groups_Ozero__class_Ozero(X25)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)),c_Groups_Ozero__class_Ozero(X25)))
| ~ class_Rings_Olinordered__ring__strict(X25) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X23),c_Groups_Ozero__class_Ozero(X25)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)),c_Groups_Ozero__class_Ozero(X25)))
| ~ class_Rings_Olinordered__ring__strict(X25) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X23),c_Groups_Ozero__class_Ozero(X25)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)),c_Groups_Ozero__class_Ozero(X25)))
| ~ class_Rings_Olinordered__ring__strict(X25) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X24),c_Groups_Ozero__class_Ozero(X25)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)),c_Groups_Ozero__class_Ozero(X25)))
| ~ class_Rings_Olinordered__ring__strict(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1441])])]) ).
fof(c_0_2711,plain,
! [X23,X24] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X24)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X24)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1442])])]) ).
fof(c_0_2712,plain,
! [X30,X31,X32,X33] :
( ~ class_Rings_Olinordered__semidom(X33)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,X32),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,c_Groups_Ozero__class_Ozero(X33)),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,hAPP(hAPP(c_Power_Opower__class_Opower(X33),X32),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X31),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1443])]) ).
fof(c_0_2713,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19)),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X17))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1444])]) ).
fof(c_0_2714,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__semiring__strict(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19)),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X17))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1445])]) ).
fof(c_0_2715,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__semiring__strict(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19)),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1446])]) ).
fof(c_0_2716,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Oordered__comm__semiring(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X17))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1447])]) ).
fof(c_0_2717,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Oordered__semiring(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X17))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1448])]) ).
fof(c_0_2718,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Oordered__semiring(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1449])]) ).
fof(c_0_2719,plain,
! [X23,X24] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X24)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X24)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1450])])]) ).
fof(c_0_2720,plain,
! [X30,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X31)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X30))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X31),c_RealDef_Oreal(tc_Nat_Onat,X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1451])]) ).
fof(c_0_2721,plain,
! [X74,X75] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X74))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X75),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk47_2(X74,X75))),X74))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1452])])])]) ).
fof(c_0_2722,plain,
! [X63,X64,X65,X66] :
( ~ class_Rings_Olinordered__semidom(X66)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65),X64))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X66,c_Groups_Oone__class_Oone(X66)),X63))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X66,hAPP(hAPP(c_Power_Opower__class_Opower(X66),X63),X65)),hAPP(hAPP(c_Power_Opower__class_Opower(X66),X63),X64))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1453])]) ).
fof(c_0_2723,plain,
! [X63,X64,X65,X66] :
( ~ class_Rings_Olinordered__semidom(X66)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X65),X64))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X66,c_Groups_Oone__class_Oone(X66)),X63))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X66,hAPP(hAPP(c_Power_Opower__class_Opower(X66),X63),X65)),hAPP(hAPP(c_Power_Opower__class_Opower(X66),X63),X64))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1454])]) ).
fof(c_0_2724,plain,
! [X13,X14,X15] :
( ~ class_Rings_Olinordered__idom(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Ozero__class_Ozero(X15)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Ozero__class_Ozero(X15)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X13),c_Groups_Oone__class_Oone(X15)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X13),X14)),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1455])]) ).
fof(c_0_2725,plain,
! [X13,X14,X15] :
( ~ class_Rings_Olinordered__idom(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Ozero__class_Ozero(X15)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Ozero__class_Ozero(X15)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X13),c_Groups_Oone__class_Oone(X15)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X13)),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1456])]) ).
fof(c_0_2726,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__ring__strict(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X16),c_Groups_Ozero__class_Ozero(X19)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X18))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1457])]) ).
fof(c_0_2727,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__ring__strict(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X16),c_Groups_Ozero__class_Ozero(X19)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1458])]) ).
fof(c_0_2728,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Oordered__ring(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X16),c_Groups_Ozero__class_Ozero(X19)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X18))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1459])]) ).
fof(c_0_2729,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Oordered__ring(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X16),c_Groups_Ozero__class_Ozero(X19)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1460])]) ).
fof(c_0_2730,plain,
! [X30,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X31)),X30))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X31)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| c_RComplete_Onatfloor(X30) = X31 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1461])]) ).
fof(c_0_2731,plain,
! [X85,X86,X87,X88,X89,X90] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X87),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X86,X85)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X87),X85)),X86)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X88)),X89))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X90),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X89,X88))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1462])])])]) ).
fof(c_0_2732,plain,
! [X51,X52,X53,X54] :
( ~ class_Groups_Omonoid__mult(X54)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53),X52))
| hAPP(hAPP(c_Power_Opower__class_Opower(X54),X51),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X52),X53)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X54),hAPP(hAPP(c_Power_Opower__class_Opower(X54),X51),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,X53))),X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1463])]) ).
fof(c_0_2733,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,X30),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,X28),X27))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X30),X28)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X29),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1464])]) ).
fof(c_0_2734,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,X30),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,X28),X27))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X30),X28)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X29),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1465])]) ).
fof(c_0_2735,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,X30),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,X28),X27))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X31,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X30),X28)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X29),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1466])]) ).
fof(c_0_2736,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Groups_Oordered__ab__semigroup__add(X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,X30),X29))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,X28),X27))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X31,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X30),X28)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X29),X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1467])]) ).
fof(c_0_2737,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X32)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X33))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1468])]) ).
fof(c_0_2738,plain,
! [X57,X58,X59] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X59),X58))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X59,X57)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X58,X57))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1469])]) ).
fof(c_0_2739,plain,
! [X57,X58,X59] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X59),X58))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X57),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X58,X57)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X59,X57))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1470])]) ).
fof(c_0_2740,plain,
! [X16,X17,X18] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16),X18))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X16)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1471])]) ).
fof(c_0_2741,plain,
! [X35,X36,X37] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37),X36))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37),X35))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X36)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X37))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1472])]) ).
fof(c_0_2742,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X32)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X34)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1473])])])]) ).
fof(c_0_2743,plain,
! [X52,X53,X54,X55,X56] :
( ~ class_Rings_Ocomm__semiring__1(X56)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X54)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X53),X52)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X54)),X52)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1474])]) ).
fof(c_0_2744,plain,
! [X93,X94,X95,X96] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X95))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X95))
| X95 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X96,X95) = X94
| X96 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X95),X94)),X93) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X95),X93))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X93),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X95))
| X95 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X96,X95) = X94
| X96 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X95),X94)),X93) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X95))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X93),X95))
| X95 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X96,X95) = X94
| X96 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X95),X94)),X93) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X95),X93))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X93),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X93),X95))
| X95 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X96,X95) = X94
| X96 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X95),X94)),X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1475])])]) ).
fof(c_0_2745,plain,
! [X23,X24,X25] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X24),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ominus__class_Ominus(X25,X24,X23)),c_Groups_Ozero__class_Ozero(X25)))
| ~ class_Groups_Oordered__ab__group__add(X25) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ominus__class_Ominus(X25,X24,X23)),c_Groups_Ozero__class_Ozero(X25)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X24),X23))
| ~ class_Groups_Oordered__ab__group__add(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1476])])]) ).
fof(c_0_2746,plain,
! [X23,X24,X25] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X25,X24),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X25,c_Groups_Ominus__class_Ominus(X25,X24,X23)),c_Groups_Ozero__class_Ozero(X25)))
| ~ class_Groups_Oordered__ab__group__add(X25) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X25,c_Groups_Ominus__class_Ominus(X25,X24,X23)),c_Groups_Ozero__class_Ozero(X25)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X25,X24),X23))
| ~ class_Groups_Oordered__ab__group__add(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1477])])]) ).
fof(c_0_2747,plain,
! [X9] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X9)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(variable_rename,[status(thm)],[c_0_1478]) ).
fof(c_0_2748,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__semidom(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Oone__class_Oone(X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Oone__class_Oone(X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),X31),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1479])]) ).
fof(c_0_2749,plain,
! [X30,X31,X32] :
( ~ class_Groups_Omonoid__mult(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X30),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X30) = hAPP(hAPP(c_Power_Opower__class_Opower(X32),X30),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1480])]) ).
fof(c_0_2750,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)),c_Groups_Ozero__class_Ozero(X8)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,X7),c_Groups_Ozero__class_Ozero(X8)))
| ~ class_Rings_Olinordered__idom(X8) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,X7),c_Groups_Ozero__class_Ozero(X8)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)),c_Groups_Ozero__class_Ozero(X8)))
| ~ class_Rings_Olinordered__idom(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1481])])]) ).
fof(c_0_2751,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)),c_Groups_Ozero__class_Ozero(X8)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,X7),c_Groups_Ozero__class_Ozero(X8)))
| ~ class_Groups_Olinordered__ab__group__add(X8) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,X7),c_Groups_Ozero__class_Ozero(X8)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)),c_Groups_Ozero__class_Ozero(X8)))
| ~ class_Groups_Olinordered__ab__group__add(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1482])])]) ).
fof(c_0_2752,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)),c_Groups_Ozero__class_Ozero(X8)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X8,X7),c_Groups_Ozero__class_Ozero(X8)))
| ~ class_Groups_Olinordered__ab__group__add(X8) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X8,X7),c_Groups_Ozero__class_Ozero(X8)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)),c_Groups_Ozero__class_Ozero(X8)))
| ~ class_Groups_Olinordered__ab__group__add(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1483])])]) ).
fof(c_0_2753,plain,
! [X26,X27,X28,X29] :
( ( ~ c_SEQ_Oincseq(X27,X26)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28),X29))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,X28)),hAPP(X26,X29)))
| ~ class_Orderings_Oorder(X27) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk15_2(X26,X27)),esk16_2(X26,X27)))
| c_SEQ_Oincseq(X27,X26)
| ~ class_Orderings_Oorder(X27) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,esk15_2(X26,X27))),hAPP(X26,esk16_2(X26,X27))))
| c_SEQ_Oincseq(X27,X26)
| ~ class_Orderings_Oorder(X27) ) ),
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_1484])])])])]) ).
fof(c_0_2754,plain,
! [X26,X27,X28,X29] :
( ( ~ c_SEQ_Odecseq(X27,X26)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28),X29))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,X29)),hAPP(X26,X28)))
| ~ class_Orderings_Oorder(X27) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk11_2(X26,X27)),esk12_2(X26,X27)))
| c_SEQ_Odecseq(X27,X26)
| ~ class_Orderings_Oorder(X27) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,esk12_2(X26,X27))),hAPP(X26,esk11_2(X26,X27))))
| c_SEQ_Odecseq(X27,X26)
| ~ class_Orderings_Oorder(X27) ) ),
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_1485])])])])]) ).
fof(c_0_2755,plain,
! [X26,X27,X28,X29,X30,X31] :
( ( ~ c_SEQ_Omonoseq(X27,X26)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28),X29))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,X28)),hAPP(X26,X29)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,X31)),hAPP(X26,X30)))
| ~ class_Orderings_Oorder(X27) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk5_2(X26,X27)),esk6_2(X26,X27)))
| c_SEQ_Omonoseq(X27,X26)
| ~ class_Orderings_Oorder(X27) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,esk5_2(X26,X27))),hAPP(X26,esk6_2(X26,X27))))
| c_SEQ_Omonoseq(X27,X26)
| ~ class_Orderings_Oorder(X27) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk7_2(X26,X27)),esk8_2(X26,X27)))
| c_SEQ_Omonoseq(X27,X26)
| ~ class_Orderings_Oorder(X27) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,hAPP(X26,esk8_2(X26,X27))),hAPP(X26,esk7_2(X26,X27))))
| c_SEQ_Omonoseq(X27,X26)
| ~ class_Orderings_Oorder(X27) ) ),
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_1486])])])])]) ).
fof(c_0_2756,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__semidom(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Ozero__class_Ozero(X32)),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,X31),c_Groups_Oone__class_Oone(X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),c_Nat_OSuc(X30))),c_Groups_Oone__class_Oone(X32))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1487])]) ).
fof(c_0_2757,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X22),X21))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X21))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1488])]) ).
fof(c_0_2758,plain,
! [X15,X16,X17] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X16),X15))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),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_1489])]) ).
fof(c_0_2759,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22),X21))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X21))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1490])]) ).
fof(c_0_2760,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22),X21))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X20))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1491])]) ).
fof(c_0_2761,plain,
! [X16,X17,X18,X19] :
( ~ class_RealVector_Oreal__normed__vector(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),c_RealVector_Onorm__class_Onorm(X19,X16))))
| X17 = c_Groups_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1492])]) ).
fof(c_0_2762,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__semidom(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X32,c_Groups_Ozero__class_Ozero(X32)),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X32,X31),c_Groups_Oone__class_Oone(X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X32,hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),c_Nat_OSuc(X30))),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1493])]) ).
fof(c_0_2763,plain,
! [X11,X12,X13,X14] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X12,X11)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,X13)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X13)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1494])])])]) ).
fof(c_0_2764,plain,
! [X40,X41,X42,X43] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X41),X40))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X41,X40)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X43,X42)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X43),X42)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1495])])])]) ).
fof(c_0_2765,plain,
! [X66,X67,X68,X69] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X69),X68))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X67),X66))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X69),X67)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),X66))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1496])]) ).
fof(c_0_2766,plain,
! [X35,X36,X37,X38] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38),X37))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X35))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),X35))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1497])]) ).
fof(c_0_2767,plain,
! [X35,X36,X37,X38] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38),X37))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36),X35))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X35))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1498])]) ).
fof(c_0_2768,plain,
! [X35,X36,X37,X38] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38),X37))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X35))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X35))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1499])]) ).
fof(c_0_2769,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X16),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X16),X17))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1500])]) ).
fof(c_0_2770,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X17),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1501])]) ).
fof(c_0_2771,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__ab__semigroup__add(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X16),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X16),X17))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1502])]) ).
fof(c_0_2772,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__ab__semigroup__add(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X17),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1503])]) ).
fof(c_0_2773,plain,
! [X13,X14] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X14),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X14)),hAPP(c_Complex_OIm,X13))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X14)),hAPP(c_Complex_ORe,X13))),
inference(variable_rename,[status(thm)],[c_0_1504]) ).
fof(c_0_2774,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__semiring__strict(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)),c_Groups_Ozero__class_Ozero(X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1505])]) ).
fof(c_0_2775,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__semiring__strict(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X12),X13)),c_Groups_Ozero__class_Ozero(X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1506])]) ).
fof(c_0_2776,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__semiring__strict(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)),c_Groups_Ozero__class_Ozero(X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1507])]) ).
fof(c_0_2777,plain,
! [X12,X13,X14] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)),c_Groups_Ozero__class_Ozero(X14)))
| ~ class_Rings_Oordered__cancel__semiring(X14) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)),c_Groups_Ozero__class_Ozero(X14)))
| ~ class_Rings_Oordered__cancel__semiring(X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1508])])]) ).
fof(c_0_2778,plain,
! [X12,X13,X14] :
( ~ class_Rings_Oordered__cancel__semiring(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)),c_Groups_Ozero__class_Ozero(X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1509])]) ).
fof(c_0_2779,plain,
! [X12,X13,X14] :
( ~ class_Rings_Oordered__cancel__semiring(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X12),X13)),c_Groups_Ozero__class_Ozero(X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1510])]) ).
fof(c_0_2780,plain,
! [X12,X13,X14] :
( ~ class_Rings_Oordered__cancel__semiring(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)),c_Groups_Ozero__class_Ozero(X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1511])]) ).
fof(c_0_2781,plain,
! [X16,X17,X18] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X16))))
| X17 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1512])]) ).
fof(c_0_2782,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X33,X31)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X32,X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1513])]) ).
fof(c_0_2783,plain,
! [X35,X36,X37] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37),X36))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X36)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X37))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1514])]) ).
fof(c_0_2784,plain,
! [X35,X36,X37] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37),X36))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X37,X35)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X35))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1515])]) ).
fof(c_0_2785,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__comm__monoid__add(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12)),c_Groups_Ozero__class_Ozero(X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1516])]) ).
fof(c_0_2786,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__comm__monoid__add(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12)),c_Groups_Ozero__class_Ozero(X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1517])]) ).
fof(c_0_2787,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__comm__monoid__add(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12)),c_Groups_Ozero__class_Ozero(X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1518])]) ).
fof(c_0_2788,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__comm__monoid__add(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12)),c_Groups_Ozero__class_Ozero(X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1519])]) ).
fof(c_0_2789,plain,
! [X71,X72,X73,X74,X75] : hAPP(hAPP(c_Power_Opower_Opower(X75,X74,X73),X72),c_Nat_OSuc(X71)) = hAPP(hAPP(X73,X72),hAPP(hAPP(c_Power_Opower_Opower(X75,X74,X73),X72),X71)),
inference(variable_rename,[status(thm)],[c_0_1520]) ).
fof(c_0_2790,plain,
! [X55,X56,X57,X58] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X56),c_Groups_Oone__class_Oone(tc_Int_Oint))),X55))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X56),X55)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X58),X57))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X58),c_Groups_Oone__class_Oone(tc_Int_Oint))),X57)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1521])])])]) ).
fof(c_0_2791,plain,
! [X6,X7] :
( ~ class_Rings_Olinordered__ring(X7)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X6)),c_Groups_Ozero__class_Ozero(X7))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1522])]) ).
fof(c_0_2792,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__semiring__strict(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1523])]) ).
fof(c_0_2793,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__semiring__strict(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1524])]) ).
fof(c_0_2794,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X32)),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1525])]) ).
fof(c_0_2795,plain,
! [X18,X19] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X18))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X19,X18)),X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1526])]) ).
fof(c_0_2796,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X32)),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1527])]) ).
fof(c_0_2797,plain,
! [X12,X13] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1528])]) ).
fof(c_0_2798,plain,
! [X12,X13] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1529])]) ).
fof(c_0_2799,plain,
! [X12,X13] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X13),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1530])]) ).
fof(c_0_2800,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31),X33))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1531])]) ).
fof(c_0_2801,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X21)),X20))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22),X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1532])]) ).
fof(c_0_2802,plain,
! [X31,X32,X33] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)),X31)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)),X31)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1533])])]) ).
fof(c_0_2803,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1534])]) ).
fof(c_0_2804,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1535])])])]) ).
fof(c_0_2805,plain,
! [X13,X14,X15] :
( ~ class_Rings_Ocomm__ring__1(X15)
| c_Groups_Ominus__class_Ominus(X15,hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X13),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Ominus__class_Ominus(X15,X14,X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1536])]) ).
fof(c_0_2806,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22),X21))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20),X21))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1537])]) ).
fof(c_0_2807,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X22),X21))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22),X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21),X20))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1538])]) ).
fof(c_0_2808,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X20))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1539])]) ).
fof(c_0_2809,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X21))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1540])]) ).
fof(c_0_2810,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22),X21))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1541])]) ).
fof(c_0_2811,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1542])]) ).
fof(c_0_2812,plain,
! [X15,X16,X17] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X15),X17)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X15),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1543])]) ).
fof(c_0_2813,plain,
! [X52,X53,X54,X55,X56] :
( ~ class_Rings_Ocomm__semiring__1(X56)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X54)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X53),X52)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X54),X52)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1544])]) ).
fof(c_0_2814,plain,
! [X52,X53,X54,X55,X56] :
( ~ class_Rings_Ocomm__semiring__1(X56)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X54)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X53),X52)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X54),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X53),X52))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1545])]) ).
fof(c_0_2815,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Rings_Ocomm__semiring__1(X31)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X30),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X28),X27)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X30),X28)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X29),X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1546])]) ).
fof(c_0_2816,plain,
! [X28,X29,X30,X31] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X29)),X28)))
| X29 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X31 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X31)),X30))) )
& ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X31)),X30))) ) ),
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_1547])])])])]) ).
fof(c_0_2817,plain,
! [X39] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X39))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X39)),esk33_0))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1548])]) ).
fof(c_0_2818,plain,
! [X39] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X39))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X39)),esk32_0))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1549])]) ).
fof(c_0_2819,plain,
! [X39] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk28_0))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X39))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X39)),esk28_0))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1550])])]) ).
fof(c_0_2820,plain,
! [X39] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk27_0))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X39))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X39)),esk27_0))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1551])])]) ).
fof(c_0_2821,plain,
! [X39] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk26_0))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X39))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X39)),esk26_0))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1552])])]) ).
fof(c_0_2822,plain,
! [X39] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk25_0))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X39))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X39)),esk25_0))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1553])])]) ).
fof(c_0_2823,plain,
! [X32,X33,X34,X35] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33))
| ~ hBOOL(hAPP(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),X33),X32))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X32))
| ~ hBOOL(hAPP(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),X33),X32))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X35))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X34))
| hBOOL(hAPP(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),X35),X34))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1554])])])])]) ).
fof(c_0_2824,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31))
| hBOOL(hAPP(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),X31),X32))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1555])]) ).
fof(c_0_2825,plain,
! [X88,X89,X90,X91,X92,X93,X94] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X89),X88))
| hBOOL(hAPP(X90,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X90,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X89,X88))) )
& ( X89 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X88),X91)
| hBOOL(hAPP(X90,X91))
| ~ hBOOL(hAPP(X90,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X89,X88))) )
& ( X93 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),esk65_3(X92,X93,X94))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X93),X92))
| hBOOL(hAPP(X94,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X93,X92))) )
& ( ~ hBOOL(hAPP(X94,esk65_3(X92,X93,X94)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X93),X92))
| hBOOL(hAPP(X94,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X93,X92))) )
& ( X93 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),esk65_3(X92,X93,X94))
| ~ hBOOL(hAPP(X94,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X94,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X93,X92))) )
& ( ~ hBOOL(hAPP(X94,esk65_3(X92,X93,X94)))
| ~ hBOOL(hAPP(X94,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X94,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X93,X92))) ) ),
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_1556])])])])])]) ).
fof(c_0_2826,plain,
! [X88,X89,X90,X91,X92,X93,X94] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X89),X88))
| hBOOL(hAPP(X90,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X90,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X89,X88))) )
& ( X89 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X88),X91)
| hBOOL(hAPP(X90,X91))
| ~ hBOOL(hAPP(X90,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X89,X88))) )
& ( X93 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),esk64_3(X92,X93,X94))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X93),X92))
| hBOOL(hAPP(X94,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X93,X92))) )
& ( ~ hBOOL(hAPP(X94,esk64_3(X92,X93,X94)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X93),X92))
| hBOOL(hAPP(X94,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X93,X92))) )
& ( X93 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),esk64_3(X92,X93,X94))
| ~ hBOOL(hAPP(X94,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X94,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X93,X92))) )
& ( ~ hBOOL(hAPP(X94,esk64_3(X92,X93,X94)))
| ~ hBOOL(hAPP(X94,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X94,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X93,X92))) ) ),
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_1557])])])])])]) ).
fof(c_0_2827,plain,
! [X23,X24,X25] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X24),c_Groups_Ozero__class_Ozero(X25)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)))
| ~ class_Rings_Olinordered__ring__strict(X25) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X23),c_Groups_Ozero__class_Ozero(X25)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)))
| ~ class_Rings_Olinordered__ring__strict(X25) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X24),c_Groups_Ozero__class_Ozero(X25)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)))
| ~ class_Rings_Olinordered__ring__strict(X25) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X23),c_Groups_Ozero__class_Ozero(X25)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)))
| ~ class_Rings_Olinordered__ring__strict(X25) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)))
| ~ class_Rings_Olinordered__ring__strict(X25) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X24),c_Groups_Ozero__class_Ozero(X25)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,X23),c_Groups_Ozero__class_Ozero(X25)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23)))
| ~ class_Rings_Olinordered__ring__strict(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1558])])]) ).
fof(c_0_2828,plain,
! [X23,X24] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X24,X23)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X24,X23)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X24,X23)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1559])])]) ).
fof(c_0_2829,plain,
! [X23,X24] :
( ( ~ hBOOL(hAPP(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,X23,X24)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
| hBOOL(hAPP(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,X23,X24)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1560])])]) ).
fof(c_0_2830,plain,
! [X20,X21] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),X21)),
inference(variable_rename,[status(thm)],[c_0_1561]) ).
fof(c_0_2831,plain,
! [X20,X21] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),X20)),
inference(variable_rename,[status(thm)],[c_0_1562]) ).
fof(c_0_2832,plain,
! [X84,X85] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X84,X85)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X85),X84))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X85)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X85),X84))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X84,X85)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X85)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1563])])]) ).
fof(c_0_2833,plain,
! [X30,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,c_Nat_OSuc(X30))),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1564])]) ).
fof(c_0_2834,plain,
! [X23,X24] :
( ( ~ hBOOL(hAPP(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,X23,X24)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(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,X23,X24)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1565])])]) ).
fof(c_0_2835,plain,
! [X14,X15,X16,X17] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,X17),X15),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X16,X17),X15),X14))
| ~ class_Orderings_Oord(X17) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,X17),X14),X15))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X16,X17),X15),X14))
| ~ class_Orderings_Oord(X17) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,X17),X15),X14))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,X17),X14),X15))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X16,X17),X15),X14))
| ~ class_Orderings_Oord(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1566])])]) ).
fof(c_0_2836,plain,
! [X30,X31] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X31))),X30)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X30)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X31)),X30))),
inference(variable_rename,[status(thm)],[c_0_1567]) ).
fof(c_0_2837,plain,
! [X31,X32,X33] :
( ~ class_Rings_Olinordered__semidom(X33)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X33,c_Groups_Oone__class_Oone(X33)),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X33,c_Groups_Oone__class_Oone(X33)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X33,c_Groups_Oone__class_Oone(X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X32),X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1568])]) ).
fof(c_0_2838,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__semiring__strict(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1569])]) ).
fof(c_0_2839,plain,
! [X12,X13,X14] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)))
| ~ class_Rings_Oordered__ring(X14) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)))
| ~ class_Rings_Oordered__ring(X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1570])])]) ).
fof(c_0_2840,plain,
! [X12,X13,X14] :
( ~ class_Rings_Oordered__cancel__semiring(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1571])]) ).
fof(c_0_2841,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__comm__monoid__add(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1572])]) ).
fof(c_0_2842,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__comm__monoid__add(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1573])]) ).
fof(c_0_2843,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__comm__monoid__add(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1574])]) ).
fof(c_0_2844,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__comm__monoid__add(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1575])]) ).
fof(c_0_2845,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X32))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1576])]) ).
fof(c_0_2846,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1577])]) ).
fof(c_0_2847,plain,
! [X30,X31,X32,X33] :
( ~ class_Rings_Olinordered__semidom(X33)
| hAPP(hAPP(c_Power_Opower__class_Opower(X33),X32),X31) != hAPP(hAPP(c_Power_Opower__class_Opower(X33),X30),X31)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,c_Groups_Ozero__class_Ozero(X33)),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,c_Groups_Ozero__class_Ozero(X33)),X30))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
| X32 = X30 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1578])]) ).
fof(c_0_2848,plain,
! [X31,X32,X33,X34] :
( ~ class_Fields_Ofield(X34)
| X33 = c_Groups_Ozero__class_Ozero(X34)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X32)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X34),hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),X31)),hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1579])]) ).
fof(c_0_2849,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_Groups_Oab__group__add(X31)
| c_Groups_Ominus__class_Ominus(X31,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X30),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),X28),X27)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31),c_Groups_Ominus__class_Ominus(X31,X30,X28)),c_Groups_Ominus__class_Ominus(X31,X29,X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1580])]) ).
fof(c_0_2850,plain,
! [X30,X31,X32,X33] :
( ~ class_Fields_Ofield(X33)
| X32 = c_Groups_Ozero__class_Ozero(X33)
| hAPP(hAPP(c_Power_Opower__class_Opower(X33),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X33),X31),X32)),X30) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X33),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X31),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X32),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1581])]) ).
fof(c_0_2851,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X32) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X32),X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1582])]) ).
fof(c_0_2852,plain,
! [X31,X32,X33,X34] :
( ( X32 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1583])])])]) ).
fof(c_0_2853,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__semidom(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Oone__class_Oone(X32)),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Oone__class_Oone(X32)),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1584])]) ).
fof(c_0_2854,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Odivision__ring(X19)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17)),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X18),X16)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1585])]) ).
fof(c_0_2855,plain,
! [X56,X57,X58,X59] :
( ~ class_RealVector_Oreal__normed__field(X59)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X59),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X59),X58),X57)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X59),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X59),X58),X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X59),X57),X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1586])]) ).
fof(c_0_2856,plain,
! [X30,X31,X32,X33] :
( ~ class_Fields_Ofield__inverse__zero(X33)
| hAPP(hAPP(c_Power_Opower__class_Opower(X33),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X33),X32),X31)),X30) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X33),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X32),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X31),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1587])]) ).
fof(c_0_2857,plain,
! [X30,X31,X32,X33] :
( ~ class_Groups_Ocomm__monoid__mult(X33)
| hAPP(hAPP(c_Power_Opower__class_Opower(X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X32),X31)),X30) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X32),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X31),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1588])]) ).
fof(c_0_2858,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Ocomm__semiring(X19)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17)),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1589])]) ).
fof(c_0_2859,plain,
! [X57,X58,X59,X60] :
( ~ class_RealVector_Oreal__normed__algebra(X60)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X60),X59),X58)),X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X60),X59),X57)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X60),X58),X57)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1590])]) ).
fof(c_0_2860,plain,
! [X56,X57,X58,X59] :
( ~ class_RealVector_Oreal__normed__algebra(X59)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X59),X58),X57)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X59),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X58),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X57),X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1591])]) ).
fof(c_0_2861,plain,
! [X31,X32,X33,X34] :
( ~ class_Rings_Ocomm__semiring__1(X34)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),X33),X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),X31),X32)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34),X33),X31)),X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1592])]) ).
fof(c_0_2862,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Ocomm__semiring__1(X19)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17)),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1593])]) ).
fof(c_0_2863,plain,
! [X50,X51,X52,X53] :
( ~ class_Rings_Ocomm__semiring__1(X53)
| hAPP(hAPP(c_Power_Opower__class_Opower(X53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X53),X52),X51)),X50) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X53),hAPP(hAPP(c_Power_Opower__class_Opower(X53),X52),X50)),hAPP(hAPP(c_Power_Opower__class_Opower(X53),X51),X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1594])]) ).
fof(c_0_2864,plain,
! [X31] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X31)))),
inference(variable_rename,[status(thm)],[c_0_1595]) ).
fof(c_0_2865,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__ring__strict(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1596])]) ).
fof(c_0_2866,plain,
! [X12,X13,X14] :
( ~ class_Rings_Oordered__ring(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1597])]) ).
fof(c_0_2867,plain,
! [X30,X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X30)),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1598])]) ).
fof(c_0_2868,plain,
! [X13,X14] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X14),X13)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X14)),hAPP(c_Complex_ORe,X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X14)),hAPP(c_Complex_OIm,X13))),
inference(variable_rename,[status(thm)],[c_0_1599]) ).
fof(c_0_2869,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),X7))
| ~ class_Groups_Olinordered__ab__group__add(X8) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),X7))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)))
| ~ class_Groups_Olinordered__ab__group__add(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1600])])]) ).
fof(c_0_2870,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8)),X7))
| ~ class_Groups_Olinordered__ab__group__add(X8) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8)),X7))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)))
| ~ class_Groups_Olinordered__ab__group__add(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1601])])]) ).
fof(c_0_2871,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X34))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X34))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1602])])])])]) ).
fof(c_0_2872,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X31),X32),X31) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X31),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1603])]) ).
fof(c_0_2873,plain,
! [X11,X12,X13,X14] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X12),X11))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X12),X11))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X14),X13))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X14),X13))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X14),X13))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X14),X13))) ) ),
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_1604])])])])]) ).
fof(c_0_2874,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Olinordered__semidom(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19)),X18))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1605])]) ).
fof(c_0_2875,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__comm__monoid__add(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X18))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1606])]) ).
fof(c_0_2876,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__comm__monoid__add(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19)),X18))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1607])]) ).
fof(c_0_2877,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__comm__monoid__add(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X18))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X16),X18))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1608])]) ).
fof(c_0_2878,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oordered__comm__monoid__add(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19)),X18))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1609])]) ).
fof(c_0_2879,plain,
! [X12,X13,X14] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| c_Groups_Oabs__class_Oabs(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),c_Groups_Oabs__class_Oabs(X14,X13)),c_Groups_Oabs__class_Oabs(X14,X12))
| ~ class_Rings_Oordered__ring__abs(X14) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X13))
| c_Groups_Oabs__class_Oabs(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),c_Groups_Oabs__class_Oabs(X14,X13)),c_Groups_Oabs__class_Oabs(X14,X12))
| ~ class_Rings_Oordered__ring__abs(X14) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Ozero__class_Ozero(X14)),X12))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| c_Groups_Oabs__class_Oabs(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),c_Groups_Oabs__class_Oabs(X14,X13)),c_Groups_Oabs__class_Oabs(X14,X12))
| ~ class_Rings_Oordered__ring__abs(X14) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X12),c_Groups_Ozero__class_Ozero(X14)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),c_Groups_Ozero__class_Ozero(X14)))
| c_Groups_Oabs__class_Oabs(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),c_Groups_Oabs__class_Oabs(X14,X13)),c_Groups_Oabs__class_Oabs(X14,X12))
| ~ class_Rings_Oordered__ring__abs(X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1610])])]) ).
fof(c_0_2880,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X8,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X8)))),
inference(variable_rename,[status(thm)],[c_0_1611]) ).
fof(c_0_2881,plain,
! [X31,X32] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X32))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X32) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X32))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X32) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X32),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1612])])]) ).
fof(c_0_2882,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31),X32))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,X32) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X32),X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1613])]) ).
fof(c_0_2883,plain,
! [X31,X32,X33,X34] :
( ( X32 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31) = X31 )
& ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X33) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1614])])])]) ).
fof(c_0_2884,plain,
! [X11,X12,X13] :
( ( X12 = c_Groups_Ozero__class_Ozero(X13)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X11),X11)) != c_Groups_Ozero__class_Ozero(X13)
| ~ class_Rings_Olinordered__ring__strict(X13) )
& ( X11 = c_Groups_Ozero__class_Ozero(X13)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X11),X11)) != c_Groups_Ozero__class_Ozero(X13)
| ~ class_Rings_Olinordered__ring__strict(X13) )
& ( X12 != c_Groups_Ozero__class_Ozero(X13)
| X11 != c_Groups_Ozero__class_Ozero(X13)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X11),X11)) = c_Groups_Ozero__class_Ozero(X13)
| ~ class_Rings_Olinordered__ring__strict(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1615])])]) ).
fof(c_0_2885,plain,
! [X17,X18] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X18),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18),c_Groups_Oone__class_Oone(tc_Int_Oint))),X17)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1616])]) ).
fof(c_0_2886,plain,
! [X50,X51,X52] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X52))
| X52 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X52),X50))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X51))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1617])]) ).
fof(c_0_2887,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))
| hBOOL(hAPP(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,X14,X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1618])]) ).
fof(c_0_2888,plain,
! [X8,X9] :
( ~ class_Rings_Oring__1(X9)
| c_Groups_Ominus__class_Ominus(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X8),c_Groups_Oone__class_Oone(X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),c_Groups_Oone__class_Oone(X9))),c_Groups_Ominus__class_Ominus(X9,X8,c_Groups_Oone__class_Oone(X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1619])]) ).
fof(c_0_2889,plain,
! [X50,X51,X52] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X52))
| X52 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X52),X50))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X51),X52))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1620])]) ).
fof(c_0_2890,plain,
! [X9,X10,X11] :
( ( ~ c_SEQ_Osubseq(X9)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X9,X10)),hAPP(X9,c_Nat_OSuc(X10)))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X11,esk53_1(X11))),hAPP(X11,c_Nat_OSuc(esk53_1(X11)))))
| c_SEQ_Osubseq(X11) ) ),
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_1621])])])])]) ).
fof(c_0_2891,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X31))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X33),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X33)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1622])]) ).
fof(c_0_2892,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X8))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(variable_rename,[status(thm)],[c_0_1623]) ).
fof(c_0_2893,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1624])]) ).
fof(c_0_2894,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))
| hBOOL(hAPP(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),X14),X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1625])]) ).
fof(c_0_2895,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X13))
| hBOOL(hAPP(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),X14),X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1626])]) ).
fof(c_0_2896,plain,
! [X32,X33,X34,X35] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
| ~ hBOOL(hAPP(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),X33),X32))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
| ~ hBOOL(hAPP(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),X33),X32))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X34))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1627])])])])]) ).
fof(c_0_2897,plain,
! [X31,X32,X33] :
( ~ class_Rings_Ocomm__semiring__1(X33)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X32),X31)),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33),X32),c_Groups_Oone__class_Oone(X33))),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1628])]) ).
fof(c_0_2898,plain,
! [X62,X63,X64] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X64),X63)),X62) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X64),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X62)),
inference(variable_rename,[status(thm)],[c_0_1629]) ).
fof(c_0_2899,plain,
! [X62,X63,X64] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X64),X63)),X62) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X64),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X63),X62)),
inference(variable_rename,[status(thm)],[c_0_1630]) ).
fof(c_0_2900,plain,
! [X31,X32,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),
inference(variable_rename,[status(thm)],[c_0_1631]) ).
fof(c_0_2901,plain,
! [X55,X56,X57,X58] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X56),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X55,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X56),X55)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X58),X57))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X57,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_1632])])])]) ).
fof(c_0_2902,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X33)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34),X35))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X34))) ) ),
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_2903,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Orderings_Oord(X18)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,X18),X16),X15))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,hAPP(X16,X14)),hAPP(X15,X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1634])]) ).
fof(c_0_2904,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Orderings_Oord(X18)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,X18),X16),X15))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,hAPP(X16,X14)),hAPP(X15,X14))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1635])]) ).
fof(c_0_2905,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X33)),X31) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1636])]) ).
fof(c_0_2906,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X33))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X33),c_Nat_OSuc(X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1637])]) ).
fof(c_0_2907,plain,
! [X13,X14] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X13)),c_Transcendental_Ocos(X14))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X13)),c_Transcendental_Osin(X14))),
inference(variable_rename,[status(thm)],[c_0_1638]) ).
fof(c_0_2908,plain,
! [X13,X14] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X14)),c_Transcendental_Ocos(X13))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X14)),c_Transcendental_Osin(X13))),
inference(variable_rename,[status(thm)],[c_0_1639]) ).
fof(c_0_2909,plain,
! [X16,X17,X18,X19] :
( ~ class_Divides_Osemiring__div(X19)
| X18 = c_Groups_Ozero__class_Ozero(X19)
| c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)),X18) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X16),c_Divides_Odiv__class_Odiv(X19,X17,X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1640])]) ).
fof(c_0_2910,plain,
! [X16,X17,X18,X19] :
( ~ class_Divides_Osemiring__div(X19)
| X18 = c_Groups_Ozero__class_Ozero(X19)
| c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X18)),X18) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X16),c_Divides_Odiv__class_Odiv(X19,X17,X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1641])]) ).
fof(c_0_2911,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Odivision__ring(X19)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),c_Groups_Ominus__class_Ominus(X19,X18,X17)),X16) = c_Groups_Ominus__class_Ominus(X19,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X18),X16),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1642])]) ).
fof(c_0_2912,plain,
! [X56,X57,X58,X59] :
( ~ class_RealVector_Oreal__normed__field(X59)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X59),c_Groups_Ominus__class_Ominus(X59,X58,X57)),X56) = c_Groups_Ominus__class_Ominus(X59,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X59),X58),X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X59),X57),X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1643])]) ).
fof(c_0_2913,plain,
! [X56,X57,X58,X59] :
( ~ class_RealVector_Oreal__normed__algebra(X59)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),c_Groups_Ominus__class_Ominus(X59,X58,X57)),X56) = c_Groups_Ominus__class_Ominus(X59,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X58),X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X59),X57),X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1644])]) ).
fof(c_0_2914,plain,
! [X57,X58,X59,X60] :
( ~ class_RealVector_Oreal__normed__algebra(X60)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X60),c_Groups_Ominus__class_Ominus(X60,X59,X58)),X57) = c_Groups_Ominus__class_Ominus(X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X60),X59),X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X60),X58),X57)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1645])]) ).
fof(c_0_2915,plain,
! [X11,X12] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X12)),c_Transcendental_Oln(X11)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X12)),c_Transcendental_Oln(X11)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1646])])]) ).
fof(c_0_2916,plain,
! [X11,X12] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X12)),c_Transcendental_Oln(X11)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X12)),c_Transcendental_Oln(X11)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1647])])]) ).
fof(c_0_2917,plain,
! [X30,X31,X32,X33] :
( ~ class_Rings_Olinordered__semidom(X33)
| hAPP(hAPP(c_Power_Opower__class_Opower(X33),X32),c_Nat_OSuc(X31)) != hAPP(hAPP(c_Power_Opower__class_Opower(X33),X30),c_Nat_OSuc(X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,c_Groups_Ozero__class_Ozero(X33)),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X33,c_Groups_Ozero__class_Ozero(X33)),X30))
| X32 = X30 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1648])]) ).
fof(c_0_2918,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__idom(X32)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X32,c_Groups_Ozero__class_Ozero(X32)),hAPP(hAPP(c_Power_Opower__class_Opower(X32),c_Groups_Oabs__class_Oabs(X32,X31)),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1649])]) ).
fof(c_0_2919,plain,
! [X59,X60,X61,X62] :
( ~ class_RealVector_Oreal__normed__algebra(X62)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X62),X61),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X62),X60),X59)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X62),X61),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X62),X61),X59)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1650])]) ).
fof(c_0_2920,plain,
! [X58,X59,X60,X61] :
( ~ class_RealVector_Oreal__normed__algebra(X61)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X61),X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X61),X59),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X61),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X61),X60),X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1651])]) ).
fof(c_0_2921,plain,
! [X15,X16,X17,X18] :
( ~ class_Rings_Ocomm__semiring__1(X18)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18),X16),X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18),X17),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18),X17),X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1652])]) ).
fof(c_0_2922,plain,
! [X52,X53,X54,X55] :
( ~ class_Rings_Ocomm__semiring__1(X55)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X55),X54),X53)),X52) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X55),X54),X52)),X53) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1653])]) ).
fof(c_0_2923,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Ocomm__semiring__1(X19)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17)),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16)),X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1654])]) ).
fof(c_0_2924,plain,
! [X13,X14] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X14),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X14)),c_Transcendental_Ocos(X13))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X14)),c_Transcendental_Osin(X13))),
inference(variable_rename,[status(thm)],[c_0_1655]) ).
fof(c_0_2925,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20),X22) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22)),X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1656])]) ).
fof(c_0_2926,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22)),X20) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20),X22) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1657])]) ).
fof(c_0_2927,plain,
! [X13,X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X14),X13) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X14)),hAPP(c_Complex_ORe,X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X14)),hAPP(c_Complex_OIm,X13))),
inference(variable_rename,[status(thm)],[c_0_1658]) ).
fof(c_0_2928,plain,
! [X43,X44,X46] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk21_2(X43,X44)),X43))
| ~ hBOOL(hAPP(X44,X43))
| hBOOL(hAPP(X44,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),esk21_2(X43,X44)))
| ~ hBOOL(hAPP(X44,X46))
| ~ hBOOL(hAPP(X44,X43))
| hBOOL(hAPP(X44,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X44,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk21_2(X43,X44)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X44,X43))
| hBOOL(hAPP(X44,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
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_1659])])])])]) ).
fof(c_0_2929,plain,
! [X28,X29,X30,X31] :
( ( ~ hBOOL(hAPP(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),X29),X28)))
| X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)) )
& ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(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),X31),X30))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
| hBOOL(hAPP(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),X31),X30))) ) ),
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_1660])])])])]) ).
fof(c_0_2930,plain,
! [X28,X29,X30,X31] :
( ( ~ hBOOL(hAPP(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),X29),X28)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
| X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
| hBOOL(hAPP(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),X31),X30))) )
& ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(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),X31),X30))) ) ),
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_1661])])])])]) ).
fof(c_0_2931,plain,
! [X26] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk22_1(X26)),esk23_1(X26)))
| c_SEQ_Oconvergent(tc_RealDef_Oreal,X26)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X26) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(X26,esk22_1(X26))),hAPP(X26,esk23_1(X26))))
| c_SEQ_Oconvergent(tc_RealDef_Oreal,X26)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X26) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1662])])])]) ).
fof(c_0_2932,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__semidom(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Oone__class_Oone(X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Oone__class_Oone(X32)),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),c_Nat_OSuc(X30)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1663])]) ).
fof(c_0_2933,plain,
! [X31,X32,X33,X34] :
( ~ class_Groups_Omonoid__mult(X34)
| hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34),hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),X32)),hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1664])]) ).
fof(c_0_2934,plain,
! [X51,X52,X53,X54] :
( ~ class_Rings_Ocomm__semiring__1(X54)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X54),hAPP(hAPP(c_Power_Opower__class_Opower(X54),X53),X52)),hAPP(hAPP(c_Power_Opower__class_Opower(X54),X53),X51)) = hAPP(hAPP(c_Power_Opower__class_Opower(X54),X53),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1665])]) ).
fof(c_0_2935,plain,
! [X74,X75,X77] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk34_2(X74,X75)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X74))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X75)) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk34_2(X74,X75)),X75) = X74
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X74))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X75)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X77))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X77),X75) != X74
| X77 = esk34_2(X74,X75)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X74))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X75)) ) ),
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_1666])])])])]) ).
fof(c_0_2936,plain,
! [X11,X12,X13,X14] :
( ( X12 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X11 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X14 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X13 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),X13)) = 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_1667])])])])]) ).
fof(c_0_2937,plain,
! [X27,X28,X29,X30,X31,X32] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X32)
| X31 = c_Groups_Ozero__class_Ozero(X32)
| X30 != X29
| X28 = X27
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),X31),X28)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),X31),X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1668])]) ).
fof(c_0_2938,plain,
! [X31,X32] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X31)),c_Nat_OSuc(X32))),
inference(variable_rename,[status(thm)],[c_0_1669]) ).
fof(c_0_2939,plain,
! [X30,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31))
| hBOOL(hAPP(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),X31),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1670])]) ).
fof(c_0_2940,plain,
! [X55,X56,X57,X58] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X56),X55))
| X56 = X55 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X58),X57))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X57),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
& ( X58 != X57
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X57),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_1671])])])])]) ).
fof(c_0_2941,plain,
! [X55,X56,X57,X58] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X56),X55)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),X57))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X57),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_2942,plain,
! [X31,X32] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X32,X31)),X32)),
inference(variable_rename,[status(thm)],[c_0_1673]) ).
fof(c_0_2943,plain,
! [X31,X32] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X31)),X32)),
inference(variable_rename,[status(thm)],[c_0_1674]) ).
fof(c_0_2944,plain,
! [X11,X12] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11),c_RComplete_Onatfloor(X12)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11)),X12))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11),c_RComplete_Onatfloor(X12)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1675])])]) ).
fof(c_0_2945,plain,
! [X62,X63,X64] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X64,X63)),X62) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X64),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X62)),
inference(variable_rename,[status(thm)],[c_0_1676]) ).
fof(c_0_2946,plain,
! [X31,X32,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X32)),X31) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),
inference(variable_rename,[status(thm)],[c_0_1677]) ).
fof(c_0_2947,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__semidom(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X32,c_Groups_Oone__class_Oone(X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X32,c_Groups_Oone__class_Oone(X32)),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1678])]) ).
fof(c_0_2948,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__semidom(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Ozero__class_Ozero(X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X32,c_Groups_Ozero__class_Ozero(X32)),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1679])]) ).
fof(c_0_2949,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__semidom(X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X32,c_Groups_Ozero__class_Ozero(X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X32,c_Groups_Ozero__class_Ozero(X32)),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1680])]) ).
fof(c_0_2950,plain,
! [X21,X22,X23,X24] :
( ( ~ c_SEQ_Osubseq(X21)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X21,X22)),hAPP(X21,X23))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk3_1(X24)),esk4_1(X24)))
| c_SEQ_Osubseq(X24) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X24,esk3_1(X24))),hAPP(X24,esk4_1(X24))))
| c_SEQ_Osubseq(X24) ) ),
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_1681])])])])])]) ).
fof(c_0_2951,plain,
! [X30,X31,X32] :
( ~ class_Fields_Ofield__inverse__zero(X32)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X32),c_Groups_Oone__class_Oone(X32)),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30)) = hAPP(hAPP(c_Power_Opower__class_Opower(X32),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X32),c_Groups_Oone__class_Oone(X32)),X31)),X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1682])]) ).
fof(c_0_2952,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X14),c_RealDef_Oreal(tc_Nat_Onat,X13))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X14),X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1683])]) ).
fof(c_0_2953,plain,
! [X8,X9] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X9)),X8))
| c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X8,c_RealDef_Oreal(tc_Nat_Onat,X9))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X8),X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1684])]) ).
fof(c_0_2954,plain,
! [X8,X9] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X9)),X8))
| c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X8,c_RealDef_Oreal(tc_Nat_Onat,X9))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X8),X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1685])]) ).
fof(c_0_2955,plain,
! [X36,X37,X38] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37),X38))
| hBOOL(hAPP(hAPP(X36,X37),X38))
| X38 = X37
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38),X37)) )
& ( ~ hBOOL(hAPP(hAPP(X36,X37),X38))
| hBOOL(hAPP(hAPP(X36,X37),X38))
| X38 = X37
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38),X37)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37),X38))
| hBOOL(hAPP(hAPP(X36,X37),X38))
| ~ hBOOL(hAPP(hAPP(X36,X37),X38))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38),X37)) )
& ( ~ hBOOL(hAPP(hAPP(X36,X37),X38))
| hBOOL(hAPP(hAPP(X36,X37),X38))
| ~ hBOOL(hAPP(hAPP(X36,X37),X38))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38),X37)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37),X38))
| hBOOL(hAPP(hAPP(X36,X37),X38))
| X38 = X37
| ~ hBOOL(hAPP(hAPP(X36,X37),X38)) )
& ( ~ hBOOL(hAPP(hAPP(X36,X37),X38))
| hBOOL(hAPP(hAPP(X36,X37),X38))
| X38 = X37
| ~ hBOOL(hAPP(hAPP(X36,X37),X38)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37),X38))
| hBOOL(hAPP(hAPP(X36,X37),X38))
| ~ hBOOL(hAPP(hAPP(X36,X37),X38))
| ~ hBOOL(hAPP(hAPP(X36,X37),X38)) )
& ( ~ hBOOL(hAPP(hAPP(X36,X37),X38))
| hBOOL(hAPP(hAPP(X36,X37),X38))
| ~ hBOOL(hAPP(hAPP(X36,X37),X38))
| ~ hBOOL(hAPP(hAPP(X36,X37),X38)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1686])])]) ).
fof(c_0_2956,plain,
! [X38,X39,X41] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk18_2(X38,X39)))
| ~ c_SEQ_OBseq(X39,X38)
| ~ class_RealVector_Oreal__normed__vector(X39) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X39,hAPP(X38,X41))),esk18_2(X38,X39)))
| ~ c_SEQ_OBseq(X39,X38)
| ~ class_RealVector_Oreal__normed__vector(X39) ) ),
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_1687])])])])]) ).
fof(c_0_2957,plain,
! [X62,X63,X64] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X64),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X63),X62)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X64),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X64),X62)),
inference(variable_rename,[status(thm)],[c_0_1688]) ).
fof(c_0_2958,plain,
! [X15,X16,X17] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),X15)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17),X16)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17),X15)),
inference(variable_rename,[status(thm)],[c_0_1689]) ).
fof(c_0_2959,plain,
! [X31,X32,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),
inference(variable_rename,[status(thm)],[c_0_1690]) ).
fof(c_0_2960,plain,
! [X30,X31] : hBOOL(hAPP(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X31)),X30))),
inference(variable_rename,[status(thm)],[c_0_1691]) ).
fof(c_0_2961,plain,
! [X31,X32] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32)))),
inference(variable_rename,[status(thm)],[c_0_1692]) ).
fof(c_0_2962,plain,
! [X31,X32] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)))),
inference(variable_rename,[status(thm)],[c_0_1693]) ).
fof(c_0_2963,plain,
! [X31,X32,X33] :
( ~ class_Rings_Ocomm__semiring__1(X33)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X31),X32)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33),X31),c_Groups_Oone__class_Oone(X33))),X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1694])]) ).
fof(c_0_2964,plain,
! [X12,X13,X14] :
( ~ class_Divides_Osemiring__div(X14)
| X13 = c_Groups_Ozero__class_Ozero(X14)
| c_Divides_Odiv__class_Odiv(X14,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12),X13) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),c_Divides_Odiv__class_Odiv(X14,X12,X13)),c_Groups_Oone__class_Oone(X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1695])]) ).
fof(c_0_2965,plain,
! [X12,X13,X14] :
( ~ class_Divides_Osemiring__div(X14)
| X13 = c_Groups_Ozero__class_Ozero(X14)
| c_Divides_Odiv__class_Odiv(X14,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X12),X13),X13) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),c_Divides_Odiv__class_Odiv(X14,X12,X13)),c_Groups_Oone__class_Oone(X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1696])]) ).
fof(c_0_2966,plain,
! [X16,X17,X18] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X18)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X17,X16),X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1697])]) ).
fof(c_0_2967,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X13))
| c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X14),X13)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(X14),c_Transcendental_Oln(X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1698])]) ).
fof(c_0_2968,plain,
! [X31,X32,X33] :
( ( X32 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X33),X31),X32) = c_Groups_Oone__class_Oone(X33)
| ~ class_Power_Opower(X33) )
& ( X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X33),X31),X32) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33),X31),hAPP(hAPP(c_Power_Opower__class_Opower(X33),X31),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X33) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1699])])]) ).
fof(c_0_2969,plain,
! [X11,X12,X13] :
( ( X12 = c_Groups_Ozero__class_Ozero(X13)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),X11) != c_Groups_Ozero__class_Ozero(X13)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X12))
| ~ class_Groups_Oordered__comm__monoid__add(X13) )
& ( X11 = c_Groups_Ozero__class_Ozero(X13)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),X11) != c_Groups_Ozero__class_Ozero(X13)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X12))
| ~ class_Groups_Oordered__comm__monoid__add(X13) )
& ( X12 != c_Groups_Ozero__class_Ozero(X13)
| X11 != c_Groups_Ozero__class_Ozero(X13)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),X11) = c_Groups_Ozero__class_Ozero(X13)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X12))
| ~ class_Groups_Oordered__comm__monoid__add(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1700])])]) ).
fof(c_0_2970,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X13))
| c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(X14)),c_Transcendental_Oln(X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1701])]) ).
fof(c_0_2971,plain,
! [X15] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X15))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1702])]) ).
fof(c_0_2972,plain,
! [X30,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X31),c_RealDef_Oreal(tc_Nat_Onat,X30)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X31)),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1703])]) ).
fof(c_0_2973,plain,
! [X11,X12] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X12)),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),c_RealDef_Oreal(tc_Nat_Onat,X11)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),c_RealDef_Oreal(tc_Nat_Onat,X11)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X12)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1704])])]) ).
fof(c_0_2974,plain,
! [X36,X37,X38,X39,X40,X41] :
( ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X38,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X37,X36))) )
& ( epred1_3(X38,X36,X37)
| ~ hBOOL(hAPP(X38,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X37,X36))) )
& ( X39 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ epred1_3(X41,X39,X40)
| hBOOL(hAPP(X41,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X40,X39))) )
& ( ~ hBOOL(hAPP(X41,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ epred1_3(X41,X39,X40)
| hBOOL(hAPP(X41,c_Divides_Odiv__class_Odiv(tc_Int_Oint,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_1705])])])])]) ).
fof(c_0_2975,plain,
! [X8] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X8)),c_Transcendental_Ocos(X8))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X8)),c_Transcendental_Osin(X8))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(variable_rename,[status(thm)],[c_0_1706]) ).
fof(c_0_2976,plain,
! [X11,X12] :
( ( hBOOL(hAPP(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),X11),X11)))
| X11 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X12 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(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),X12),X12))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1707])])])]) ).
fof(c_0_2977,plain,
! [X58,X59,X60,X61] :
( ~ class_RealVector_Oreal__normed__algebra(X61)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X61),X60),c_Groups_Ominus__class_Ominus(X61,X59,X58)) = c_Groups_Ominus__class_Ominus(X61,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X61),X60),X59),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X61),X60),X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1708])]) ).
fof(c_0_2978,plain,
! [X59,X60,X61,X62] :
( ~ class_RealVector_Oreal__normed__algebra(X62)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X62),X61),c_Groups_Ominus__class_Ominus(X62,X60,X59)) = c_Groups_Ominus__class_Ominus(X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X62),X61),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X62),X61),X59)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1709])]) ).
fof(c_0_2979,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X32,X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1710])]) ).
fof(c_0_2980,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X22),X21) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1711])]) ).
fof(c_0_2981,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X14,X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1712])]) ).
fof(c_0_2982,plain,
! [X75,X76] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk35_2(X75,X76)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X75))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76)) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk35_2(X75,X76)),X76) = X75
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X75))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1713])])])]) ).
fof(c_0_2983,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Odivision__ring(X19)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X17),X16)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17)),X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1714])]) ).
fof(c_0_2984,plain,
! [X30,X31,X32] :
( ~ class_Groups_Omonoid__mult(X32)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30)),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),X31),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1715])]) ).
fof(c_0_2985,plain,
! [X52,X53,X54,X55] :
( ~ class_Rings_Ocomm__semiring__1(X55)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X55),X54),X53)),X52) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X55),X54),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X55),X53),X52)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1716])]) ).
fof(c_0_2986,plain,
! [X49,X50,X51,X52] :
( ~ class_Rings_Ocomm__semiring__1(X52)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),X50),X49)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),X51),X50)),X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1717])]) ).
fof(c_0_2987,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oab__semigroup__mult(X19)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17)),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1718])]) ).
fof(c_0_2988,plain,
! [X27,X28,X29,X30] :
( ~ class_Rings_Ocomm__semiring__1(X30)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30),X28),X27)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30),X29),X28)),X27) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1719])]) ).
fof(c_0_2989,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Ocomm__semiring__1(X19)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17)),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1720])]) ).
fof(c_0_2990,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Oab__semigroup__add(X19)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17)),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1721])]) ).
fof(c_0_2991,plain,
! [X13,X14] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,X13)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X14)),c_Transcendental_Ocos(X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X14)),c_Transcendental_Osin(X13))),
inference(variable_rename,[status(thm)],[c_0_1722]) ).
fof(c_0_2992,plain,
! [X13,X14] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X14,X13)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X13)),c_Transcendental_Osin(X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X13)),c_Transcendental_Ocos(X14))),
inference(variable_rename,[status(thm)],[c_0_1723]) ).
fof(c_0_2993,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Osgn__class_Osgn(X8,X7)),c_Groups_Ozero__class_Ozero(X8)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,X7),c_Groups_Ozero__class_Ozero(X8)))
| ~ class_Rings_Olinordered__idom(X8) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,X7),c_Groups_Ozero__class_Ozero(X8)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Osgn__class_Osgn(X8,X7)),c_Groups_Ozero__class_Ozero(X8)))
| ~ class_Rings_Olinordered__idom(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1724])])]) ).
fof(c_0_2994,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X21),X22) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1725])]) ).
fof(c_0_2995,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X21),X22) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1726])]) ).
fof(c_0_2996,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X33)),c_RealDef_Oreal(tc_Nat_Onat,X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X35)),c_RealDef_Oreal(tc_Nat_Onat,X34))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1727])])])]) ).
fof(c_0_2997,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X33)),c_RealDef_Oreal(tc_Nat_Onat,X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X35)),c_RealDef_Oreal(tc_Nat_Onat,X34))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1728])])])]) ).
fof(c_0_2998,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__ab__group__add__abs(X14)
| c_Groups_Oabs__class_Oabs(X14,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),c_Groups_Oabs__class_Oabs(X14,X13)),c_Groups_Oabs__class_Oabs(X14,X12))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),c_Groups_Oabs__class_Oabs(X14,X13)),c_Groups_Oabs__class_Oabs(X14,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1729])]) ).
fof(c_0_2999,plain,
! [X34,X35,X36] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X36) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X36)
| X35 = X34
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X35)) )
& ( X35 != X34
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X36) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X36)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X34))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36),X35)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1730])])]) ).
fof(c_0_3000,plain,
! [X30,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))
| hBOOL(hAPP(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),X31),X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1731])]) ).
fof(c_0_3001,plain,
! [X31,X32,X33,X34] :
( ~ class_Groups_Omonoid__mult(X34)
| hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)) = hAPP(hAPP(c_Power_Opower__class_Opower(X34),hAPP(hAPP(c_Power_Opower__class_Opower(X34),X33),X32)),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1732])]) ).
fof(c_0_3002,plain,
! [X51,X52,X53,X54] :
( ~ class_Rings_Ocomm__semiring__1(X54)
| hAPP(hAPP(c_Power_Opower__class_Opower(X54),hAPP(hAPP(c_Power_Opower__class_Opower(X54),X53),X52)),X51) = hAPP(hAPP(c_Power_Opower__class_Opower(X54),X53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X52),X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1733])]) ).
fof(c_0_3003,plain,
! [X51,X52,X53,X54] :
( ( X52 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X51),X52) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X54 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X53),X54) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X53),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,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_1734])])])]) ).
fof(c_0_3004,plain,
! [X13,X14] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X14),X13)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X14)),c_Transcendental_Ocos(X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X14)),c_Transcendental_Osin(X13))),
inference(variable_rename,[status(thm)],[c_0_1735]) ).
fof(c_0_3005,plain,
! [X15] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X15)),X15) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[c_0_1736]) ).
fof(c_0_3006,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X8))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X8))),
inference(variable_rename,[status(thm)],[c_0_1737]) ).
fof(c_0_3007,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X8))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X8))),
inference(variable_rename,[status(thm)],[c_0_1738]) ).
fof(c_0_3008,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
c_0_1739 ).
fof(c_0_3009,plain,
! [X13,X14,X15] :
( ~ class_Rings_Olinordered__idom(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Ozero__class_Ozero(X15)),X14))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Oabs__class_Oabs(X15,X13)),X14) = c_Groups_Oabs__class_Oabs(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1740])]) ).
fof(c_0_3010,plain,
! [X6] :
( ~ class_Rings_Olinordered__semidom(X6)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),c_Groups_Oone__class_Oone(X6)),c_Groups_Oone__class_Oone(X6)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1741])]) ).
fof(c_0_3011,plain,
! [X53,X54,X55,X56,X57] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X57,X56),X55))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X57,X54),X53))
| c_Groups_Ominus__class_Ominus(X57,X56,X55) != c_Groups_Ominus__class_Ominus(X57,X54,X53)
| ~ class_Groups_Oordered__ab__group__add(X57) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X57,X54),X53))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X57,X56),X55))
| c_Groups_Ominus__class_Ominus(X57,X56,X55) != c_Groups_Ominus__class_Ominus(X57,X54,X53)
| ~ class_Groups_Oordered__ab__group__add(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1742])])]) ).
fof(c_0_3012,plain,
! [X53,X54,X55,X56,X57] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X57,X56),X55))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X57,X54),X53))
| c_Groups_Ominus__class_Ominus(X57,X56,X55) != c_Groups_Ominus__class_Ominus(X57,X54,X53)
| ~ class_Groups_Oordered__ab__group__add(X57) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X57,X54),X53))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X57,X56),X55))
| c_Groups_Ominus__class_Ominus(X57,X56,X55) != c_Groups_Ominus__class_Ominus(X57,X54,X53)
| ~ class_Groups_Oordered__ab__group__add(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1743])])]) ).
fof(c_0_3013,plain,
! [X31,X32] :
( ~ class_Rings_Ocomm__semiring__1(X32)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32),X31),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32),c_Groups_Oone__class_Oone(X32)),c_Groups_Oone__class_Oone(X32))),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1744])]) ).
fof(c_0_3014,plain,
! [X11] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X11)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X11)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1745])])]) ).
fof(c_0_3015,plain,
! [X11] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X11)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X11)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1746])])]) ).
fof(c_0_3016,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X8)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X8))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1747])]) ).
fof(c_0_3017,plain,
! [X11] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X11)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X11)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1748])])]) ).
fof(c_0_3018,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X8)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X8))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1749])]) ).
fof(c_0_3019,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X8)))),
inference(variable_rename,[status(thm)],[c_0_1750]) ).
fof(c_0_3020,plain,
! [X30,X31,X32] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X32,X31)),X30) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X32),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),X31)),
inference(variable_rename,[status(thm)],[c_0_1751]) ).
fof(c_0_3021,plain,
! [X62,X63,X64] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X64),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X63,X62)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X64),X63),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X64),X62)),
inference(variable_rename,[status(thm)],[c_0_1752]) ).
fof(c_0_3022,plain,
! [X31,X32,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X31)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)),
inference(variable_rename,[status(thm)],[c_0_1753]) ).
fof(c_0_3023,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__ab__group__add__abs(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,c_Groups_Oabs__class_Oabs(X14,X13)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1754])]) ).
fof(c_0_3024,plain,
! [X15,X16,X17] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),X15))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1755])]) ).
fof(c_0_3025,plain,
! [X15,X16,X17] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1756])]) ).
fof(c_0_3026,plain,
! [X15,X16,X17] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1757])]) ).
fof(c_0_3027,plain,
! [X15,X16,X17] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),X15))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1758])]) ).
fof(c_0_3028,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1759])]) ).
fof(c_0_3029,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1760])]) ).
fof(c_0_3030,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1761])]) ).
fof(c_0_3031,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1762])]) ).
fof(c_0_3032,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X8))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X8)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1763])]) ).
fof(c_0_3033,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X32)),X32) = X31 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1764])]) ).
fof(c_0_3034,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),c_Groups_Osgn__class_Osgn(X8,X7)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),X7))
| ~ class_Rings_Olinordered__idom(X8) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),X7))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),c_Groups_Osgn__class_Osgn(X8,X7)))
| ~ class_Rings_Olinordered__idom(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1765])])]) ).
fof(c_0_3035,plain,
! [X24,X25] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X25)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X24),X25),
inference(variable_rename,[status(thm)],[c_0_1766]) ).
fof(c_0_3036,plain,
! [X64,X65,X66] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X66),X65)),X64) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X65),X64)),
inference(variable_rename,[status(thm)],[c_0_1767]) ).
fof(c_0_3037,plain,
! [X64,X65,X66] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X66),X65)),X64) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X65),X64)),
inference(variable_rename,[status(thm)],[c_0_1768]) ).
fof(c_0_3038,plain,
! [X64,X65,X66] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X66),X65)),X64) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X65),X64)),
inference(variable_rename,[status(thm)],[c_0_1769]) ).
fof(c_0_3039,plain,
! [X31,X32,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32)),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),
inference(variable_rename,[status(thm)],[c_0_1770]) ).
fof(c_0_3040,plain,
! [X15,X16,X17] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17),X16)),X15) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X15)),
inference(variable_rename,[status(thm)],[c_0_1771]) ).
fof(c_0_3041,plain,
! [X31,X32,X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)),
inference(variable_rename,[status(thm)],[c_0_1772]) ).
fof(c_0_3042,plain,
! [X24] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,esk58_1(X24))),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X24)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk58_1(X24)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X24)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1773])])])]) ).
fof(c_0_3043,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X8))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X8))),X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1774])]) ).
fof(c_0_3044,plain,
! [X8,X9] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X9)),X8))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),c_RComplete_Onatfloor(X8))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1775])]) ).
fof(c_0_3045,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Opreorder(X18)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X17),X16))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,X16),X15))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X17),X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1776])]) ).
fof(c_0_3046,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Oorder(X18)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X17),X16))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,X15),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X15),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1777])]) ).
fof(c_0_3047,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Opreorder(X18)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,X17),X16))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X16),X15))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X17),X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1778])]) ).
fof(c_0_3048,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Oorder(X18)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,X17),X16))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X15),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X15),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1779])]) ).
fof(c_0_3049,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Opreorder(X18)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X17),X16))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X16),X15))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X17),X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1780])]) ).
fof(c_0_3050,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Oorder(X18)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X17),X16))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X15),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X18,X15),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1781])]) ).
fof(c_0_3051,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Opreorder(X18)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,X17),X16))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,X16),X15))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,X17),X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1782])]) ).
fof(c_0_3052,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Oorder(X18)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,X17),X16))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,X15),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,X15),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1783])]) ).
fof(c_0_3053,plain,
! [X9] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X9))),v_r)),
inference(variable_rename,[status(thm)],[c_0_1784]) ).
fof(c_0_3054,plain,
! [X32,X33,X34,X35] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X35),X34),X33) != hAPP(hAPP(c_Power_Opower__class_Opower(X35),X34),X32)
| X33 = X32
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X35,c_Groups_Oone__class_Oone(X35)),X34))
| ~ class_Rings_Olinordered__semidom(X35) )
& ( X33 != X32
| hAPP(hAPP(c_Power_Opower__class_Opower(X35),X34),X33) = hAPP(hAPP(c_Power_Opower__class_Opower(X35),X34),X32)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X35,c_Groups_Oone__class_Oone(X35)),X34))
| ~ class_Rings_Olinordered__semidom(X35) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1785])])]) ).
fof(c_0_3055,plain,
! [X35,X36,X37,X38] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38),X37))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X37) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X35)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36),X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1786])]) ).
fof(c_0_3056,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22),X21))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21),X20))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X22)),X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1787])]) ).
fof(c_0_3057,plain,
! [X8,X9] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X9))
| c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X9),c_RealDef_Oreal(tc_Nat_Onat,X8))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X9)),X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1788])]) ).
fof(c_0_3058,plain,
! [X8,X9] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X9))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X9),c_RealDef_Oreal(tc_Nat_Onat,X8))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X9)),X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1789])]) ).
fof(c_0_3059,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X32)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X31),c_RealDef_Oreal(tc_Nat_Onat,X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1790])]) ).
fof(c_0_3060,plain,
! [X31,X32,X33] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X33),X32),c_Nat_OSuc(X31)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X32),X31),
inference(variable_rename,[status(thm)],[c_0_1791]) ).
fof(c_0_3061,plain,
! [X30,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X31))
| c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X31),X30)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),c_Transcendental_Oln(X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1792])]) ).
fof(c_0_3062,plain,
! [X27,X28,X29,X30] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X30,X29),c_Complex_Ocomplex_OComplex(X28,X27)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X30,X28),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X29,X27)),
inference(variable_rename,[status(thm)],[c_0_1793]) ).
fof(c_0_3063,plain,
! [X16,X17,X18,X19] :
( ~ class_Divides_Osemiring__div(X19)
| X18 = c_Groups_Ozero__class_Ozero(X19)
| c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)) = c_Divides_Odiv__class_Odiv(X19,X17,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1794])]) ).
fof(c_0_3064,plain,
! [X16,X17,X18,X19] :
( ~ class_Divides_Osemiring__div(X19)
| X18 = c_Groups_Ozero__class_Ozero(X19)
| c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X18)) = c_Divides_Odiv__class_Odiv(X19,X17,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1795])]) ).
fof(c_0_3065,plain,
! [X16,X17,X18,X19] :
( ( X18 != c_Groups_Ozero__class_Ozero(X19)
| c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)) = c_Groups_Ozero__class_Ozero(X19)
| ~ class_Divides_Osemiring__div(X19) )
& ( X18 = c_Groups_Ozero__class_Ozero(X19)
| c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)) = c_Divides_Odiv__class_Odiv(X19,X17,X16)
| ~ class_Divides_Osemiring__div(X19) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1796])])]) ).
fof(c_0_3066,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,X7)),c_Groups_Ozero__class_Ozero(X8)))
| X7 = c_Groups_Ozero__class_Ozero(X8)
| ~ class_Groups_Oordered__ab__group__add__abs(X8) )
& ( X7 != c_Groups_Ozero__class_Ozero(X8)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,X7)),c_Groups_Ozero__class_Ozero(X8)))
| ~ class_Groups_Oordered__ab__group__add__abs(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1797])])]) ).
fof(c_0_3067,plain,
! [X83,X84,X86,X87,X88] :
( ( X84 = c_Nat_OSuc(esk48_2(X83,X84))
| X84 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X84),c_Nat_OSuc(X83))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk48_2(X83,X84)),X83))
| X84 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X84),c_Nat_OSuc(X83))) )
& ( X87 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X87),c_Nat_OSuc(X86))) )
& ( X87 != c_Nat_OSuc(X88)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X88),X86))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X87),c_Nat_OSuc(X86))) ) ),
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_1798])])])])])]) ).
fof(c_0_3068,plain,
! [X50,X51,X52] :
( ~ class_Rings_Ocomm__semiring__1(X52)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),hAPP(hAPP(c_Power_Opower__class_Opower(X52),X51),X50)),X51) = hAPP(hAPP(c_Power_Opower__class_Opower(X52),X51),c_Nat_OSuc(X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1799])]) ).
fof(c_0_3069,plain,
! [X30,X31,X32] :
( ~ class_Groups_Omonoid__mult(X32)
| hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),c_Nat_OSuc(X30)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30)),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1800])]) ).
fof(c_0_3070,plain,
! [X6,X7] :
( ~ class_Groups_Oordered__ab__group__add__abs(X7)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,X6)),c_Groups_Ozero__class_Ozero(X7))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1801])]) ).
fof(c_0_3071,plain,
! [X6,X7] :
( ~ class_Rings_Olinordered__ring(X7)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X6))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1802])]) ).
fof(c_0_3072,plain,
! [X6,X7] :
( ~ class_Rings_Olinordered__semidom(X7)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X7,X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X6),c_Groups_Oone__class_Oone(X7)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1803])]) ).
fof(c_0_3073,plain,
! [X27,X28,X29,X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X30,X29)),c_Complex_Ocomplex_OComplex(X28,X27)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X30),X28),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X29),X27)),
inference(variable_rename,[status(thm)],[c_0_1804]) ).
fof(c_0_3074,plain,
! [X77,X78,X79,X80] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X80,X79)),c_Complex_Orcis(X78,X77)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X80),X78),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X79),X77)),
inference(variable_rename,[status(thm)],[c_0_1805]) ).
fof(c_0_3075,plain,
! [X49,X50,X51,X52] :
( ~ class_Rings_Ocomm__semiring__1(X52)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),X50),X49)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),X50),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),X51),X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1806])]) ).
fof(c_0_3076,plain,
! [X27,X28,X29,X30] :
( ~ class_Rings_Ocomm__semiring__1(X30)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30),X28),X27)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30),X28),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30),X29),X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1807])]) ).
fof(c_0_3077,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22),X21))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21),X20))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22),X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1808])]) ).
fof(c_0_3078,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1809])]) ).
fof(c_0_3079,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22),X21))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21),X20))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22),X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1810])]) ).
fof(c_0_3080,plain,
! [X84,X85,X86,X87] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X85),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X85))
| X84 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X85,X84) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X84),X85))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X85))
| X84 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X85,X84) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X85),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X85),X84))
| X84 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X85,X84) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X84),X85))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X85),X84))
| X84 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X85,X84) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X86 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X87,X86) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X87),X86))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X87,X86) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X86),X87))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X87,X86) = c_Groups_Ozero__class_Ozero(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_1811])])])])]) ).
fof(c_0_3081,plain,
! [X12,X13] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X13),X12))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1812])]) ).
fof(c_0_3082,plain,
! [X20,X21,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21),X20) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X20),X21),
inference(variable_rename,[status(thm)],[c_0_1813]) ).
fof(c_0_3083,plain,
! [X11] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1814])]) ).
fof(c_0_3084,plain,
! [X11] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1815])]) ).
fof(c_0_3085,plain,
! [X11] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1816])]) ).
fof(c_0_3086,plain,
! [X30,X31] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X31)),X30)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X30)),X31)),
inference(variable_rename,[status(thm)],[c_0_1817]) ).
fof(c_0_3087,plain,
! [X30,X31] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X31)),X30)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X30)),X31)),
inference(variable_rename,[status(thm)],[c_0_1818]) ).
fof(c_0_3088,plain,
! [X12,X13] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X12),X13))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1819])]) ).
fof(c_0_3089,plain,
! [X11,X12] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X12,X11)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| X11 = c_Groups_Ozero__class_Ozero(X12)
| ~ class_RealVector_Oreal__normed__vector(X12) )
& ( X11 != c_Groups_Ozero__class_Ozero(X12)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X12,X11)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_RealVector_Oreal__normed__vector(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1820])])]) ).
fof(c_0_3090,plain,
! [X11,X12,X13] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Opreorder(X13) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X12))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Opreorder(X13) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Opreorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1821])])]) ).
fof(c_0_3091,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X8))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X8),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X8)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1822])]) ).
fof(c_0_3092,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X8))
| c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X8),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X8)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1823])]) ).
fof(c_0_3093,plain,
! [X16,X17,X18] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X16)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X18,X17),X16),
inference(variable_rename,[status(thm)],[c_0_1824]) ).
fof(c_0_3094,plain,
! [X20,X21,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21),X20) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),
inference(variable_rename,[status(thm)],[c_0_1825]) ).
fof(c_0_3095,plain,
! [X8,X9] :
( ~ class_RealVector_Oreal__normed__vector(X9)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X9,X8)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1826])]) ).
fof(c_0_3096,plain,
! [X28,X29] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X28)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X29))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1827])])])]) ).
fof(c_0_3097,plain,
! [X11,X12] :
( ( c_Transcendental_Oln(X12) != c_Transcendental_Oln(X11)
| X12 = X11
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12)) )
& ( X12 != X11
| c_Transcendental_Oln(X12) = c_Transcendental_Oln(X11)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X12)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1828])])]) ).
fof(c_0_3098,plain,
! [X8,X9] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9),c_RealDef_Oreal(tc_Nat_Onat,X8)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X9)),X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1829])]) ).
fof(c_0_3099,plain,
! [X31,X32,X33,X34,X35,X36] :
( ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X31)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X35,X34) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1830])])])]) ).
fof(c_0_3100,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X31),X32) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1831])]) ).
fof(c_0_3101,plain,
! [X34,X35,X36] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34)
| X35 = X34
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)) )
& ( X35 != X34
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1832])])]) ).
fof(c_0_3102,plain,
! [X31,X32,X33] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X31)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X31),
inference(variable_rename,[status(thm)],[c_0_1833]) ).
fof(c_0_3103,plain,
! [X31,X32,X33] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X31),
inference(variable_rename,[status(thm)],[c_0_1834]) ).
fof(c_0_3104,plain,
! [X13] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_Transcendental_Ocos(c_Transcendental_Oarccos(X13)) = X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1835])]) ).
fof(c_0_3105,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31),X32) = X31 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1836])]) ).
fof(c_0_3106,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X32),X32) = X31 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1837])]) ).
fof(c_0_3107,plain,
! [X75,X76] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk60_2(X75,X76)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X76)) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk60_2(X75,X76)),c_Nat_OSuc(X75)) = X76
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X76)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1838])])])]) ).
fof(c_0_3108,plain,
! [X32,X33,X34,X35] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X32)),X33)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X34)),X35))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1839])])])]) ).
fof(c_0_3109,plain,
! [X30,X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X30))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X31)) = X31 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1840])]) ).
fof(c_0_3110,plain,
! [X28,X29] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X28)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,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_1841])])])]) ).
fof(c_0_3111,plain,
! [X54,X55] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X54)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X54 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X55 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X55)),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_1842])])])]) ).
fof(c_0_3112,plain,
! [X12,X13,X14] :
( ~ class_Groups_Ogroup__add(X14)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),c_Groups_Ominus__class_Ominus(X14,X13,X12)),X12) = X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1843])]) ).
fof(c_0_3113,plain,
! [X30] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[c_0_1844]) ).
fof(c_0_3114,plain,
! [X30] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X30 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1845])]) ).
fof(c_0_3115,plain,
! [X15,X16,X17] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17),X15)),
inference(variable_rename,[status(thm)],[c_0_1846]) ).
fof(c_0_3116,plain,
! [X15,X16,X17] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X15)),
inference(variable_rename,[status(thm)],[c_0_1847]) ).
fof(c_0_3117,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X32)) = X31 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1848])]) ).
fof(c_0_3118,plain,
! [X11,X12,X13] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| X12 = X11
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| ~ class_Orderings_Olinorder(X13) )
& ( X12 != X11
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| ~ class_Orderings_Olinorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1849])])]) ).
fof(c_0_3119,plain,
! [X11,X12,X13] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| X12 != X11
| ~ class_Orderings_Oorder(X13) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X12))
| X12 != X11
| ~ class_Orderings_Oorder(X13) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X12))
| X12 = X11
| ~ class_Orderings_Oorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1850])])]) ).
fof(c_0_3120,plain,
! [X11,X12,X13] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X12))
| X11 = X12
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| ~ class_Orderings_Oorder(X13) )
& ( X11 != X12
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X12))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| ~ class_Orderings_Oorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1851])])]) ).
fof(c_0_3121,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X14),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X13),X14))
| X14 = X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1852])]) ).
fof(c_0_3122,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X14),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X13),X14))
| X13 = X14 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1853])]) ).
fof(c_0_3123,plain,
! [X33,X34,X36,X37,X38] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34),X33))
| X33 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),esk50_2(X33,X34))) )
& ( X36 != c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X38))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37),X36)) ) ),
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_1854])])])])]) ).
fof(c_0_3124,plain,
! [X11,X12,X13] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X12))
| ~ class_Orderings_Olinorder(X13) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X12))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Olinorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1855])])]) ).
fof(c_0_3125,plain,
! [X11,X12,X13] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X11),X12))
| ~ class_Orderings_Olinorder(X13) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X11),X12))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| ~ class_Orderings_Olinorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1856])])]) ).
fof(c_0_3126,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X14),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1857])]) ).
fof(c_0_3127,plain,
! [X11,X12,X13] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X11),X12))
| X12 = X11
| ~ class_Orderings_Olinorder(X13) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X11),X12))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Olinorder(X13) )
& ( X12 != X11
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Olinorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1858])])]) ).
fof(c_0_3128,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Opreorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1859])]) ).
fof(c_0_3129,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Opreorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1860])]) ).
fof(c_0_3130,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X13),X12))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X12),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1861])]) ).
fof(c_0_3131,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X13),X12))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X12),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1862])]) ).
fof(c_0_3132,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Opreorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1863])]) ).
fof(c_0_3133,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),c_Groups_Oabs__class_Oabs(X8,X7)))
| X7 != c_Groups_Ozero__class_Ozero(X8)
| ~ class_Groups_Oordered__ab__group__add__abs(X8) )
& ( X7 = c_Groups_Ozero__class_Ozero(X8)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),c_Groups_Oabs__class_Oabs(X8,X7)))
| ~ class_Groups_Oordered__ab__group__add__abs(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1864])])]) ).
fof(c_0_3134,plain,
! [X32,X33] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),c_Nat_OSuc(X33)))
| X32 = X33
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32)) )
& ( X32 != X33
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),c_Nat_OSuc(X33)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1865])])]) ).
fof(c_0_3135,plain,
! [X32,X33,X34,X35] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),c_Nat_OSuc(X33))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34),c_Nat_OSuc(X35)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1866])])])]) ).
fof(c_0_3136,plain,
! [X71,X72,X73,X74] : hAPP(hAPP(c_Power_Opower_Opower(X74,X73,X72),X71),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X73,
inference(variable_rename,[status(thm)],[c_0_1867]) ).
fof(c_0_3137,plain,
! [X31] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X31))),
inference(variable_rename,[status(thm)],[c_0_1868]) ).
fof(c_0_3138,plain,
! [X31,X32] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31))),
inference(variable_rename,[status(thm)],[c_0_1869]) ).
fof(c_0_3139,plain,
! [X31,X32] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32))),
inference(variable_rename,[status(thm)],[c_0_1870]) ).
fof(c_0_3140,plain,
! [X12,X13,X14] :
( ~ class_Fields_Ofield__inverse__zero(X14)
| ~ class_RealVector_Oreal__normed__field(X14)
| c_RealVector_Onorm__class_Onorm(X14,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14),X13),X12)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_1871])]) ).
fof(c_0_3141,plain,
! [X30] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X30 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1872])]) ).
fof(c_0_3142,plain,
! [X30] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
| X30 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1873])]) ).
fof(c_0_3143,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X33)),c_Nat_OSuc(X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X35)),c_Nat_OSuc(X34))) ) ),
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_3144,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X33)),c_Nat_OSuc(X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X35)),c_Nat_OSuc(X34))) ) ),
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_3145,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X32)),c_Nat_OSuc(X31)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1876])]) ).
fof(c_0_3146,plain,
! [X13,X14,X15] :
( ~ class_RealVector_Oreal__normed__div__algebra(X15)
| c_Groups_Osgn__class_Osgn(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Osgn__class_Osgn(X15,X14)),c_Groups_Osgn__class_Osgn(X15,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1877])]) ).
fof(c_0_3147,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__idom(X14)
| c_Groups_Osgn__class_Osgn(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),c_Groups_Osgn__class_Osgn(X14,X13)),c_Groups_Osgn__class_Osgn(X14,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1878])]) ).
fof(c_0_3148,plain,
! [X12,X13,X14] :
( ~ class_Rings_Olinordered__idom(X14)
| c_Groups_Oabs__class_Oabs(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),c_Groups_Oabs__class_Oabs(X14,X13)),c_Groups_Oabs__class_Oabs(X14,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1879])]) ).
fof(c_0_3149,plain,
! [X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__field(X14)
| X13 = c_Groups_Ozero__class_Ozero(X14)
| c_RealVector_Onorm__class_Onorm(X14,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14),X12),X13)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X14,X12)),c_RealVector_Onorm__class_Onorm(X14,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1880])]) ).
fof(c_0_3150,plain,
! [X85,X86,X87] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X86,X87) != X85
| X86 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),X87)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X87),X86)) )
& ( X86 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),X87)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X86,X87) = X85
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X87),X86)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1881])])]) ).
fof(c_0_3151,plain,
! [X11,X12] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X11)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X12)),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_1882])])])]) ).
fof(c_0_3152,plain,
! [X12,X13,X14] :
( ~ class_Groups_Oordered__ab__group__add__abs(X14)
| c_Groups_Oabs__class_Oabs(X14,c_Groups_Ominus__class_Ominus(X14,X13,X12)) = c_Groups_Oabs__class_Oabs(X14,c_Groups_Ominus__class_Ominus(X14,X12,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1883])]) ).
fof(c_0_3153,plain,
! [X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__vector(X14)
| c_RealVector_Onorm__class_Onorm(X14,c_Groups_Ominus__class_Ominus(X14,X13,X12)) = c_RealVector_Onorm__class_Onorm(X14,c_Groups_Ominus__class_Ominus(X14,X12,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1884])]) ).
fof(c_0_3154,plain,
! [X13,X14,X15] :
( ~ class_RealVector_Oreal__normed__div__algebra(X15)
| c_RealVector_Onorm__class_Onorm(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X15,X14)),c_RealVector_Onorm__class_Onorm(X15,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1885])]) ).
fof(c_0_3155,plain,
! [X11,X12] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X11)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X11)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X12))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1886])])])]) ).
fof(c_0_3156,plain,
! [X30,X31] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X31)),X30) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),X31)),
inference(variable_rename,[status(thm)],[c_0_1887]) ).
fof(c_0_3157,plain,
! [X17,X18] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17),X18))
| X18 = X17 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1888])]) ).
fof(c_0_3158,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X32))
| X32 = X31 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1889])]) ).
fof(c_0_3159,plain,
! [X17,X18] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18),X17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17),X18))
| X18 = X17 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1890])]) ).
fof(c_0_3160,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X8))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X8))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1891])]) ).
fof(c_0_3161,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X8))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X8))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1892])]) ).
fof(c_0_3162,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X8))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X8)),X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1893])]) ).
fof(c_0_3163,plain,
! [X11,X12] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X12,X11)))
| X11 != c_Groups_Ozero__class_Ozero(X12)
| ~ class_RealVector_Oreal__normed__vector(X12) )
& ( X11 = c_Groups_Ozero__class_Ozero(X12)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X12,X11)))
| ~ class_RealVector_Oreal__normed__vector(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1894])])]) ).
fof(c_0_3164,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X33)),X32)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X35)),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1895])])])]) ).
fof(c_0_3165,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X33)),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X35)),X34)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1896])])])]) ).
fof(c_0_3166,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1897])]) ).
fof(c_0_3167,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1898])]) ).
fof(c_0_3168,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X32)),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1899])]) ).
fof(c_0_3169,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X32)),c_Nat_OSuc(X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1900])]) ).
fof(c_0_3170,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X14)),c_RComplete_Onatceiling(X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1901])]) ).
fof(c_0_3171,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X14)),c_RComplete_Onatfloor(X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1902])]) ).
fof(c_0_3172,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| X8 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X8 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1903])]) ).
fof(c_0_3173,plain,
! [X30,X31,X32] :
( ~ class_Rings_Olinordered__idom(X32)
| c_Groups_Oabs__class_Oabs(X32,hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30)) = hAPP(hAPP(c_Power_Opower__class_Opower(X32),c_Groups_Oabs__class_Oabs(X32,X31)),X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1904])]) ).
fof(c_0_3174,plain,
! [X54,X55] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X54))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X54)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X55)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1905])])])]) ).
fof(c_0_3175,plain,
! [X31,X32] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X31)) = X32 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1906])]) ).
fof(c_0_3176,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| c_Nat_OSuc(X32) = X31
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X32)),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1907])]) ).
fof(c_0_3177,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X8))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[c_0_1908]) ).
fof(c_0_3178,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(X8))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[c_0_1909]) ).
fof(c_0_3179,plain,
! [X11,X12,X13] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X11),X12))
| X11 = X12
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Olinorder(X13) )
& ( X11 != X12
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X11),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Olinorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1910])])]) ).
fof(c_0_3180,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oord(X19)
| X18 != X17
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1911])]) ).
fof(c_0_3181,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| X18 != X17
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X16),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X16),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1912])]) ).
fof(c_0_3182,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oord(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X17))
| X17 != X16
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1913])]) ).
fof(c_0_3183,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X18),X17))
| X18 != X16
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X19,X16),X17)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1914])]) ).
fof(c_0_3184,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oord(X19)
| X18 != X17
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X17),X16))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1915])]) ).
fof(c_0_3185,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| X18 != X17
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X16),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X16),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1916])]) ).
fof(c_0_3186,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oord(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| X17 != X16
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1917])]) ).
fof(c_0_3187,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X18),X17))
| X18 != X16
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X19,X16),X17)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1918])]) ).
fof(c_0_3188,plain,
! [X31,X32] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,c_Nat_OSuc(X31)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X31),
inference(variable_rename,[status(thm)],[c_0_1919]) ).
fof(c_0_3189,plain,
! [X30,X31,X32] :
( ~ class_RealVector_Oreal__normed__div__algebra(X32)
| c_RealVector_Onorm__class_Onorm(X32,hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X32,X31)),X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1920])]) ).
fof(c_0_3190,plain,
! [X11,X12,X13] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Oorder(X13) )
& ( X12 != X11
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Oorder(X13) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| X12 = X11
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Oorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1921])])]) ).
fof(c_0_3191,plain,
! [X11,X12,X13] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| X12 = X11
| ~ class_Orderings_Oorder(X13) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| ~ class_Orderings_Oorder(X13) )
& ( X12 != X11
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| ~ class_Orderings_Oorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1922])])]) ).
fof(c_0_3192,plain,
! [X11,X12,X13] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| X12 = X11
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Olinorder(X13) )
& ( X12 != X11
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| ~ class_Orderings_Olinorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1923])])]) ).
fof(c_0_3193,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| X13 = X12
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1924])]) ).
fof(c_0_3194,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| X13 = X12
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X12),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X12),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1925])]) ).
fof(c_0_3195,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| X14 = X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1926])]) ).
fof(c_0_3196,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),X12))
| X13 = X12
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1927])]) ).
fof(c_0_3197,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,X13),X12))
| X12 = X13
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X14,X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1928])]) ).
fof(c_0_3198,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),c_Nat_OSuc(X31)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| X32 = c_Nat_OSuc(X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1929])]) ).
fof(c_0_3199,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),c_Nat_OSuc(X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| X33 = c_Nat_OSuc(X32) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),c_Nat_OSuc(X34))) )
& ( X35 != c_Nat_OSuc(X34)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),c_Nat_OSuc(X34))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1930])])])])]) ).
fof(c_0_3200,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X32)),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1931])]) ).
fof(c_0_3201,plain,
! [X50,X51,X52] :
( ~ class_Rings_Ocomm__semiring__1(X52)
| hAPP(hAPP(c_Power_Opower__class_Opower(X52),X51),c_Nat_OSuc(X50)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),X51),hAPP(hAPP(c_Power_Opower__class_Opower(X52),X51),X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1932])]) ).
fof(c_0_3202,plain,
! [X50,X51,X52] :
( ~ class_Rings_Ocomm__semiring__1(X52)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X52),X51),hAPP(hAPP(c_Power_Opower__class_Opower(X52),X51),X50)) = hAPP(hAPP(c_Power_Opower__class_Opower(X52),X51),c_Nat_OSuc(X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1933])]) ).
fof(c_0_3203,plain,
! [X30,X31,X32] :
( ~ class_Power_Opower(X32)
| hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),c_Nat_OSuc(X30)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32),X31),hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1934])]) ).
fof(c_0_3204,plain,
! [X32,X33] :
( ( X33 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X32) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33)) )
& ( X32 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X32) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33)) )
& ( X33 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X32 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X32) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1935])])]) ).
fof(c_0_3205,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Opreorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X14),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1936])]) ).
fof(c_0_3206,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),c_Nat_OSuc(X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32))
| X33 = X32 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),c_Nat_OSuc(X34))) )
& ( X35 != X34
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),c_Nat_OSuc(X34))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1937])])])])]) ).
fof(c_0_3207,plain,
! [X32,X33] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),c_Nat_OSuc(X32)))
| X33 = X32
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32)) )
& ( X33 != X32
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),c_Nat_OSuc(X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1938])])]) ).
fof(c_0_3208,plain,
! [X31,X32] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),c_Nat_OSuc(X31)))
| X31 = X32 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1939])]) ).
fof(c_0_3209,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),c_Nat_OSuc(X31)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| X32 = X31 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1940])]) ).
fof(c_0_3210,plain,
! [X31,X32] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X32)),c_RealDef_Oreal(tc_Nat_Onat,X31)),
inference(variable_rename,[status(thm)],[c_0_1941]) ).
fof(c_0_3211,plain,
! [X31,X32] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X32)),c_RealDef_Oreal(tc_Nat_Onat,X31)),
inference(variable_rename,[status(thm)],[c_0_1942]) ).
fof(c_0_3212,plain,
! [X13,X14] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X14),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X14)),hAPP(c_Complex_OIm,X13)),
inference(variable_rename,[status(thm)],[c_0_1943]) ).
fof(c_0_3213,plain,
! [X13,X14] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X14),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X14)),hAPP(c_Complex_ORe,X13)),
inference(variable_rename,[status(thm)],[c_0_1944]) ).
fof(c_0_3214,plain,
! [X13] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X13))
| c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1945])]) ).
fof(c_0_3215,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),c_Nat_OSuc(X32)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),c_Nat_OSuc(X34))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1946])])])]) ).
fof(c_0_3216,plain,
! [X13,X14] : hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,X13)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X14),hAPP(c_Complex_OIm,X13)),
inference(variable_rename,[status(thm)],[c_0_1947]) ).
fof(c_0_3217,plain,
! [X13,X14] : hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,X13)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X14),hAPP(c_Complex_ORe,X13)),
inference(variable_rename,[status(thm)],[c_0_1948]) ).
fof(c_0_3218,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X8)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X8))),
inference(variable_rename,[status(thm)],[c_0_1949]) ).
fof(c_0_3219,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),c_Nat_OSuc(X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1950])]) ).
fof(c_0_3220,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),c_Nat_OSuc(X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1951])]) ).
fof(c_0_3221,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),c_Nat_OSuc(X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1952])]) ).
fof(c_0_3222,plain,
! [X13] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1953])]) ).
fof(c_0_3223,plain,
! [X55,X56,X57,X58] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X56),X55))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X56),X55)) )
& ( X56 != X55
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X56),X55)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58),X57))
| X58 = X57
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X58),X57)) ) ),
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_1954])])])])]) ).
fof(c_0_3224,plain,
! [X32,X33,X34,X35] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32)) )
& ( X33 != X32
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34))
| X35 = X34
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1955])])])])]) ).
fof(c_0_3225,plain,
! [X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32))
| X33 = X32 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34)) )
& ( X35 != X34
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1956])])])])]) ).
fof(c_0_3226,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| X32 = X31
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1957])]) ).
fof(c_0_3227,plain,
! [X11,X12,X13,X14] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12),X11))
| X12 = X11 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X13)) )
& ( X14 != X13
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X13)) ) ),
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_1958])])])])]) ).
fof(c_0_3228,plain,
! [X11,X12,X13,X14] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),X11))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12),X11)) )
& ( X12 != X11
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12),X11)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X13))
| X14 = X13
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14),X13)) ) ),
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_1959])])])])]) ).
fof(c_0_3229,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1960])]) ).
fof(c_0_3230,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1961])]) ).
fof(c_0_3231,plain,
! [X31,X32] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31)) )
& ( X32 != X31
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1962])])]) ).
fof(c_0_3232,plain,
! [X31,X32] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X32)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),
inference(variable_rename,[status(thm)],[c_0_1963]) ).
fof(c_0_3233,plain,
! [X31,X32] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X32)),X31) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X32),X31)),
inference(variable_rename,[status(thm)],[c_0_1964]) ).
fof(c_0_3234,plain,
! [X31,X32] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X32),X31)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X32)),X31),
inference(variable_rename,[status(thm)],[c_0_1965]) ).
fof(c_0_3235,plain,
! [X6] :
( ~ class_Rings_Olinordered__semidom(X6)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6)),c_Groups_Ozero__class_Ozero(X6))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1966])]) ).
fof(c_0_3236,plain,
! [X6] :
( ~ class_Rings_Olinordered__semidom(X6)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6)),c_Groups_Ozero__class_Ozero(X6))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1967])]) ).
fof(c_0_3237,plain,
! [X7,X8] :
( ( c_Groups_Osgn__class_Osgn(X8,X7) != c_Groups_Oone__class_Oone(X8)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),X7))
| ~ class_Rings_Olinordered__idom(X8) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8)),X7))
| c_Groups_Osgn__class_Osgn(X8,X7) = c_Groups_Oone__class_Oone(X8)
| ~ class_Rings_Olinordered__idom(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1968])])]) ).
fof(c_0_3238,plain,
! [X6,X7] :
( ~ class_Rings_Olinordered__idom(X7)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7)),X6))
| c_Groups_Osgn__class_Osgn(X7,X6) = c_Groups_Oone__class_Oone(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1969])]) ).
fof(c_0_3239,plain,
! [X40,X41,X43,X44,X45] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41),X40))
| X40 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X41),esk17_2(X40,X41)) )
& ( X43 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X45)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43)) ) ),
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_1970])])])])]) ).
fof(c_0_3240,plain,
! [X33,X34,X36,X37,X38] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34),X33))
| X33 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),esk10_2(X33,X34)) )
& ( X36 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X38)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37),X36)) ) ),
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_1971])])])])]) ).
fof(c_0_3241,plain,
! [X6,X7] :
( ~ class_Groups_Oordered__ab__group__add__abs(X7)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7)),X6))
| c_Groups_Oabs__class_Oabs(X7,X6) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1972])]) ).
fof(c_0_3242,plain,
! [X6,X7] :
( ~ class_Groups_Oordered__ab__group__add__abs(X7)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7)),X6))
| c_Groups_Oabs__class_Oabs(X7,X6) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1973])]) ).
fof(c_0_3243,plain,
! [X6,X7] :
( ~ class_Rings_Olinordered__idom(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oabs__class_Oabs(X7,X6)),c_Groups_Oabs__class_Oabs(X7,X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1974])]) ).
fof(c_0_3244,plain,
! [X31,X32] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),c_Nat_OSuc(X31)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),
inference(variable_rename,[status(thm)],[c_0_1975]) ).
fof(c_0_3245,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14),X13))
| c_Nat__Transfer_Otsub(X13,X14) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X13,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1976])]) ).
fof(c_0_3246,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14),X13))
| c_Nat__Transfer_Otsub(X13,X14) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X13,X14) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16),X15))
| c_Nat__Transfer_Otsub(X15,X16) = 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_1977])])])]) ).
fof(c_0_3247,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X36)),X35) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X36)),X34)
| X35 = X34 )
& ( X38 != X37
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X37) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1978])])])]) ).
fof(c_0_3248,plain,
! [X53,X54,X55,X56,X57] :
( ( X56 != X55
| X54 = X53
| c_Groups_Ominus__class_Ominus(X57,X56,X55) != c_Groups_Ominus__class_Ominus(X57,X54,X53)
| ~ class_Groups_Oab__group__add(X57) )
& ( X54 != X53
| X56 = X55
| c_Groups_Ominus__class_Ominus(X57,X56,X55) != c_Groups_Ominus__class_Ominus(X57,X54,X53)
| ~ class_Groups_Oab__group__add(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1979])])]) ).
fof(c_0_3249,plain,
! [X30,X31] :
( X31 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X31))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X31),X30)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X31)),X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1980])]) ).
fof(c_0_3250,plain,
! [X31,X32] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X31)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X32) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1981])]) ).
fof(c_0_3251,plain,
! [X31,X32] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X31) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X32) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X32 = X31 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1982])]) ).
fof(c_0_3252,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X32,X31) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1983])]) ).
fof(c_0_3253,plain,
! [X32,X33,X34,X35] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X32) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33),X32)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X34))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X34) = 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_1984])])])]) ).
fof(c_0_3254,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X31) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1985])]) ).
fof(c_0_3255,plain,
! [X13,X14,X15] :
( ~ class_Rings_Olinordered__idom(X15)
| X14 = X13
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1986])]) ).
fof(c_0_3256,plain,
! [X11,X12,X13] :
( ( X12 = X11
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X11),X12))
| ~ class_Orderings_Olinorder(X13) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X12),X11))
| X12 != X11
| ~ class_Orderings_Olinorder(X13) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X13,X11),X12))
| X12 != X11
| ~ class_Orderings_Olinorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1987])])]) ).
fof(c_0_3257,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| X14 = X13
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1988])]) ).
fof(c_0_3258,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| X14 = X13
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1989])]) ).
fof(c_0_3259,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| X14 = X13
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1990])]) ).
fof(c_0_3260,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Ocancel__semigroup__add(X19)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X16),X17)
| X18 = X16 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1991])]) ).
fof(c_0_3261,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X19)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16)
| X17 = X16 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1992])]) ).
fof(c_0_3262,plain,
! [X16,X17,X18,X19] :
( ~ class_Groups_Ocancel__semigroup__add(X19)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X17) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19),X18),X16)
| X17 = X16 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1993])]) ).
fof(c_0_3263,plain,
! [X23,X24,X25,X26] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X23),X24)
| X25 = X23
| ~ class_Groups_Ocancel__semigroup__add(X26) )
& ( X25 != X23
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X23),X24)
| ~ class_Groups_Ocancel__semigroup__add(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1994])])]) ).
fof(c_0_3264,plain,
! [X23,X24,X25,X26] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X23)
| X24 = X23
| ~ class_Groups_Ocancel__semigroup__add(X26) )
& ( X24 != X23
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26),X25),X23)
| ~ class_Groups_Ocancel__semigroup__add(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1995])])]) ).
fof(c_0_3265,plain,
! [X12,X13] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(X13)),c_Complex_Ocis(X12)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X13,X12)),
inference(variable_rename,[status(thm)],[c_0_1996]) ).
fof(c_0_3266,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1997])]) ).
fof(c_0_3267,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1998])]) ).
fof(c_0_3268,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1999])]) ).
fof(c_0_3269,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2000])]) ).
fof(c_0_3270,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2001])]) ).
fof(c_0_3271,plain,
! [X12,X13,X14] :
( ~ class_Divides_Osemiring__div(X14)
| X13 = c_Groups_Ozero__class_Ozero(X14)
| c_Divides_Odiv__class_Odiv(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12),X13) = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2002])]) ).
fof(c_0_3272,plain,
! [X12,X13,X14] :
( ~ class_Divides_Osemiring__div(X14)
| X13 = c_Groups_Ozero__class_Ozero(X14)
| c_Divides_Odiv__class_Odiv(X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X12),X13),X13) = X12 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2003])]) ).
fof(c_0_3273,plain,
! [X6,X7] :
( ~ class_Groups_Oordered__ab__group__add__abs(X7)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7)),c_Groups_Oabs__class_Oabs(X7,X6))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2004])]) ).
fof(c_0_3274,plain,
! [X12,X13,X14] :
( ~ class_Groups_Ogroup__add(X14)
| c_Groups_Ominus__class_Ominus(X14,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14),X13),X12),X12) = X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2005])]) ).
fof(c_0_3275,plain,
! [X28,X29] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29),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_2006])])])]) ).
fof(c_0_3276,plain,
! [X12,X13] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X13)),c_Complex_Ocis(X12)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X13),X12)),
inference(variable_rename,[status(thm)],[c_0_2007]) ).
fof(c_0_3277,plain,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X30)))),
inference(variable_rename,[status(thm)],[c_0_2008]) ).
fof(c_0_3278,plain,
! [X12,X13] : c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X13)),c_Complex_Oexpi(X12)),
inference(variable_rename,[status(thm)],[c_0_2009]) ).
fof(c_0_3279,plain,
! [X30] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X30)),X30)),
inference(variable_rename,[status(thm)],[c_0_2010]) ).
fof(c_0_3280,plain,
! [X13,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X14),X13))
| X14 = X13
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X13),X14)) ),
inference(variable_rename,[status(thm)],[c_0_2011]) ).
fof(c_0_3281,plain,
! [X32,X33,X34,X35] :
( ( X33 = X32
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33),X32))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X33)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35),X34))
| X35 != X34 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34),X35))
| X35 != X34 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2012])])])])]) ).
fof(c_0_3282,plain,
! [X13,X14] :
( X14 = X13
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13),X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2013])]) ).
fof(c_0_3283,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X8))
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2014])]) ).
fof(c_0_3284,plain,
! [X11] :
( ( c_Transcendental_Oln(X11) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X11 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11)) )
& ( X11 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Oln(X11) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X11)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2015])])]) ).
fof(c_0_3285,plain,
! [X31,X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X32)),X31) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)),
inference(variable_rename,[status(thm)],[c_0_2016]) ).
fof(c_0_3286,plain,
! [X17,X18] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17),X18)) ),
inference(variable_rename,[status(thm)],[c_0_2017]) ).
fof(c_0_3287,plain,
! [X31,X32] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X32)) ),
inference(variable_rename,[status(thm)],[c_0_2018]) ).
fof(c_0_3288,plain,
! [X17,X18] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17),X18)) ),
inference(variable_rename,[status(thm)],[c_0_2019]) ).
fof(c_0_3289,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34)
| X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X35 = X34 )
& ( X39 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X37) )
& ( X38 != X37
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X37) ) ),
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_2020])])])])]) ).
fof(c_0_3290,plain,
! [X23,X24,X25] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X23)
| X24 = X23
| X25 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X24 != X23
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X23)
| X25 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2021])])]) ).
fof(c_0_3291,plain,
! [X23,X24,X25] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X25) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X25)
| X24 = X23
| X25 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X24 != X23
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X25)
| X25 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2022])])]) ).
fof(c_0_3292,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X35)
| X36 = X34
| X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X39 != X37
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),X38) )
& ( X38 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),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_2023])])])])]) ).
fof(c_0_3293,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X34)
| X35 = X34
| X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X38 != X37
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X37) )
& ( X39 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X37) ) ),
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_2024])])])])]) ).
fof(c_0_3294,plain,
! [X28,X30,X31] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28))
| X28 = c_Nat_OSuc(esk49_1(X28)) )
& ( X30 != c_Nat_OSuc(X31)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)) ) ),
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_2025])])])])]) ).
fof(c_0_3295,plain,
! [X15] : hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X15)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X15)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X15)),
inference(variable_rename,[status(thm)],[c_0_2026]) ).
fof(c_0_3296,plain,
! [X15] : hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X15)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X15)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X15)),
inference(variable_rename,[status(thm)],[c_0_2027]) ).
fof(c_0_3297,plain,
! [X23,X24,X25,X26] :
( ( X24 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26),X23),X25)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X24),X25) = X23
| X25 = c_Groups_Ozero__class_Ozero(X26)
| ~ class_Rings_Odivision__ring(X26) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X24),X25) != X23
| X24 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26),X23),X25)
| X25 = c_Groups_Ozero__class_Ozero(X26)
| ~ class_Rings_Odivision__ring(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2028])])]) ).
fof(c_0_3298,plain,
! [X23,X24,X25,X26] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26),X24),X25) != X23
| X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X23),X25)
| X25 = c_Groups_Ozero__class_Ozero(X26)
| ~ class_Rings_Odivision__ring(X26) )
& ( X24 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26),X23),X25)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26),X24),X25) = X23
| X25 = c_Groups_Ozero__class_Ozero(X26)
| ~ class_Rings_Odivision__ring(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2029])])]) ).
fof(c_0_3299,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Odivision__ring(X19)
| X18 = c_Groups_Ozero__class_Ozero(X19)
| X17 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X18)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X17),X18) = X16 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2030])]) ).
fof(c_0_3300,plain,
! [X16,X17,X18,X19] :
( ~ class_Rings_Odivision__ring(X19)
| X18 = c_Groups_Ozero__class_Ozero(X19)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X18) != X16
| X17 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X19),X16),X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2031])]) ).
fof(c_0_3301,plain,
! [X8,X9] :
( ~ class_RealVector_Oreal__normed__vector(X9)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X9,X8))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2032])]) ).
fof(c_0_3302,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X35) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X34)
| X35 = X34 )
& ( X38 != X37
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X38) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X37) ) ),
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_3303,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X35) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X35)
| X36 = X34 )
& ( X39 != X37
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X38) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X38) ) ),
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_3304,plain,
! [X31,X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),c_Nat_OSuc(X31)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)),
inference(variable_rename,[status(thm)],[c_0_2035]) ).
fof(c_0_3305,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X8)))),
inference(variable_rename,[status(thm)],[c_0_2036]) ).
fof(c_0_3306,plain,
! [X31,X32] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2037]) ).
fof(c_0_3307,plain,
! [X28,X29] :
( ( X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))
| X29 != 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_2038])])])]) ).
fof(c_0_3308,plain,
! [X31,X32] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31),X31) = X32,
inference(variable_rename,[status(thm)],[c_0_2039]) ).
fof(c_0_3309,plain,
! [X31,X32] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31),X32) = X31,
inference(variable_rename,[status(thm)],[c_0_2040]) ).
fof(c_0_3310,plain,
! [X6,X7] :
( ~ class_Groups_Oordered__ab__group__add__abs(X7)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,X6),c_Groups_Oabs__class_Oabs(X7,X6))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2041])]) ).
fof(c_0_3311,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| X14 != X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2042])]) ).
fof(c_0_3312,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| X14 != X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2043])]) ).
fof(c_0_3313,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X15,X14),X13))
| X13 != X14 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2044])]) ).
fof(c_0_3314,plain,
! [X8,X9] :
( ~ class_Rings_Olinordered__idom(X9)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Groups_Osgn__class_Osgn(X9,X8)),c_Groups_Oabs__class_Oabs(X9,X8)) = X8 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2045])]) ).
fof(c_0_3315,plain,
! [X8,X9] :
( ~ class_Orderings_Opreorder(X9)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X9,X8),X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2046])]) ).
fof(c_0_3316,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_RComplete_Onatceiling(X8) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2047])]) ).
fof(c_0_3317,plain,
! [X8] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_RComplete_Onatfloor(X8) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2048])]) ).
fof(c_0_3318,plain,
! [X28,X29] :
( ~ c_SEQ_Osubseq(X29)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28),hAPP(X29,X28))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2049])]) ).
fof(c_0_3319,plain,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X30))),
inference(variable_rename,[status(thm)],[c_0_2050]) ).
fof(c_0_3320,plain,
! [X28,X29] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),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_2051])])])]) ).
fof(c_0_3321,plain,
! [X30] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[c_0_2052]) ).
fof(c_0_3322,plain,
! [X30] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[c_0_2053]) ).
fof(c_0_3323,plain,
! [X30] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[c_0_2054]) ).
fof(c_0_3324,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_2055])])]) ).
fof(c_0_3325,plain,
! [X6] :
( ~ class_Rings_Olinordered__semidom(X6)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6)),c_Groups_Oone__class_Oone(X6))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2056])]) ).
fof(c_0_3326,plain,
! [X6] :
( ~ class_Rings_Olinordered__semidom(X6)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6)),c_Groups_Oone__class_Oone(X6))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2057])]) ).
fof(c_0_3327,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| X31 != 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_2058])])])]) ).
fof(c_0_3328,plain,
! [X22,X23] :
( ~ class_RealVector_Ometric__space(X23)
| c_SEQ_Oconvergent(X23,c_COMBK(X23,tc_Nat_Onat,X22)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2059])]) ).
fof(c_0_3329,plain,
! [X28,X29,X30] :
( ( X29 = c_Groups_Ozero__class_Ozero(X30)
| hAPP(hAPP(c_Power_Opower__class_Opower(X30),X29),X28) != c_Groups_Ozero__class_Ozero(X30)
| ~ class_Power_Opower(X30)
| ~ class_Rings_Omult__zero(X30)
| ~ class_Rings_Ono__zero__divisors(X30)
| ~ class_Rings_Ozero__neq__one(X30) )
& ( X28 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X30),X29),X28) != c_Groups_Ozero__class_Ozero(X30)
| ~ class_Power_Opower(X30)
| ~ class_Rings_Omult__zero(X30)
| ~ class_Rings_Ono__zero__divisors(X30)
| ~ class_Rings_Ozero__neq__one(X30) )
& ( X29 != c_Groups_Ozero__class_Ozero(X30)
| X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X30),X29),X28) = c_Groups_Ozero__class_Ozero(X30)
| ~ class_Power_Opower(X30)
| ~ class_Rings_Omult__zero(X30)
| ~ class_Rings_Ono__zero__divisors(X30)
| ~ class_Rings_Ozero__neq__one(X30) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2060])])]) ).
fof(c_0_3330,plain,
! [X31,X32] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32),X31))
| X31 != X32 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2061])]) ).
fof(c_0_3331,plain,
! [X37,X38] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38),X37))
| X38 != X37 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2062])]) ).
fof(c_0_3332,plain,
! [X107,X108,X109,X110] : hAPP(c_COMBK(X110,X109,X108),X107) = X108,
inference(variable_rename,[status(thm)],[c_0_2063]) ).
fof(c_0_3333,plain,
! [X102,X103,X104,X105] : c_Complex_Ocomplex_Ocomplex__case(X105,X104,c_Complex_Ocomplex_OComplex(X103,X102)) = hAPP(hAPP(X104,X103),X102),
inference(variable_rename,[status(thm)],[c_0_2064]) ).
fof(c_0_3334,plain,
! [X102,X103,X104,X105] : c_Complex_Ocomplex_Ocomplex__rec(X105,X104,c_Complex_Ocomplex_OComplex(X103,X102)) = hAPP(hAPP(X104,X103),X102),
inference(variable_rename,[status(thm)],[c_0_2065]) ).
fof(c_0_3335,plain,
! [X30] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X30)),
inference(variable_rename,[status(thm)],[c_0_2066]) ).
fof(c_0_3336,plain,
! [X30] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),X30)),
inference(variable_rename,[status(thm)],[c_0_2067]) ).
fof(c_0_3337,plain,
! [X31,X32] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X32),c_Nat_OSuc(X31)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X31),
inference(variable_rename,[status(thm)],[c_0_2068]) ).
fof(c_0_3338,plain,
! [X30] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X30)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[c_0_2069]) ).
fof(c_0_3339,plain,
! [X12,X13,X14] :
( ~ class_Rings_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X12),X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2070])]) ).
fof(c_0_3340,plain,
! [X16,X17,X18] :
( ~ class_Rings_Ocomm__semiring__1(X18)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18),X17),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18),X16),X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2071])]) ).
fof(c_0_3341,plain,
! [X31,X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X32)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),c_Nat_OSuc(X31)),
inference(variable_rename,[status(thm)],[c_0_2072]) ).
fof(c_0_3342,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(X8)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[c_0_2073]) ).
fof(c_0_3343,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(X8)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[c_0_2074]) ).
fof(c_0_3344,plain,
! [X12,X13,X14] :
( ~ class_Rings_Ono__zero__divisors(X14)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12) != c_Groups_Ozero__class_Ozero(X14)
| X13 = c_Groups_Ozero__class_Ozero(X14)
| X12 = c_Groups_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2075])]) ).
fof(c_0_3345,plain,
! [X12,X13,X14] :
( ~ class_Rings_Ono__zero__divisors(X14)
| X13 = c_Groups_Ozero__class_Ozero(X14)
| X12 = c_Groups_Ozero__class_Ozero(X14)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),X13),X12) != c_Groups_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2076])]) ).
fof(c_0_3346,plain,
! [X23,X24,X25] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23) != c_Groups_Ozero__class_Ozero(X25)
| X24 = c_Groups_Ozero__class_Ozero(X25)
| X23 = c_Groups_Ozero__class_Ozero(X25)
| ~ class_Rings_Oring__no__zero__divisors(X25) )
& ( X24 != c_Groups_Ozero__class_Ozero(X25)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23) = c_Groups_Ozero__class_Ozero(X25)
| ~ class_Rings_Oring__no__zero__divisors(X25) )
& ( X23 != c_Groups_Ozero__class_Ozero(X25)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23) = c_Groups_Ozero__class_Ozero(X25)
| ~ class_Rings_Oring__no__zero__divisors(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2077])])]) ).
fof(c_0_3347,plain,
! [X23,X24,X25] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25),X23),X24) != c_Groups_Oone__class_Oone(X25)
| X23 = X24
| X24 = c_Groups_Ozero__class_Ozero(X25)
| ~ class_Rings_Odivision__ring(X25) )
& ( X23 != X24
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25),X23),X24) = c_Groups_Oone__class_Oone(X25)
| X24 = c_Groups_Ozero__class_Ozero(X25)
| ~ class_Rings_Odivision__ring(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2078])])]) ).
fof(c_0_3348,plain,
! [X23,X24,X25] :
( ( c_Groups_Ominus__class_Ominus(X25,X24,X23) != c_Groups_Ozero__class_Ozero(X25)
| X24 = X23
| ~ class_Groups_Ogroup__add(X25) )
& ( X24 != X23
| c_Groups_Ominus__class_Ominus(X25,X24,X23) = c_Groups_Ozero__class_Ozero(X25)
| ~ class_Groups_Ogroup__add(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2079])])]) ).
fof(c_0_3349,plain,
! [X23,X24,X25] :
( ( X24 != X23
| c_Groups_Ominus__class_Ominus(X25,X24,X23) = c_Groups_Ozero__class_Ozero(X25)
| ~ class_Groups_Oab__group__add(X25) )
& ( c_Groups_Ominus__class_Ominus(X25,X24,X23) != c_Groups_Ozero__class_Ozero(X25)
| X24 = X23
| ~ class_Groups_Oab__group__add(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2080])])]) ).
fof(c_0_3350,plain,
! [X30,X31,X32] :
( ~ class_Rings_Oring__1__no__zero__divisors(X32)
| X31 = c_Groups_Ozero__class_Ozero(X32)
| hAPP(hAPP(c_Power_Opower__class_Opower(X32),X31),X30) != c_Groups_Ozero__class_Ozero(X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2081])]) ).
fof(c_0_3351,plain,
! [X7,X8] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7) != c_Groups_Ozero__class_Ozero(X8)
| X7 = c_Groups_Ozero__class_Ozero(X8)
| ~ class_Groups_Olinordered__ab__group__add(X8) )
& ( X7 != c_Groups_Ozero__class_Ozero(X8)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7) = c_Groups_Ozero__class_Ozero(X8)
| ~ class_Groups_Olinordered__ab__group__add(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2082])])]) ).
fof(c_0_3352,plain,
! [X7,X8] :
( ( c_Groups_Ozero__class_Ozero(X8) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)
| X7 = c_Groups_Ozero__class_Ozero(X8)
| ~ class_Groups_Olinordered__ab__group__add(X8) )
& ( X7 != c_Groups_Ozero__class_Ozero(X8)
| c_Groups_Ozero__class_Ozero(X8) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X7)
| ~ class_Groups_Olinordered__ab__group__add(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2083])])]) ).
fof(c_0_3353,plain,
! [X32,X33,X34,X35] :
( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X33 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X32 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X33 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X32 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X35 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X34 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X34) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X35 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X34 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X34) = 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_2084])])])])]) ).
fof(c_0_3354,plain,
! [X32,X33,X34,X35] :
( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X33 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32) )
& ( X32 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X33 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32) )
& ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32) )
& ( X32 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32) )
& ( X35 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X34 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X34) )
& ( X35 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X34 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X34) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2085])])])])]) ).
fof(c_0_3355,plain,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(X30))),
inference(variable_rename,[status(thm)],[c_0_2086]) ).
fof(c_0_3356,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(X8))),
inference(variable_rename,[status(thm)],[c_0_2087]) ).
fof(c_0_3357,plain,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X8))),
inference(variable_rename,[status(thm)],[c_0_2088]) ).
fof(c_0_3358,plain,
! [X18,X19] :
( ~ class_Rings_Olinordered__idom(X19)
| c_Groups_Oabs__class_Oabs(X19,X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),c_Groups_Osgn__class_Osgn(X19,X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2089])]) ).
fof(c_0_3359,plain,
! [X23,X24,X25] :
( ( X24 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25),X24),X23)
| X23 = c_Groups_Ozero__class_Ozero(X25)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X25) )
& ( X23 != c_Groups_Ozero__class_Ozero(X25)
| X24 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25),X24),X23)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2090])])]) ).
fof(c_0_3360,plain,
! [X32,X33,X34,X35] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X33),X32) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X33 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X34 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X35),X34) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X35 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X35),X34) = 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_2091])])])])]) ).
fof(c_0_3361,axiom,
hBOOL(hAPP(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_2092 ).
fof(c_0_3362,axiom,
hBOOL(hAPP(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_2093 ).
fof(c_0_3363,axiom,
hBOOL(hAPP(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_2094 ).
fof(c_0_3364,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Opreorder(X15)
| X14 != X13
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,X14),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2095])]) ).
fof(c_0_3365,plain,
! [X32,X33,X34,X35] :
( ( X33 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X32 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X35 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X34 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X34) = 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_2096])])])])]) ).
fof(c_0_3366,plain,
! [X17,X18] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17),X18),
inference(variable_rename,[status(thm)],[c_0_2097]) ).
fof(c_0_3367,plain,
! [X17,X18] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X18),
inference(variable_rename,[status(thm)],[c_0_2098]) ).
fof(c_0_3368,plain,
! [X17,X18] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X18),
inference(variable_rename,[status(thm)],[c_0_2099]) ).
fof(c_0_3369,plain,
! [X31,X32] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X32),
inference(variable_rename,[status(thm)],[c_0_2100]) ).
fof(c_0_3370,plain,
! [X31,X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32),
inference(variable_rename,[status(thm)],[c_0_2101]) ).
fof(c_0_3371,plain,
! [X30] :
( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2102])]) ).
fof(c_0_3372,plain,
! [X24,X25] : hAPP(c_Complex_ORe,c_Complex_Orcis(X25,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),c_Transcendental_Ocos(X24)),
inference(variable_rename,[status(thm)],[c_0_2103]) ).
fof(c_0_3373,plain,
! [X24,X25] : hAPP(c_Complex_OIm,c_Complex_Orcis(X25,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),c_Transcendental_Osin(X24)),
inference(variable_rename,[status(thm)],[c_0_2104]) ).
fof(c_0_3374,plain,
! [X8,X9] :
( ~ class_Orderings_Opreorder(X9)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X8),X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2105])]) ).
fof(c_0_3375,plain,
! [X30,X31] :
( ~ class_Power_Opower(X31)
| ~ class_Rings_Osemiring__0(X31)
| hAPP(hAPP(c_Power_Opower__class_Opower(X31),c_Groups_Ozero__class_Ozero(X31)),c_Nat_OSuc(X30)) = c_Groups_Ozero__class_Ozero(X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2106])]) ).
fof(c_0_3376,plain,
! [X30,X31] :
( ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X31),c_Groups_Ozero__class_Ozero(X31)),X30) = c_Groups_Oone__class_Oone(X31)
| ~ class_Power_Opower(X31)
| ~ class_Rings_Osemiring__0(X31) )
& ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X31),c_Groups_Ozero__class_Ozero(X31)),X30) = c_Groups_Ozero__class_Ozero(X31)
| ~ class_Power_Opower(X31)
| ~ class_Rings_Osemiring__0(X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2107])])]) ).
fof(c_0_3377,plain,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30),c_Nat_OSuc(X30))),
inference(variable_rename,[status(thm)],[c_0_2108]) ).
fof(c_0_3378,plain,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)),
inference(variable_rename,[status(thm)],[c_0_2109]) ).
fof(c_0_3379,plain,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)),
inference(variable_rename,[status(thm)],[c_0_2110]) ).
fof(c_0_3380,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
c_0_2111 ).
fof(c_0_3381,plain,
! [X32,X33,X34,X35] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X35 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X34) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X34 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X34) = 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_2112])])])])]) ).
fof(c_0_3382,plain,
! [X31,X32] :
( X32 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)
| X31 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2113])]) ).
fof(c_0_3383,plain,
! [X8] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X8),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X8)),
inference(variable_rename,[status(thm)],[c_0_2114]) ).
fof(c_0_3384,plain,
! [X11,X12,X13,X14] :
( ( hAPP(c_Complex_ORe,X12) = hAPP(c_Complex_ORe,X11)
| X12 != X11 )
& ( hAPP(c_Complex_OIm,X12) = hAPP(c_Complex_OIm,X11)
| X12 != X11 )
& ( hAPP(c_Complex_ORe,X14) != hAPP(c_Complex_ORe,X13)
| hAPP(c_Complex_OIm,X14) != hAPP(c_Complex_OIm,X13)
| X14 = X13 ) ),
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_2115])])])])]) ).
fof(c_0_3385,plain,
! [X13,X14] :
( hAPP(c_Complex_ORe,X14) != hAPP(c_Complex_ORe,X13)
| hAPP(c_Complex_OIm,X14) != hAPP(c_Complex_OIm,X13)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2116])]) ).
fof(c_0_3386,plain,
! [X13] :
( X13 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2117])]) ).
fof(c_0_3387,plain,
! [X32,X33,X34,X35] :
( ( X33 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X32 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X35 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X34 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X34) = 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_2118])])])])]) ).
fof(c_0_3388,plain,
! [X32,X33,X34,X35] :
( ( X33 = 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),X33),X32) )
& ( X32 = 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),X33),X32) )
& ( X35 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X34 != 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),X35),X34) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2119])])])])]) ).
fof(c_0_3389,plain,
! [X32,X33,X34,X35] :
( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X35 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X34 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X34) = 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_2120])])])])]) ).
fof(c_0_3390,plain,
! [X31,X32] :
( X32 != X31
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32),X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2121])]) ).
fof(c_0_3391,plain,
! [X6] :
( ~ class_Power_Opower(X6)
| c_Power_Opower__class_Opower(X6) = c_Power_Opower_Opower(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Otimes__class_Otimes(X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2122])]) ).
fof(c_0_3392,plain,
! [X31,X32] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31) != X32
| X31 = 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_2123])])])]) ).
fof(c_0_3393,plain,
! [X30] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X30) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[c_0_2124]) ).
fof(c_0_3394,plain,
! [X17] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17),X17)),
inference(variable_rename,[status(thm)],[c_0_2125]) ).
fof(c_0_3395,plain,
! [X30] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30),X30)),
inference(variable_rename,[status(thm)],[c_0_2126]) ).
fof(c_0_3396,plain,
! [X17] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17),X17)),
inference(variable_rename,[status(thm)],[c_0_2127]) ).
fof(c_0_3397,plain,
! [X6,X7] :
( ~ class_Rings_Odivision__ring(X7)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),c_Groups_Ozero__class_Ozero(X7)),X6) = c_Groups_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2128])]) ).
fof(c_0_3398,plain,
! [X13,X14] :
( ~ class_RealVector_Oreal__normed__field(X14)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14),c_Groups_Ozero__class_Ozero(X14)),X13) = c_Groups_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2129])]) ).
fof(c_0_3399,plain,
! [X30,X31] :
( ~ class_Groups_Omonoid__mult(X31)
| hAPP(hAPP(c_Power_Opower__class_Opower(X31),c_Groups_Oone__class_Oone(X31)),X30) = c_Groups_Oone__class_Oone(X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2130])]) ).
fof(c_0_3400,plain,
! [X6,X7] :
( ~ class_Rings_Omult__zero(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X6) = c_Groups_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2131])]) ).
fof(c_0_3401,plain,
! [X13,X14] :
( ~ class_RealVector_Oreal__normed__algebra(X14)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14),c_Groups_Ozero__class_Ozero(X14)),X13) = c_Groups_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2132])]) ).
fof(c_0_3402,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_2133])]) ).
fof(c_0_3403,plain,
! [X6,X7] :
( ~ class_Rings_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X6) = c_Groups_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2134])]) ).
fof(c_0_3404,plain,
! [X6,X7] :
( ~ class_Groups_Ocomm__monoid__mult(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oone__class_Oone(X7)),X6) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2135])]) ).
fof(c_0_3405,plain,
! [X6,X7] :
( ~ class_Groups_Omonoid__mult(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oone__class_Oone(X7)),X6) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2136])]) ).
fof(c_0_3406,plain,
! [X6,X7] :
( ~ class_Rings_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oone__class_Oone(X7)),X6) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2137])]) ).
fof(c_0_3407,plain,
! [X6,X7] :
( ~ class_Rings_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),c_Groups_Ozero__class_Ozero(X7)),X6) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2138])]) ).
fof(c_0_3408,plain,
! [X6,X7] :
( ~ class_Groups_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),c_Groups_Ozero__class_Ozero(X7)),X6) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2139])]) ).
fof(c_0_3409,plain,
! [X6,X7] :
( ~ class_Groups_Omonoid__add(X7)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),c_Groups_Ozero__class_Ozero(X7)),X6) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2140])]) ).
fof(c_0_3410,plain,
! [X6,X7] :
( ( X6 != c_Groups_Ozero__class_Ozero(X7)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X6),X6) = c_Groups_Ozero__class_Ozero(X7)
| ~ class_Rings_Odivision__ring__inverse__zero(X7) )
& ( X6 = c_Groups_Ozero__class_Ozero(X7)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X6),X6) = c_Groups_Oone__class_Oone(X7)
| ~ class_Rings_Odivision__ring__inverse__zero(X7) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2141])])]) ).
fof(c_0_3411,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Odiv(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2142])]) ).
fof(c_0_3412,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Odiv(X7,c_Groups_Ozero__class_Ozero(X7),X6) = c_Groups_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2143])]) ).
fof(c_0_3413,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| X6 = c_Groups_Ozero__class_Ozero(X7)
| c_Divides_Odiv__class_Odiv(X7,X6,X6) = c_Groups_Oone__class_Oone(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2144])]) ).
fof(c_0_3414,plain,
! [X6,X7] :
( ~ class_Rings_Odivision__ring__inverse__zero(X7)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X6),c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2145])]) ).
fof(c_0_3415,plain,
! [X6,X7] :
( ~ class_Rings_Omult__zero(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2146])]) ).
fof(c_0_3416,plain,
! [X8,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X9)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2147])]) ).
fof(c_0_3417,plain,
! [X6,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2148])]) ).
fof(c_0_3418,plain,
! [X6,X7] :
( ~ class_Rings_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2149])]) ).
fof(c_0_3419,plain,
! [X6,X7] :
( ~ class_Rings_Odivision__ring(X7)
| X6 = c_Groups_Ozero__class_Ozero(X7)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X6),X6) = c_Groups_Oone__class_Oone(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2150])]) ).
fof(c_0_3420,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Odiv(X7,X6,c_Groups_Oone__class_Oone(X7)) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2151])]) ).
fof(c_0_3421,plain,
! [X6,X7] :
( ~ class_Groups_Ogroup__add(X7)
| c_Groups_Ominus__class_Ominus(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2152])]) ).
fof(c_0_3422,plain,
! [X6,X7] :
( ~ class_Rings_Odivision__ring(X7)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X6),c_Groups_Oone__class_Oone(X7)) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2153])]) ).
fof(c_0_3423,plain,
! [X6,X7] :
( ~ class_Power_Opower(X7)
| hAPP(hAPP(c_Power_Opower__class_Opower(X7),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2154])]) ).
fof(c_0_3424,plain,
! [X8,X9] :
( ~ class_Rings_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2155])]) ).
fof(c_0_3425,plain,
! [X6,X7] :
( ~ class_Groups_Ocomm__monoid__mult(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),c_Groups_Oone__class_Oone(X7)) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2156])]) ).
fof(c_0_3426,plain,
! [X6,X7] :
( ~ class_Groups_Omonoid__mult(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),c_Groups_Oone__class_Oone(X7)) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2157])]) ).
fof(c_0_3427,plain,
! [X6,X7] :
( ~ class_Rings_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),c_Groups_Oone__class_Oone(X7)) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2158])]) ).
fof(c_0_3428,plain,
! [X6,X7] :
( ~ class_Rings_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X6),c_Groups_Ozero__class_Ozero(X7)) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2159])]) ).
fof(c_0_3429,plain,
! [X6,X7] :
( ~ class_Groups_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X6),c_Groups_Ozero__class_Ozero(X7)) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2160])]) ).
fof(c_0_3430,plain,
! [X6,X7] :
( ~ class_Groups_Omonoid__add(X7)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X6),c_Groups_Ozero__class_Ozero(X7)) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2161])]) ).
fof(c_0_3431,plain,
! [X31] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X31,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X31,
inference(variable_rename,[status(thm)],[c_0_2162]) ).
fof(c_0_3432,plain,
! [X6,X7] :
( ~ class_Groups_Ogroup__add(X7)
| c_Groups_Ominus__class_Ominus(X7,X6,X6) = c_Groups_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2163])]) ).
fof(c_0_3433,plain,
! [X5] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X5),c_Transcendental_Osin(X5))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(variable_rename,[status(thm)],[c_0_2164]) ).
fof(c_0_3434,plain,
! [X6,X7] :
( ~ class_Groups_Omonoid__mult(X7)
| hAPP(hAPP(c_Power_Opower__class_Opower(X7),X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2165])]) ).
fof(c_0_3435,plain,
! [X8,X9] :
( ~ class_Rings_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X8 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2166])]) ).
fof(c_0_3436,plain,
! [X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X30),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X30,
inference(variable_rename,[status(thm)],[c_0_2167]) ).
fof(c_0_3437,plain,
! [X6,X7] :
( ~ class_Rings_Olinordered__idom(X7)
| c_Groups_Osgn__class_Osgn(X7,c_Groups_Osgn__class_Osgn(X7,X6)) = c_Groups_Osgn__class_Osgn(X7,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2168])]) ).
fof(c_0_3438,plain,
! [X6,X7] :
( ~ class_Groups_Oordered__ab__group__add__abs(X7)
| c_Groups_Oabs__class_Oabs(X7,c_Groups_Oabs__class_Oabs(X7,X6)) = c_Groups_Oabs__class_Oabs(X7,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2169])]) ).
fof(c_0_3439,plain,
! [X15] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X15),hAPP(c_Complex_OIm,X15)) = X15,
inference(variable_rename,[status(thm)],[c_0_2170]) ).
fof(c_0_3440,plain,
! [X6,X7] :
( ~ class_RealVector_Oreal__normed__vector(X7)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6)) = c_RealVector_Onorm__class_Onorm(X7,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2171])]) ).
fof(c_0_3441,plain,
! [X5] :
( X5 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5,X5) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2172])]) ).
fof(c_0_3442,plain,
! [X12] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[c_0_2173]) ).
fof(c_0_3443,plain,
! [X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2174]) ).
fof(c_0_3444,plain,
! [X8,X9] :
( ( X8 != c_Groups_Ozero__class_Ozero(X9)
| c_RealVector_Onorm__class_Onorm(X9,c_Groups_Osgn__class_Osgn(X9,X8)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X9) )
& ( X8 = c_Groups_Ozero__class_Ozero(X9)
| c_RealVector_Onorm__class_Onorm(X9,c_Groups_Osgn__class_Osgn(X9,X8)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X9) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2175])])]) ).
fof(c_0_3445,plain,
! [X31] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X31,
inference(variable_rename,[status(thm)],[c_0_2176]) ).
fof(c_0_3446,plain,
! [X30] : c_Nat_OSuc(X30) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X30),
inference(variable_rename,[status(thm)],[c_0_2177]) ).
fof(c_0_3447,plain,
! [X31] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X31) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2178]) ).
fof(c_0_3448,plain,
! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2179]) ).
fof(c_0_3449,plain,
! [X26] :
( ~ c_SEQ_OBseq(tc_RealDef_Oreal,X26)
| ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,X26)
| c_SEQ_Oconvergent(tc_RealDef_Oreal,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2180])]) ).
fof(c_0_3450,plain,
! [X30] : c_Nat_OSuc(X30) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[c_0_2181]) ).
fof(c_0_3451,plain,
! [X15] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15) = X15,
inference(variable_rename,[status(thm)],[c_0_2182]) ).
fof(c_0_3452,plain,
! [X15] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X15) = X15,
inference(variable_rename,[status(thm)],[c_0_2183]) ).
fof(c_0_3453,plain,
! [X15] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X15) = X15,
inference(variable_rename,[status(thm)],[c_0_2184]) ).
fof(c_0_3454,plain,
! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X30) = X30,
inference(variable_rename,[status(thm)],[c_0_2185]) ).
fof(c_0_3455,plain,
! [X30] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30) = X30,
inference(variable_rename,[status(thm)],[c_0_2186]) ).
fof(c_0_3456,plain,
! [X31] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2187]) ).
fof(c_0_3457,plain,
! [X24,X25] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X25,X24)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X25),
inference(variable_rename,[status(thm)],[c_0_2188]) ).
fof(c_0_3458,plain,
! [X15] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X15,
inference(variable_rename,[status(thm)],[c_0_2189]) ).
fof(c_0_3459,plain,
! [X15] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X15,
inference(variable_rename,[status(thm)],[c_0_2190]) ).
fof(c_0_3460,plain,
! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X30,
inference(variable_rename,[status(thm)],[c_0_2191]) ).
fof(c_0_3461,plain,
! [X31] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X31,
inference(variable_rename,[status(thm)],[c_0_2192]) ).
fof(c_0_3462,plain,
! [X8] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X8)) = c_RealDef_Oreal(tc_Nat_Onat,X8),
inference(variable_rename,[status(thm)],[c_0_2193]) ).
fof(c_0_3463,plain,
! [X97,X98,X99,X100,X101,X102,X103,X104] :
( ( X100 = X98
| c_Complex_Ocomplex_OComplex(X100,X99) != c_Complex_Ocomplex_OComplex(X98,X97) )
& ( X99 = X97
| c_Complex_Ocomplex_OComplex(X100,X99) != c_Complex_Ocomplex_OComplex(X98,X97) )
& ( X104 != X102
| X103 != X101
| c_Complex_Ocomplex_OComplex(X104,X103) = c_Complex_Ocomplex_OComplex(X102,X101) ) ),
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_2194])])])])]) ).
fof(c_0_3464,plain,
! [X44,X45] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X45,X44) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X44 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X45))
| ~ class_Groups_Ozero(X45) )
& ( X44 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X45))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X45,X44) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X45) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2195])])]) ).
fof(c_0_3465,plain,
! [X26,X27] :
( ~ class_Orderings_Oorder(X27)
| ~ c_SEQ_Odecseq(X27,X26)
| c_SEQ_Omonoseq(X27,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2196])]) ).
fof(c_0_3466,plain,
! [X26,X27] :
( ~ class_Orderings_Oorder(X27)
| ~ c_SEQ_Oincseq(X27,X26)
| c_SEQ_Omonoseq(X27,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2197])]) ).
fof(c_0_3467,plain,
! [X32,X33,X34,X35] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X33) != c_RealDef_Oreal(tc_Nat_Onat,X32)
| X33 = X32 )
& ( X35 != X34
| c_RealDef_Oreal(tc_Nat_Onat,X35) = c_RealDef_Oreal(tc_Nat_Onat,X34) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2198])])])]) ).
fof(c_0_3468,plain,
! [X11,X12] :
( ( c_Groups_Osgn__class_Osgn(X12,X11) != c_Groups_Ozero__class_Ozero(X12)
| X11 = c_Groups_Ozero__class_Ozero(X12)
| ~ class_RealVector_Oreal__normed__vector(X12) )
& ( X11 != c_Groups_Ozero__class_Ozero(X12)
| c_Groups_Osgn__class_Osgn(X12,X11) = c_Groups_Ozero__class_Ozero(X12)
| ~ class_RealVector_Oreal__normed__vector(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2199])])]) ).
fof(c_0_3469,plain,
! [X7,X8] :
( ( c_Groups_Osgn__class_Osgn(X8,X7) != c_Groups_Ozero__class_Ozero(X8)
| X7 = c_Groups_Ozero__class_Ozero(X8)
| ~ class_Rings_Olinordered__idom(X8) )
& ( X7 != c_Groups_Ozero__class_Ozero(X8)
| c_Groups_Osgn__class_Osgn(X8,X7) = c_Groups_Ozero__class_Ozero(X8)
| ~ class_Rings_Olinordered__idom(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2200])])]) ).
fof(c_0_3470,plain,
! [X7,X8] :
( ( c_Groups_Oabs__class_Oabs(X8,X7) != c_Groups_Ozero__class_Ozero(X8)
| X7 = c_Groups_Ozero__class_Ozero(X8)
| ~ class_Groups_Oordered__ab__group__add__abs(X8) )
& ( X7 != c_Groups_Ozero__class_Ozero(X8)
| c_Groups_Oabs__class_Oabs(X8,X7) = c_Groups_Ozero__class_Ozero(X8)
| ~ class_Groups_Oordered__ab__group__add__abs(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2201])])]) ).
fof(c_0_3471,plain,
! [X101,X102] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X102,X101)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2202]) ).
fof(c_0_3472,plain,
! [X13,X14] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X14,X13)) = X14,
inference(variable_rename,[status(thm)],[c_0_2203]) ).
fof(c_0_3473,plain,
! [X13,X14] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X14,X13)) = X13,
inference(variable_rename,[status(thm)],[c_0_2204]) ).
fof(c_0_3474,plain,
! [X11,X12] :
( ( c_RealVector_Onorm__class_Onorm(X12,X11) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X11 = c_Groups_Ozero__class_Ozero(X12)
| ~ class_RealVector_Oreal__normed__vector(X12) )
& ( X11 != c_Groups_Ozero__class_Ozero(X12)
| c_RealVector_Onorm__class_Onorm(X12,X11) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2205])])]) ).
fof(c_0_3475,plain,
! [X105,X106] :
( ~ class_Orderings_Oord(X106)
| class_Orderings_Oord(tc_fun(X105,X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2206])]) ).
fof(c_0_3476,plain,
! [X105,X106] :
( ~ class_Orderings_Oorder(X106)
| class_Orderings_Oorder(tc_fun(X105,X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2207])]) ).
fof(c_0_3477,plain,
! [X105,X106] :
( ~ class_Orderings_Opreorder(X106)
| class_Orderings_Opreorder(tc_fun(X105,X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2208])]) ).
fof(c_0_3478,plain,
! [X101,X102] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(X102,X101)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2209]) ).
fof(c_0_3479,plain,
! [X8] :
( c_Transcendental_Osin(X8) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X8)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2210])]) ).
fof(c_0_3480,plain,
! [X6] :
( ~ class_RealVector_Oreal__normed__algebra__1(X6)
| c_Groups_Osgn__class_Osgn(X6,c_Groups_Oone__class_Oone(X6)) = c_Groups_Oone__class_Oone(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2211])]) ).
fof(c_0_3481,plain,
! [X6] :
( ~ class_RealVector_Oreal__normed__vector(X6)
| c_Groups_Osgn__class_Osgn(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2212])]) ).
fof(c_0_3482,plain,
! [X6] :
( ~ class_Groups_Osgn__if(X6)
| c_Groups_Osgn__class_Osgn(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2213])]) ).
fof(c_0_3483,plain,
! [X6] :
( ~ class_Rings_Olinordered__idom(X6)
| c_Groups_Oabs__class_Oabs(X6,c_Groups_Oone__class_Oone(X6)) = c_Groups_Oone__class_Oone(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2214])]) ).
fof(c_0_3484,plain,
! [X6] :
( ~ class_Groups_Oordered__ab__group__add__abs(X6)
| c_Groups_Oabs__class_Oabs(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2215])]) ).
fof(c_0_3485,plain,
! [X28] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X28)),
inference(variable_rename,[status(thm)],[c_0_2216]) ).
fof(c_0_3486,plain,
! [X5] : c_Complex_Ocis(X5) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X5),c_Transcendental_Osin(X5)),
inference(variable_rename,[status(thm)],[c_0_2217]) ).
fof(c_0_3487,plain,
! [X23,X24,X25,X26] :
( ( X24 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X24,X23) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
& ( X23 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X24,X23) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
& ( X26 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X25 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X26,X25) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
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_2218])])])])]) ).
fof(c_0_3488,plain,
! [X23,X24,X25,X26] :
( ( X24 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X24,X23) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
& ( X23 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X24,X23) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
& ( X26 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X25 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X26,X25) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
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_2219])])])])]) ).
fof(c_0_3489,plain,
! [X6] :
( ~ class_RealVector_Oreal__normed__algebra__1(X6)
| c_RealVector_Onorm__class_Onorm(X6,c_Groups_Oone__class_Oone(X6)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2220])]) ).
fof(c_0_3490,plain,
! [X6] :
( ~ class_RealVector_Oreal__normed__vector(X6)
| c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2221])]) ).
fof(c_0_3491,plain,
! [X30] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X30)) = X30,
inference(variable_rename,[status(thm)],[c_0_2222]) ).
fof(c_0_3492,plain,
! [X30] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X30)) = X30,
inference(variable_rename,[status(thm)],[c_0_2223]) ).
fof(c_0_3493,plain,
! [X28,X29] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X28) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,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_2224])])])]) ).
fof(c_0_3494,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_2225 ).
fof(c_0_3495,plain,
! [X11,X12,X13,X14] :
( ( X12 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X12,X11) != c_Complex_Oii )
& ( X11 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X12,X11) != c_Complex_Oii )
& ( X14 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X13 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X14,X13) = c_Complex_Oii ) ),
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_2226])])])])]) ).
fof(c_0_3496,plain,
! [X24] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X24) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X24),
inference(variable_rename,[status(thm)],[c_0_2227]) ).
fof(c_0_3497,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
c_0_2228 ).
fof(c_0_3498,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
c_0_2229 ).
fof(c_0_3499,plain,
! [X5] : hAPP(c_Complex_ORe,c_Complex_Ocis(X5)) = c_Transcendental_Ocos(X5),
inference(variable_rename,[status(thm)],[c_0_2230]) ).
fof(c_0_3500,plain,
! [X5] : hAPP(c_Complex_OIm,c_Complex_Ocis(X5)) = c_Transcendental_Osin(X5),
inference(variable_rename,[status(thm)],[c_0_2231]) ).
fof(c_0_3501,plain,
! [X5] : c_Complex_Ocis(X5) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5),
inference(variable_rename,[status(thm)],[c_0_2232]) ).
fof(c_0_3502,plain,
! [X11,X12] :
( ( c_Groups_Oone__class_Oone(X12) != X11
| X11 = c_Groups_Oone__class_Oone(X12)
| ~ class_Groups_Oone(X12) )
& ( X11 != c_Groups_Oone__class_Oone(X12)
| c_Groups_Oone__class_Oone(X12) = X11
| ~ class_Groups_Oone(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2233])])]) ).
fof(c_0_3503,plain,
! [X11,X12] :
( ( c_Groups_Ozero__class_Ozero(X12) != X11
| X11 = c_Groups_Ozero__class_Ozero(X12)
| ~ class_Groups_Ozero(X12) )
& ( X11 != c_Groups_Ozero__class_Ozero(X12)
| c_Groups_Ozero__class_Ozero(X12) = X11
| ~ class_Groups_Ozero(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2234])])]) ).
fof(c_0_3504,axiom,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
c_0_2235 ).
fof(c_0_3505,plain,
! [X6] :
( ~ class_Rings_Ozero__neq__one(X6)
| c_Groups_Oone__class_Oone(X6) != c_Groups_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2236])]) ).
fof(c_0_3506,plain,
! [X6] :
( ~ class_Rings_Ozero__neq__one(X6)
| c_Groups_Ozero__class_Ozero(X6) != c_Groups_Oone__class_Oone(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2237])]) ).
fof(c_0_3507,plain,
! [X5] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(variable_rename,[status(thm)],[c_0_2238]) ).
fof(c_0_3508,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_2239 ).
fof(c_0_3509,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_2240 ).
fof(c_0_3510,axiom,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_2241 ).
fof(c_0_3511,axiom,
hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_2242 ).
fof(c_0_3512,axiom,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_2243 ).
fof(c_0_3513,axiom,
hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_2244 ).
fof(c_0_3514,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__1(X104)
| class_Groups_Oone(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2245])]) ).
fof(c_0_3515,plain,
! [X104] :
( ~ class_Rings_Ocomm__ring(X104)
| class_Rings_Oring(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2246])]) ).
fof(c_0_3516,plain,
! [X104] :
( ~ class_Groups_Ozero(X104)
| class_Groups_Ozero(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2247])]) ).
fof(c_0_3517,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__1(X104)
| class_Power_Opower(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2248])]) ).
fof(c_0_3518,plain,
! [X104] :
( ~ class_Rings_Ocomm__ring__1(X104)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2249])]) ).
fof(c_0_3519,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Groups_Osgn__if(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2250])]) ).
fof(c_0_3520,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Orderings_Oord(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2251])]) ).
fof(c_0_3521,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__0(X104)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2252])]) ).
fof(c_0_3522,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2253])]) ).
fof(c_0_3523,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__0(X104)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2254])]) ).
fof(c_0_3524,plain,
! [X104] :
( ~ class_Groups_Oab__group__add(X104)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2255])]) ).
fof(c_0_3525,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__0(X104)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2256])]) ).
fof(c_0_3526,plain,
! [X104] :
( ~ class_Groups_Ocomm__monoid__add(X104)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2257])]) ).
fof(c_0_3527,plain,
! [X104] :
( ~ class_Rings_Ocomm__ring__1(X104)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2258])]) ).
fof(c_0_3528,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__1(X104)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2259])]) ).
fof(c_0_3529,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2260])]) ).
fof(c_0_3530,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2261])]) ).
fof(c_0_3531,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2262])]) ).
fof(c_0_3532,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__1(X104)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2263])]) ).
fof(c_0_3533,plain,
! [X104] :
( ~ class_Groups_Oab__group__add(X104)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2264])]) ).
fof(c_0_3534,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__0(X104)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2265])]) ).
fof(c_0_3535,plain,
! [X104] :
( ~ class_Fields_Ofield(X104)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2266])]) ).
fof(c_0_3536,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__1(X104)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2267])]) ).
fof(c_0_3537,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2268])]) ).
fof(c_0_3538,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2269])]) ).
fof(c_0_3539,plain,
! [X104] :
( ~ class_Groups_Ocomm__monoid__add(X104)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2270])]) ).
fof(c_0_3540,plain,
! [X104] :
( ~ class_Rings_Oidom(X104)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2271])]) ).
fof(c_0_3541,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2272])]) ).
fof(c_0_3542,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2273])]) ).
fof(c_0_3543,plain,
! [X104] :
( ~ class_Groups_Ocomm__monoid__add(X104)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2274])]) ).
fof(c_0_3544,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__1(X104)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2275])]) ).
fof(c_0_3545,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__0(X104)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2276])]) ).
fof(c_0_3546,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2277])]) ).
fof(c_0_3547,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2278])]) ).
fof(c_0_3548,plain,
! [X104] :
( ~ class_Groups_Ocancel__comm__monoid__add(X104)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2279])]) ).
fof(c_0_3549,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2280])]) ).
fof(c_0_3550,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2281])]) ).
fof(c_0_3551,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2282])]) ).
fof(c_0_3552,plain,
! [X104] :
( ~ class_Rings_Oidom(X104)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2283])]) ).
fof(c_0_3553,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2284])]) ).
fof(c_0_3554,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2285])]) ).
fof(c_0_3555,plain,
! [X104] :
( ~ class_Rings_Oidom(X104)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2286])]) ).
fof(c_0_3556,plain,
! [X104] :
( ~ class_Groups_Ocancel__comm__monoid__add(X104)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2287])]) ).
fof(c_0_3557,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2288])]) ).
fof(c_0_3558,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2289])]) ).
fof(c_0_3559,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2290])]) ).
fof(c_0_3560,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2291])]) ).
fof(c_0_3561,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2292])]) ).
fof(c_0_3562,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2293])]) ).
fof(c_0_3563,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2294])]) ).
fof(c_0_3564,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2295])]) ).
fof(c_0_3565,plain,
! [X104] :
( ~ class_Rings_Olinordered__idom(X104)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2296])]) ).
fof(c_0_3566,plain,
! [X104] :
( ~ class_Rings_Oidom(X104)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2297])]) ).
fof(c_0_3567,plain,
! [X104] :
( ~ class_Rings_Ocomm__ring(X104)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2298])]) ).
fof(c_0_3568,plain,
! [X104] :
( ~ class_Rings_Ocomm__semiring__0(X104)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2299])]) ).
fof(c_0_3569,plain,
! [X104] :
( ~ class_Groups_Ocancel__comm__monoid__add(X104)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2300])]) ).
fof(c_0_3570,plain,
! [X104] :
( ~ class_Rings_Oidom(X104)
| class_Rings_Oidom(tc_Polynomial_Opoly(X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2301])]) ).
fof(c_0_3571,plain,
! [X8] :
( c_Transcendental_Ocos(X8) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(X8) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2302])]) ).
fof(c_0_3572,plain,
! [X82,X83,X84,X85] :
( ( c_Nat_OSuc(X83) != c_Nat_OSuc(X82)
| X83 = X82 )
& ( X85 != X84
| c_Nat_OSuc(X85) = c_Nat_OSuc(X84) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2303])])])]) ).
fof(c_0_3573,plain,
! [X13,X14] :
( c_Nat_OSuc(X14) != c_Nat_OSuc(X13)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2304])]) ).
fof(c_0_3574,axiom,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_2305 ).
fof(c_0_3575,axiom,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_2306 ).
fof(c_0_3576,plain,
! [X31] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X31),
inference(variable_rename,[status(thm)],[c_0_2307]) ).
fof(c_0_3577,plain,
! [X80] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X80),
inference(variable_rename,[status(thm)],[c_0_2308]) ).
fof(c_0_3578,plain,
! [X31] : c_Nat_OSuc(X31) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2309]) ).
fof(c_0_3579,plain,
! [X79] : c_Nat_OSuc(X79) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2310]) ).
fof(c_0_3580,plain,
! [X31] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X31),
inference(variable_rename,[status(thm)],[c_0_2311]) ).
fof(c_0_3581,plain,
! [X31] : c_Nat_OSuc(X31) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[c_0_2312]) ).
fof(c_0_3582,axiom,
c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_2313 ).
fof(c_0_3583,axiom,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_2314 ).
fof(c_0_3584,axiom,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_2315 ).
fof(c_0_3585,axiom,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_2316 ).
fof(c_0_3586,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
c_0_2317 ).
fof(c_0_3587,axiom,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
c_0_2318 ).
fof(c_0_3588,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_2319 ).
fof(c_0_3589,axiom,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
c_0_2320 ).
fof(c_0_3590,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_2321 ).
fof(c_0_3591,axiom,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_2322 ).
fof(c_0_3592,plain,
! [X30] : X30 != c_Nat_OSuc(X30),
inference(variable_rename,[status(thm)],[c_0_2323]) ).
fof(c_0_3593,plain,
! [X30] : c_Nat_OSuc(X30) != X30,
inference(variable_rename,[status(thm)],[c_0_2324]) ).
fof(c_0_3594,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
c_0_2325 ).
fof(c_0_3595,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_2326 ).
fof(c_0_3596,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_2327 ).
fof(c_0_3597,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_2328 ).
fof(c_0_3598,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
c_0_2329 ).
fof(c_0_3599,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
c_0_2330 ).
fof(c_0_3600,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
c_0_2331 ).
fof(c_0_3601,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_2332 ).
fof(c_0_3602,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
c_0_2333 ).
fof(c_0_3603,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
c_0_2334 ).
fof(c_0_3604,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
c_0_2335 ).
fof(c_0_3605,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
c_0_2336 ).
fof(c_0_3606,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
c_0_2337 ).
fof(c_0_3607,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
c_0_2338 ).
fof(c_0_3608,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
c_0_2339 ).
fof(c_0_3609,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_2340 ).
fof(c_0_3610,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
c_0_2341 ).
fof(c_0_3611,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_2342 ).
fof(c_0_3612,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
c_0_2343 ).
fof(c_0_3613,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_2344 ).
fof(c_0_3614,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
c_0_2345 ).
fof(c_0_3615,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
c_0_2346 ).
fof(c_0_3616,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_2347 ).
fof(c_0_3617,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_2348 ).
fof(c_0_3618,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_2349 ).
fof(c_0_3619,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_2350 ).
fof(c_0_3620,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_2351 ).
fof(c_0_3621,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
c_0_2352 ).
fof(c_0_3622,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_2353 ).
fof(c_0_3623,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
c_0_2354 ).
fof(c_0_3624,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_2355 ).
fof(c_0_3625,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_2356 ).
fof(c_0_3626,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
c_0_2357 ).
fof(c_0_3627,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
c_0_2358 ).
fof(c_0_3628,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_2359 ).
fof(c_0_3629,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_2360 ).
fof(c_0_3630,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_2361 ).
fof(c_0_3631,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
c_0_2362 ).
fof(c_0_3632,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
c_0_2363 ).
fof(c_0_3633,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
c_0_2364 ).
fof(c_0_3634,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
c_0_2365 ).
fof(c_0_3635,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
c_0_2366 ).
fof(c_0_3636,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
c_0_2367 ).
fof(c_0_3637,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
c_0_2368 ).
fof(c_0_3638,axiom,
class_Power_Opower(tc_RealDef_Oreal),
c_0_2369 ).
fof(c_0_3639,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
c_0_2370 ).
fof(c_0_3640,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
c_0_2371 ).
fof(c_0_3641,axiom,
class_Groups_Osgn__if(tc_RealDef_Oreal),
c_0_2372 ).
fof(c_0_3642,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
c_0_2373 ).
fof(c_0_3643,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
c_0_2374 ).
fof(c_0_3644,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
c_0_2375 ).
fof(c_0_3645,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
c_0_2376 ).
fof(c_0_3646,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
c_0_2377 ).
fof(c_0_3647,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
c_0_2378 ).
fof(c_0_3648,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
c_0_2379 ).
fof(c_0_3649,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
c_0_2380 ).
fof(c_0_3650,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
c_0_2381 ).
fof(c_0_3651,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
c_0_2382 ).
fof(c_0_3652,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
c_0_2383 ).
fof(c_0_3653,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
c_0_2384 ).
fof(c_0_3654,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
c_0_2385 ).
fof(c_0_3655,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
c_0_2386 ).
fof(c_0_3656,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
c_0_2387 ).
fof(c_0_3657,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
c_0_2388 ).
fof(c_0_3658,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
c_0_2389 ).
fof(c_0_3659,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
c_0_2390 ).
fof(c_0_3660,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
c_0_2391 ).
fof(c_0_3661,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
c_0_2392 ).
fof(c_0_3662,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
c_0_2393 ).
fof(c_0_3663,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
c_0_2394 ).
fof(c_0_3664,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
c_0_2395 ).
fof(c_0_3665,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
c_0_2396 ).
fof(c_0_3666,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
c_0_2397 ).
fof(c_0_3667,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
c_0_2398 ).
fof(c_0_3668,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
c_0_2399 ).
fof(c_0_3669,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
c_0_2400 ).
fof(c_0_3670,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
c_0_2401 ).
fof(c_0_3671,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
c_0_2402 ).
fof(c_0_3672,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
c_0_2403 ).
fof(c_0_3673,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
c_0_2404 ).
fof(c_0_3674,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
c_0_2405 ).
fof(c_0_3675,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
c_0_2406 ).
fof(c_0_3676,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
c_0_2407 ).
fof(c_0_3677,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
c_0_2408 ).
fof(c_0_3678,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
c_0_2409 ).
fof(c_0_3679,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
c_0_2410 ).
fof(c_0_3680,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
c_0_2411 ).
fof(c_0_3681,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
c_0_2412 ).
fof(c_0_3682,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
c_0_2413 ).
fof(c_0_3683,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
c_0_2414 ).
fof(c_0_3684,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_2415 ).
fof(c_0_3685,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
c_0_2416 ).
fof(c_0_3686,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
c_0_2417 ).
fof(c_0_3687,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
c_0_2418 ).
fof(c_0_3688,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
c_0_2419 ).
fof(c_0_3689,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
c_0_2420 ).
fof(c_0_3690,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
c_0_2421 ).
fof(c_0_3691,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
c_0_2422 ).
fof(c_0_3692,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
c_0_2423 ).
fof(c_0_3693,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
c_0_2424 ).
fof(c_0_3694,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
c_0_2425 ).
fof(c_0_3695,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
c_0_2426 ).
fof(c_0_3696,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
c_0_2427 ).
fof(c_0_3697,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
c_0_2428 ).
fof(c_0_3698,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_2429 ).
fof(c_0_3699,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
c_0_2430 ).
fof(c_0_3700,axiom,
class_Orderings_Oord(tc_HOL_Obool),
c_0_2431 ).
fof(c_0_3701,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
c_0_2432 ).
fof(c_0_3702,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
c_0_2433 ).
fof(c_0_3703,axiom,
class_Groups_Oone(tc_Nat_Onat),
c_0_2434 ).
fof(c_0_3704,axiom,
class_Groups_Ozero(tc_Nat_Onat),
c_0_2435 ).
fof(c_0_3705,axiom,
class_Power_Opower(tc_Nat_Onat),
c_0_2436 ).
fof(c_0_3706,axiom,
class_Orderings_Oord(tc_Nat_Onat),
c_0_2437 ).
fof(c_0_3707,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
c_0_2438 ).
fof(c_0_3708,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
c_0_2439 ).
fof(c_0_3709,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
c_0_2440 ).
fof(c_0_3710,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
c_0_2441 ).
fof(c_0_3711,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
c_0_2442 ).
fof(c_0_3712,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
c_0_2443 ).
fof(c_0_3713,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
c_0_2444 ).
fof(c_0_3714,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
c_0_2445 ).
fof(c_0_3715,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
c_0_2446 ).
fof(c_0_3716,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
c_0_2447 ).
fof(c_0_3717,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
c_0_2448 ).
fof(c_0_3718,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
c_0_2449 ).
fof(c_0_3719,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
c_0_2450 ).
fof(c_0_3720,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
c_0_2451 ).
fof(c_0_3721,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
c_0_2452 ).
fof(c_0_3722,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
c_0_2453 ).
fof(c_0_3723,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
c_0_2454 ).
fof(c_0_3724,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
c_0_2455 ).
fof(c_0_3725,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
c_0_2456 ).
fof(c_0_3726,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
c_0_2457 ).
fof(c_0_3727,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
c_0_2458 ).
fof(c_0_3728,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
c_0_2459 ).
fof(c_0_3729,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
c_0_2460 ).
fof(c_0_3730,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
c_0_2461 ).
fof(c_0_3731,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
c_0_2462 ).
fof(c_0_3732,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
c_0_2463 ).
fof(c_0_3733,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
c_0_2464 ).
fof(c_0_3734,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
c_0_2465 ).
fof(c_0_3735,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
c_0_2466 ).
fof(c_0_3736,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
c_0_2467 ).
fof(c_0_3737,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
c_0_2468 ).
fof(c_0_3738,axiom,
class_Groups_Oone(tc_Int_Oint),
c_0_2469 ).
fof(c_0_3739,axiom,
class_Rings_Oring(tc_Int_Oint),
c_0_2470 ).
fof(c_0_3740,axiom,
class_Groups_Ozero(tc_Int_Oint),
c_0_2471 ).
fof(c_0_3741,axiom,
class_Power_Opower(tc_Int_Oint),
c_0_2472 ).
fof(c_0_3742,axiom,
class_Rings_Oring__1(tc_Int_Oint),
c_0_2473 ).
fof(c_0_3743,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
c_0_2474 ).
fof(c_0_3744,axiom,
class_Orderings_Oord(tc_Int_Oint),
c_0_2475 ).
fof(c_0_3745,axiom,
class_Rings_Osemiring(tc_Int_Oint),
c_0_2476 ).
fof(c_0_3746,axiom,
class_Orderings_Oorder(tc_Int_Oint),
c_0_2477 ).
fof(c_0_3747,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
c_0_2478 ).
fof(c_0_3748,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
c_0_2479 ).
fof(c_0_3749,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
c_0_2480 ).
fof(c_0_3750,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
c_0_2481 ).
fof(c_0_3751,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
c_0_2482 ).
fof(c_0_3752,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
c_0_2483 ).
fof(c_0_3753,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
c_0_2484 ).
fof(c_0_3754,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
c_0_2485 ).
fof(c_0_3755,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
c_0_2486 ).
fof(c_0_3756,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
c_0_2487 ).
fof(c_0_3757,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
c_0_2488 ).
fof(c_0_3758,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
c_0_2489 ).
fof(c_0_3759,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
c_0_2490 ).
fof(c_0_3760,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
c_0_2491 ).
fof(c_0_3761,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
c_0_2492 ).
fof(c_0_3762,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
c_0_2493 ).
fof(c_0_3763,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
c_0_2494 ).
fof(c_0_3764,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
c_0_2495 ).
fof(c_0_3765,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
c_0_2496 ).
fof(c_0_3766,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
c_0_2497 ).
fof(c_0_3767,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
c_0_2498 ).
fof(c_0_3768,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
c_0_2499 ).
fof(c_0_3769,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
c_0_2500 ).
fof(c_0_3770,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
c_0_2501 ).
fof(c_0_3771,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
c_0_2502 ).
fof(c_0_3772,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
c_0_2503 ).
fof(c_0_3773,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
c_0_2504 ).
fof(c_0_3774,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
c_0_2505 ).
fof(c_0_3775,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
c_0_2506 ).
fof(c_0_3776,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
c_0_2507 ).
fof(c_0_3777,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
c_0_2508 ).
fof(c_0_3778,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
c_0_2509 ).
fof(c_0_3779,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
c_0_2510 ).
fof(c_0_3780,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
c_0_2511 ).
fof(c_0_3781,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
c_0_2512 ).
fof(c_0_3782,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
c_0_2513 ).
fof(c_0_3783,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
c_0_2514 ).
fof(c_0_3784,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
c_0_2515 ).
fof(c_0_3785,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
c_0_2516 ).
fof(c_0_3786,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
c_0_2517 ).
fof(c_0_3787,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
c_0_2518 ).
fof(c_0_3788,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
c_0_2519 ).
fof(c_0_3789,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
c_0_2520 ).
fof(c_0_3790,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
c_0_2521 ).
fof(c_0_3791,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
c_0_2522 ).
fof(c_0_3792,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
c_0_2523 ).
fof(c_0_3793,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
c_0_2524 ).
fof(c_0_3794,axiom,
class_Rings_Oidom(tc_Int_Oint),
c_0_2525 ).
fof(c_0_3795,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
c_0_2526 ).
fof(c_0_3796,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
c_0_2527 ).
fof(c_0_3797,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
c_0_2528 ).
fof(c_0_3798,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
c_0_2529 ).
fof(c_0_3799,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
c_0_2530 ).
fof(c_0_3800,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
c_0_2531 ).
fof(c_0_3801,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
c_0_2532 ).
fof(c_0_3802,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_2533 ).
fof(c_0_3803,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_2534 ).
fof(c_0_3804,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
c_0_2535 ).
fof(c_0_3805,axiom,
c_SEQ_Osubseq(v_ga____),
c_0_2536 ).
fof(c_0_3806,axiom,
c_SEQ_Osubseq(v_f____),
c_0_2537 ).
cnf(c_0_3807,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_3808,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4))
| ~ hBOOL(hAPP(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,esk67_4(X3,X5,X1,X2))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_3809,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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_2540]) ).
cnf(c_0_3810,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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_2541]) ).
cnf(c_0_3811,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2542]) ).
cnf(c_0_3812,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,esk9_0)))),
inference(split_conjunct,[status(thm)],[c_0_2543]) ).
cnf(c_0_3813,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
inference(split_conjunct,[status(thm)],[c_0_2544]) ).
cnf(c_0_3814,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2545]) ).
cnf(c_0_3815,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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_2546]) ).
cnf(c_0_3816,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
inference(split_conjunct,[status(thm)],[c_0_2540]) ).
cnf(c_0_3817,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
inference(split_conjunct,[status(thm)],[c_0_2541]) ).
cnf(c_0_3818,plain,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk20_4(X3,X2,X4,X1)))),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2547]) ).
cnf(c_0_3819,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(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_2545]) ).
cnf(c_0_3820,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(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_2546]) ).
cnf(c_0_3821,plain,
( c_SEQ_OBseq(X1,X2)
| ~ c_SEQ_OBseq(X1,c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2548]) ).
cnf(c_0_3822,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),hAPP(hAPP(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_2549]) ).
cnf(c_0_3823,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),hAPP(hAPP(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_2550]) ).
cnf(c_0_3824,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,esk2_4(X4,X3,X2,X1))),hAPP(X4,esk2_4(X4,X3,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2551]) ).
cnf(c_0_3825,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),hAPP(hAPP(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_2552]) ).
cnf(c_0_3826,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),hAPP(hAPP(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_2553]) ).
cnf(c_0_3827,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
inference(split_conjunct,[status(thm)],[c_0_2549]) ).
cnf(c_0_3828,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
inference(split_conjunct,[status(thm)],[c_0_2550]) ).
cnf(c_0_3829,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X3),hAPP(X1,X2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2))),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X3),hAPP(X1,X2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2))),X3)),
inference(split_conjunct,[status(thm)],[c_0_2554]) ).
cnf(c_0_3830,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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_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_2555]) ).
cnf(c_0_3831,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(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_2552]) ).
cnf(c_0_3832,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(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_2553]) ).
cnf(c_0_3833,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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),esk24_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_2556]) ).
cnf(c_0_3834,plain,
( c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X3)
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2557]) ).
cnf(c_0_3835,plain,
( c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X3)
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2558]) ).
cnf(c_0_3836,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5)))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2559]) ).
cnf(c_0_3837,plain,
( c_SEQ_Oconvergent(X1,c_COMBC(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2560]) ).
cnf(c_0_3838,plain,
( c_SEQ_Oconvergent(X1,c_COMBC(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2561]) ).
cnf(c_0_3839,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_2562]) ).
cnf(c_0_3840,plain,
( c_SEQ_OBseq(X1,c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3)))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2563]) ).
cnf(c_0_3841,plain,
c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
inference(split_conjunct,[status(thm)],[c_0_2564]) ).
cnf(c_0_3842,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
inference(split_conjunct,[status(thm)],[c_0_2565]) ).
cnf(c_0_3843,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1),hAPP(c_Complex_ORe,X2)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1),hAPP(c_Complex_OIm,X2)))))),
inference(split_conjunct,[status(thm)],[c_0_2566]) ).
cnf(c_0_3844,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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),X4),X5))),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X3,X5)),X6))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X6)),X5))
| ~ class_RealVector_Oreal__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2567]) ).
cnf(c_0_3845,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5)),hAPP(hAPP(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_2568]) ).
cnf(c_0_3846,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4)),hAPP(hAPP(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_2569]) ).
cnf(c_0_3847,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2570]) ).
cnf(c_0_3848,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2570]) ).
cnf(c_0_3849,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2571]) ).
cnf(c_0_3850,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_3851,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X6) != hAPP(hAPP(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_2573]) ).
cnf(c_0_3852,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[c_0_2574]) ).
cnf(c_0_3853,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk44_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk43_3(X2,X1,X4)))),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_3854,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk40_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk39_3(X2,X1,X4)))),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2576]) ).
cnf(c_0_3855,plain,
( hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_2577]) ).
cnf(c_0_3856,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4))),esk46_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk45_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_3857,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4))),esk42_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk41_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2576]) ).
cnf(c_0_3858,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2578]) ).
cnf(c_0_3859,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2579]) ).
cnf(c_0_3860,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk46_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk45_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_3861,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk42_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk41_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2576]) ).
cnf(c_0_3862,plain,
( c_SEQ_OBseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk19_3(X2,X3,X1)))),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2580]) ).
cnf(c_0_3863,plain,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk14_3(X2,X1,X3)))),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2581]) ).
cnf(c_0_3864,plain,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk57_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2582]) ).
cnf(c_0_3865,plain,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk55_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2583]) ).
cnf(c_0_3866,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2584]) ).
cnf(c_0_3867,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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_3868,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),hAPP(hAPP(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,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2586]) ).
cnf(c_0_3869,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),hAPP(hAPP(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,hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2587]) ).
cnf(c_0_3870,plain,
( hBOOL(hAPP(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))),esk62_1(X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2588]) ).
cnf(c_0_3871,plain,
( hBOOL(hAPP(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))),esk36_1(X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2589]) ).
cnf(c_0_3872,plain,
( hBOOL(hAPP(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))),esk29_1(X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2590]) ).
cnf(c_0_3873,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))
| ~ 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_2570]) ).
cnf(c_0_3874,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5) != hAPP(hAPP(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_2591]) ).
cnf(c_0_3875,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_OIm,X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_ORe,X2)))),
inference(split_conjunct,[status(thm)],[c_0_2592]) ).
cnf(c_0_3876,plain,
( c_SEQ_Oconvergent(X1,c_COMBB(X1,X1,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2593]) ).
cnf(c_0_3877,plain,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_2594]) ).
cnf(c_0_3878,plain,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_2595]) ).
cnf(c_0_3879,plain,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_2596]) ).
cnf(c_0_3880,plain,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_2597]) ).
cnf(c_0_3881,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,X1))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2598]) ).
cnf(c_0_3882,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,X1))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2599]) ).
cnf(c_0_3883,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2600]) ).
cnf(c_0_3884,plain,
hBOOL(hAPP(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,hAPP(hAPP(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_2601]) ).
cnf(c_0_3885,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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_2602]) ).
cnf(c_0_3886,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2603]) ).
cnf(c_0_3887,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| ~ class_Rings_Oring(X1)
| X4 != hAPP(hAPP(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_2604]) ).
cnf(c_0_3888,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| ~ class_Rings_Oring(X1)
| hAPP(hAPP(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_2605]) ).
cnf(c_0_3889,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X4 != hAPP(hAPP(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_2606]) ).
cnf(c_0_3890,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4) != X5 ),
inference(split_conjunct,[status(thm)],[c_0_2607]) ).
cnf(c_0_3891,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),esk68_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_3892,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),esk68_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_3893,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2584]) ).
cnf(c_0_3894,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2603]) ).
cnf(c_0_3895,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))))),
inference(split_conjunct,[status(thm)],[c_0_2609]) ).
cnf(c_0_3896,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),esk67_4(X3,X5,X1,X2)))
| ~ class_Orderings_Oord(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_3897,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_2610]) ).
cnf(c_0_3898,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2603]) ).
cnf(c_0_3899,plain,
( X2 = hAPP(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2604]) ).
cnf(c_0_3900,plain,
( hAPP(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2605]) ).
cnf(c_0_3901,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk59_2(X2,X1))),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2611]) ).
cnf(c_0_3902,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X3)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X4))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2612]) ).
cnf(c_0_3903,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(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_2613]) ).
cnf(c_0_3904,plain,
( X3 = hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3) != hAPP(hAPP(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_2606]) ).
cnf(c_0_3905,plain,
( hAPP(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) != hAPP(hAPP(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_2607]) ).
cnf(c_0_3906,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2614]) ).
cnf(c_0_3907,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(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_2615]) ).
cnf(c_0_3908,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| ~ hBOOL(hAPP(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_2616]) ).
cnf(c_0_3909,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| ~ hBOOL(hAPP(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_2617]) ).
cnf(c_0_3910,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),esk71_3(X3,X2,X1))),X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_3911,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),esk71_3(X3,X2,X1))),X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_3912,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk59_2(X2,X1)))),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2611]) ).
cnf(c_0_3913,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)),X4),
inference(split_conjunct,[status(thm)],[c_0_2619]) ).
cnf(c_0_3914,plain,
( epred1_3(X1,X2,X3)
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X3,X2,X1))),esk73_3(X3,X2,X1))
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk74_3(X3,X2,X1))),esk75_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_3915,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2621]) ).
cnf(c_0_3916,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2597]) ).
cnf(c_0_3917,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2597]) ).
cnf(c_0_3918,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(esk71_3(X3,X2,X1)))))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_3919,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2622]) ).
cnf(c_0_3920,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),hAPP(hAPP(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_2623]) ).
cnf(c_0_3921,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2624]) ).
cnf(c_0_3922,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(esk71_3(X3,X2,X1)))))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_3923,plain,
( hBOOL(hAPP(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)),esk63_2(X2,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2625]) ).
cnf(c_0_3924,plain,
( hBOOL(hAPP(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)),esk61_2(X3,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2626]) ).
cnf(c_0_3925,plain,
( hBOOL(hAPP(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)),esk38_2(X3,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2627]) ).
cnf(c_0_3926,plain,
( hBOOL(hAPP(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)),esk37_2(X2,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2628]) ).
cnf(c_0_3927,plain,
( hBOOL(hAPP(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)),esk31_2(X3,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2629]) ).
cnf(c_0_3928,plain,
( hBOOL(hAPP(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)),esk30_2(X2,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2630]) ).
cnf(c_0_3929,plain,
( hBOOL(hAPP(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_2631]) ).
cnf(c_0_3930,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(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_2632]) ).
cnf(c_0_3931,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2633]) ).
cnf(c_0_3932,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)) = hAPP(hAPP(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_2634]) ).
cnf(c_0_3933,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2635]) ).
cnf(c_0_3934,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2636]) ).
cnf(c_0_3935,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))),
inference(split_conjunct,[status(thm)],[c_0_2637]) ).
cnf(c_0_3936,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2638]) ).
cnf(c_0_3937,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_2639]) ).
cnf(c_0_3938,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_2640]) ).
cnf(c_0_3939,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(X4))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_3940,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2641]) ).
cnf(c_0_3941,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2642]) ).
cnf(c_0_3942,plain,
( hBOOL(hAPP(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_2643]) ).
cnf(c_0_3943,plain,
( hBOOL(hAPP(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_2644]) ).
cnf(c_0_3944,plain,
( hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_3945,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2646]) ).
cnf(c_0_3946,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_2647]) ).
cnf(c_0_3947,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_2648]) ).
cnf(c_0_3948,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_2649]) ).
cnf(c_0_3949,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_2650]) ).
cnf(c_0_3950,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_2651]) ).
cnf(c_0_3951,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_2652]) ).
cnf(c_0_3952,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_2653]) ).
cnf(c_0_3953,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_2654]) ).
cnf(c_0_3954,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(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_2655]) ).
cnf(c_0_3955,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_2656]) ).
cnf(c_0_3956,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_2657]) ).
cnf(c_0_3957,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(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_2658]) ).
cnf(c_0_3958,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2659]) ).
cnf(c_0_3959,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2660]) ).
cnf(c_0_3960,plain,
( epred1_3(X1,X2,X3)
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X3,X2,X1))),esk73_3(X3,X2,X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_3961,plain,
( X2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2661]) ).
cnf(c_0_3962,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X3,X2,X1)),X2))
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk74_3(X3,X2,X1))),esk75_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_3963,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2662]) ).
cnf(c_0_3964,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2663]) ).
cnf(c_0_3965,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1)),
inference(split_conjunct,[status(thm)],[c_0_2664]) ).
cnf(c_0_3966,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2665]) ).
cnf(c_0_3967,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2666]) ).
cnf(c_0_3968,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2667]) ).
cnf(c_0_3969,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2668]) ).
cnf(c_0_3970,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2669]) ).
cnf(c_0_3971,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2670]) ).
cnf(c_0_3972,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2662]) ).
cnf(c_0_3973,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2663]) ).
cnf(c_0_3974,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(esk52_2(X2,X1)))),hAPP(X2,esk52_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2671]) ).
cnf(c_0_3975,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk66_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2672]) ).
cnf(c_0_3976,plain,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_2673]) ).
cnf(c_0_3977,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2662]) ).
cnf(c_0_3978,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2663]) ).
cnf(c_0_3979,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_2674]) ).
cnf(c_0_3980,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_2675]) ).
cnf(c_0_3981,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2662]) ).
cnf(c_0_3982,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2663]) ).
cnf(c_0_3983,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2676]) ).
cnf(c_0_3984,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X1,X2)),c_Complex_Ocomplex_OComplex(X3,X4)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(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),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))),
inference(split_conjunct,[status(thm)],[c_0_2677]) ).
cnf(c_0_3985,plain,
( epred1_3(X1,X2,X3)
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X3,X2,X1))),esk73_3(X3,X2,X1))
| ~ hBOOL(hAPP(X1,esk74_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_3986,plain,
( epred1_3(X1,X2,X3)
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk74_3(X3,X2,X1))),esk75_3(X3,X2,X1))
| ~ hBOOL(hAPP(X1,esk72_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_3987,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_2678]) ).
cnf(c_0_3988,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_2679]) ).
cnf(c_0_3989,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2680]) ).
cnf(c_0_3990,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(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_2681]) ).
cnf(c_0_3991,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(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_2682]) ).
cnf(c_0_3992,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(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_2683]) ).
cnf(c_0_3993,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(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_2684]) ).
cnf(c_0_3994,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(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_2685]) ).
cnf(c_0_3995,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2686]) ).
cnf(c_0_3996,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2687]) ).
cnf(c_0_3997,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2688]) ).
cnf(c_0_3998,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2689]) ).
cnf(c_0_3999,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2690]) ).
cnf(c_0_4000,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2691]) ).
cnf(c_0_4001,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2692]) ).
cnf(c_0_4002,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2693]) ).
cnf(c_0_4003,plain,
( X2 = X3
| X4 = X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2694]) ).
cnf(c_0_4004,plain,
( X3 = X5
| X2 = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2695]) ).
cnf(c_0_4005,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2696]) ).
cnf(c_0_4006,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2697]) ).
cnf(c_0_4007,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2698]) ).
cnf(c_0_4008,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X3,X2,X1)))
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk74_3(X3,X2,X1))),esk75_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4009,plain,
( epred1_3(X1,X2,X3)
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X3,X2,X1))),esk73_3(X3,X2,X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),esk75_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4010,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(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_2699]) ).
cnf(c_0_4011,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2700]) ).
cnf(c_0_4012,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2701]) ).
cnf(c_0_4013,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk51_2(X2,X1))),hAPP(X2,c_Nat_OSuc(esk51_2(X2,X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_2671]) ).
cnf(c_0_4014,plain,
( c_SEQ_OBseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),esk20_4(X4,X2,X3,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2547]) ).
cnf(c_0_4015,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X3,X2,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4016,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2639]) ).
cnf(c_0_4017,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2640]) ).
cnf(c_0_4018,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4019,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(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_2703]) ).
cnf(c_0_4020,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_2704]) ).
cnf(c_0_4021,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),esk69_3(X3,X2,X1))),esk70_3(X3,X2,X1))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4022,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_2703]) ).
cnf(c_0_4023,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(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_2704]) ).
cnf(c_0_4024,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2706]) ).
cnf(c_0_4025,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2707]) ).
cnf(c_0_4026,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(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_2708]) ).
cnf(c_0_4027,plain,
( c_RComplete_Onatceiling(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2709]) ).
cnf(c_0_4028,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2710]) ).
cnf(c_0_4029,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),esk69_3(X3,X2,X1))),esk70_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4030,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2711]) ).
cnf(c_0_4031,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_2700]) ).
cnf(c_0_4032,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2712]) ).
cnf(c_0_4033,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2653]) ).
cnf(c_0_4034,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__comm__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2713]) ).
cnf(c_0_4035,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2714]) ).
cnf(c_0_4036,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2715]) ).
cnf(c_0_4037,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2654]) ).
cnf(c_0_4038,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2662]) ).
cnf(c_0_4039,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2663]) ).
cnf(c_0_4040,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Oordered__comm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2716]) ).
cnf(c_0_4041,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2717]) ).
cnf(c_0_4042,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2718]) ).
cnf(c_0_4043,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2710]) ).
cnf(c_0_4044,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2710]) ).
cnf(c_0_4045,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2719]) ).
cnf(c_0_4046,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2720]) ).
cnf(c_0_4047,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk47_2(X2,X1))),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2721]) ).
cnf(c_0_4048,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2638]) ).
cnf(c_0_4049,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2722]) ).
cnf(c_0_4050,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2655]) ).
cnf(c_0_4051,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2723]) ).
cnf(c_0_4052,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2658]) ).
cnf(c_0_4053,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2710]) ).
cnf(c_0_4054,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_2724]) ).
cnf(c_0_4055,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2725]) ).
cnf(c_0_4056,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2659]) ).
cnf(c_0_4057,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2726]) ).
cnf(c_0_4058,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2727]) ).
cnf(c_0_4059,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2660]) ).
cnf(c_0_4060,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2662]) ).
cnf(c_0_4061,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2663]) ).
cnf(c_0_4062,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2728]) ).
cnf(c_0_4063,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2729]) ).
cnf(c_0_4064,plain,
( c_RComplete_Onatfloor(X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2730]) ).
cnf(c_0_4065,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2731]) ).
cnf(c_0_4066,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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2732]) ).
cnf(c_0_4067,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2733]) ).
cnf(c_0_4068,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2734]) ).
cnf(c_0_4069,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2735]) ).
cnf(c_0_4070,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2736]) ).
cnf(c_0_4071,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2737]) ).
cnf(c_0_4072,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2738]) ).
cnf(c_0_4073,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,esk72_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4074,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2739]) ).
cnf(c_0_4075,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X3,X2,X1)),X2))
| ~ hBOOL(hAPP(X1,esk74_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4076,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2740]) ).
cnf(c_0_4077,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2741]) ).
cnf(c_0_4078,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(split_conjunct,[status(thm)],[c_0_2742]) ).
cnf(c_0_4079,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_2743]) ).
cnf(c_0_4080,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2744]) ).
cnf(c_0_4081,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ hBOOL(hAPP(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_2745]) ).
cnf(c_0_4082,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ hBOOL(hAPP(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_2746]) ).
cnf(c_0_4083,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk74_3(X3,X2,X1))),esk75_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4084,plain,
( epred1_3(X1,X2,X3)
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X3,X2,X1))),esk73_3(X3,X2,X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4085,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(split_conjunct,[status(thm)],[c_0_2747]) ).
cnf(c_0_4086,plain,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_2748]) ).
cnf(c_0_4087,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)
| ~ hBOOL(hAPP(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_2749]) ).
cnf(c_0_4088,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2708]) ).
cnf(c_0_4089,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2750]) ).
cnf(c_0_4090,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2751]) ).
cnf(c_0_4091,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2752]) ).
cnf(c_0_4092,plain,
( hBOOL(hAPP(X1,X4))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4093,plain,
( c_SEQ_Oincseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk15_2(X2,X1))),hAPP(X2,esk16_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2753]) ).
cnf(c_0_4094,plain,
( c_SEQ_Odecseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk12_2(X2,X1))),hAPP(X2,esk11_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2754]) ).
cnf(c_0_4095,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk5_2(X2,X1))),hAPP(X2,esk6_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2755]) ).
cnf(c_0_4096,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk8_2(X2,X1))),hAPP(X2,esk7_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2755]) ).
cnf(c_0_4097,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2674]) ).
cnf(c_0_4098,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2675]) ).
cnf(c_0_4099,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
| ~ hBOOL(hAPP(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_2731]) ).
cnf(c_0_4100,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(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_2756]) ).
cnf(c_0_4101,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2678]) ).
cnf(c_0_4102,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2757]) ).
cnf(c_0_4103,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2679]) ).
cnf(c_0_4104,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2683]) ).
cnf(c_0_4105,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2684]) ).
cnf(c_0_4106,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2758]) ).
cnf(c_0_4107,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2685]) ).
cnf(c_0_4108,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2759]) ).
cnf(c_0_4109,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2760]) ).
cnf(c_0_4110,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2703]) ).
cnf(c_0_4111,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2704]) ).
cnf(c_0_4112,plain,
( hBOOL(hAPP(X1,X4))
| ~ epred1_3(X1,X2,X3)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4113,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_2761]) ).
cnf(c_0_4114,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4115,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(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_2762]) ).
cnf(c_0_4116,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(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_2763]) ).
cnf(c_0_4117,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(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_2764]) ).
cnf(c_0_4118,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2765]) ).
cnf(c_0_4119,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2766]) ).
cnf(c_0_4120,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2767]) ).
cnf(c_0_4121,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2768]) ).
cnf(c_0_4122,plain,
( hBOOL(hAPP(X1,X4))
| ~ epred1_3(X1,X2,X3)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4123,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X3,X2,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),esk75_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4124,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2769]) ).
cnf(c_0_4125,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2770]) ).
cnf(c_0_4126,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2688]) ).
cnf(c_0_4127,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2689]) ).
cnf(c_0_4128,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2771]) ).
cnf(c_0_4129,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2772]) ).
cnf(c_0_4130,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2692]) ).
cnf(c_0_4131,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2693]) ).
cnf(c_0_4132,plain,
hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_OIm,X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_ORe,X2))),
inference(split_conjunct,[status(thm)],[c_0_2773]) ).
cnf(c_0_4133,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2774]) ).
cnf(c_0_4134,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2775]) ).
cnf(c_0_4135,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2776]) ).
cnf(c_0_4136,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2777]) ).
cnf(c_0_4137,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2777]) ).
cnf(c_0_4138,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2778]) ).
cnf(c_0_4139,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2779]) ).
cnf(c_0_4140,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2780]) ).
cnf(c_0_4141,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2710]) ).
cnf(c_0_4142,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2710]) ).
cnf(c_0_4143,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_2781]) ).
cnf(c_0_4144,plain,
( epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,esk72_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,esk74_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4145,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2782]) ).
cnf(c_0_4146,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2783]) ).
cnf(c_0_4147,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2784]) ).
cnf(c_0_4148,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2744]) ).
cnf(c_0_4149,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2785]) ).
cnf(c_0_4150,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2786]) ).
cnf(c_0_4151,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2787]) ).
cnf(c_0_4152,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2788]) ).
cnf(c_0_4153,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_2789]) ).
cnf(c_0_4154,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(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_2790]) ).
cnf(c_0_4155,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk70_3(X3,X2,X1)),X3))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4156,plain,
( ~ hBOOL(hAPP(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_2791]) ).
cnf(c_0_4157,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2792]) ).
cnf(c_0_4158,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2793]) ).
cnf(c_0_4159,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2794]) ).
cnf(c_0_4160,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2795]) ).
cnf(c_0_4161,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2796]) ).
cnf(c_0_4162,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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_2797]) ).
cnf(c_0_4163,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2798]) ).
cnf(c_0_4164,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2711]) ).
cnf(c_0_4165,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2719]) ).
cnf(c_0_4166,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2799]) ).
cnf(c_0_4167,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2800]) ).
cnf(c_0_4168,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2801]) ).
cnf(c_0_4169,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2802]) ).
cnf(c_0_4170,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2802]) ).
cnf(c_0_4171,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2803]) ).
cnf(c_0_4172,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2804]) ).
cnf(c_0_4173,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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2805]) ).
cnf(c_0_4174,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2744]) ).
cnf(c_0_4175,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X5)),hAPP(X2,X6)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X6))
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2755]) ).
cnf(c_0_4176,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk70_3(X3,X2,X1)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4177,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,esk74_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4178,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2806]) ).
cnf(c_0_4179,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2807]) ).
cnf(c_0_4180,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2681]) ).
cnf(c_0_4181,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2682]) ).
cnf(c_0_4182,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2808]) ).
cnf(c_0_4183,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2809]) ).
cnf(c_0_4184,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2706]) ).
cnf(c_0_4185,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2810]) ).
cnf(c_0_4186,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2811]) ).
cnf(c_0_4187,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2707]) ).
cnf(c_0_4188,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2812]) ).
cnf(c_0_4189,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_2694]) ).
cnf(c_0_4190,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X5 ),
inference(split_conjunct,[status(thm)],[c_0_2694]) ).
cnf(c_0_4191,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_2695]) ).
cnf(c_0_4192,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X5 ),
inference(split_conjunct,[status(thm)],[c_0_2695]) ).
cnf(c_0_4193,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),esk75_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,esk72_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4194,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_2813]) ).
cnf(c_0_4195,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_2814]) ).
cnf(c_0_4196,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2815]) ).
cnf(c_0_4197,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2)),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2816]) ).
cnf(c_0_4198,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk33_0))),
inference(split_conjunct,[status(thm)],[c_0_2817]) ).
cnf(c_0_4199,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk32_0))),
inference(split_conjunct,[status(thm)],[c_0_2818]) ).
cnf(c_0_4200,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk28_0))),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_4201,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk27_0))),
inference(split_conjunct,[status(thm)],[c_0_2820]) ).
cnf(c_0_4202,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk26_0))),
inference(split_conjunct,[status(thm)],[c_0_2821]) ).
cnf(c_0_4203,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk25_0))),
inference(split_conjunct,[status(thm)],[c_0_2822]) ).
cnf(c_0_4204,plain,
( hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2681]) ).
cnf(c_0_4205,plain,
( hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2682]) ).
cnf(c_0_4206,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(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_2823]) ).
cnf(c_0_4207,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(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_2824]) ).
cnf(c_0_4208,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(X1,esk65_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2825]) ).
cnf(c_0_4209,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(X1,esk64_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2826]) ).
cnf(c_0_4210,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2827]) ).
cnf(c_0_4211,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2827]) ).
cnf(c_0_4212,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2827]) ).
cnf(c_0_4213,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_2827]) ).
cnf(c_0_4214,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk56_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2582]) ).
cnf(c_0_4215,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk54_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2583]) ).
cnf(c_0_4216,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2828]) ).
cnf(c_0_4217,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(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,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2829]) ).
cnf(c_0_4218,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2828]) ).
cnf(c_0_4219,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_2830]) ).
cnf(c_0_4220,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(split_conjunct,[status(thm)],[c_0_2831]) ).
cnf(c_0_4221,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2832]) ).
cnf(c_0_4222,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2828]) ).
cnf(c_0_4223,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,esk69_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4224,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,esk65_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2825]) ).
cnf(c_0_4225,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,esk64_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2826]) ).
cnf(c_0_4226,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2833]) ).
cnf(c_0_4227,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2834]) ).
cnf(c_0_4228,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2835]) ).
cnf(c_0_4229,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2742]) ).
cnf(c_0_4230,plain,
c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X2)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2))),
inference(split_conjunct,[status(thm)],[c_0_2836]) ).
cnf(c_0_4231,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2661]) ).
cnf(c_0_4232,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2750]) ).
cnf(c_0_4233,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2751]) ).
cnf(c_0_4234,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2752]) ).
cnf(c_0_4235,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2745]) ).
cnf(c_0_4236,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2746]) ).
cnf(c_0_4237,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,esk71_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_4238,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X3))
| ~ hBOOL(hAPP(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_2837]) ).
cnf(c_0_4239,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2838]) ).
cnf(c_0_4240,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2839]) ).
cnf(c_0_4241,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2840]) ).
cnf(c_0_4242,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2827]) ).
cnf(c_0_4243,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2841]) ).
cnf(c_0_4244,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2842]) ).
cnf(c_0_4245,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2843]) ).
cnf(c_0_4246,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_2844]) ).
cnf(c_0_4247,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4248,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(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_2845]) ).
cnf(c_0_4249,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(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_2846]) ).
cnf(c_0_4250,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X2))
| ~ hBOOL(hAPP(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_2847]) ).
cnf(c_0_4251,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2848]) ).
cnf(c_0_4252,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),esk75_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4253,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2744]) ).
cnf(c_0_4254,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X3,X2,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4255,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),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_2849]) ).
cnf(c_0_4256,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2850]) ).
cnf(c_0_4257,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2851]) ).
cnf(c_0_4258,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_2852]) ).
cnf(c_0_4259,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,esk69_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4260,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(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_2853]) ).
cnf(c_0_4261,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2854]) ).
cnf(c_0_4262,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2855]) ).
cnf(c_0_4263,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2856]) ).
cnf(c_0_4264,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_2857]) ).
cnf(c_0_4265,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2858]) ).
cnf(c_0_4266,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2859]) ).
cnf(c_0_4267,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2860]) ).
cnf(c_0_4268,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2861]) ).
cnf(c_0_4269,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2862]) ).
cnf(c_0_4270,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_2863]) ).
cnf(c_0_4271,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,esk71_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_4272,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2763]) ).
cnf(c_0_4273,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2764]) ).
cnf(c_0_4274,plain,
hBOOL(hAPP(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_2864]) ).
cnf(c_0_4275,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2865]) ).
cnf(c_0_4276,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2839]) ).
cnf(c_0_4277,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_2866]) ).
cnf(c_0_4278,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2827]) ).
cnf(c_0_4279,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2867]) ).
cnf(c_0_4280,plain,
hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2))),
inference(split_conjunct,[status(thm)],[c_0_2868]) ).
cnf(c_0_4281,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(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_2823]) ).
cnf(c_0_4282,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(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_2823]) ).
cnf(c_0_4283,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2869]) ).
cnf(c_0_4284,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2870]) ).
cnf(c_0_4285,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2871]) ).
cnf(c_0_4286,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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_4287,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_4288,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_4289,plain,
( ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2835]) ).
cnf(c_0_4290,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(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_2874]) ).
cnf(c_0_4291,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(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_2875]) ).
cnf(c_0_4292,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(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_2876]) ).
cnf(c_0_4293,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(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_2877]) ).
cnf(c_0_4294,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(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_2878]) ).
cnf(c_0_4295,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2879]) ).
cnf(c_0_4296,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)))),
inference(split_conjunct,[status(thm)],[c_0_2880]) ).
cnf(c_0_4297,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2881]) ).
cnf(c_0_4298,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2882]) ).
cnf(c_0_4299,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(hAPP(hAPP(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_2883]) ).
cnf(c_0_4300,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2884]) ).
cnf(c_0_4301,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2884]) ).
cnf(c_0_4302,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2885]) ).
cnf(c_0_4303,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2790]) ).
cnf(c_0_4304,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(X3))),hAPP(X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4)),hAPP(X2,c_Nat_OSuc(X4))))
| ~ class_Orderings_Oorder(X1)
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2671]) ).
cnf(c_0_4305,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2886]) ).
cnf(c_0_4306,plain,
( hBOOL(hAPP(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,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2829]) ).
cnf(c_0_4307,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(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_2887]) ).
cnf(c_0_4308,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),hAPP(hAPP(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_2888]) ).
cnf(c_0_4309,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2879]) ).
cnf(c_0_4310,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2879]) ).
cnf(c_0_4311,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2889]) ).
cnf(c_0_4312,plain,
( c_SEQ_Osubseq(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,esk53_1(X1))),hAPP(X1,c_Nat_OSuc(esk53_1(X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_2890]) ).
cnf(c_0_4313,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2832]) ).
cnf(c_0_4314,plain,
( hBOOL(hAPP(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,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2834]) ).
cnf(c_0_4315,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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2891]) ).
cnf(c_0_4316,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2879]) ).
cnf(c_0_4317,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(split_conjunct,[status(thm)],[c_0_2892]) ).
cnf(c_0_4318,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_4319,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(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_2893]) ).
cnf(c_0_4320,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(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_2894]) ).
cnf(c_0_4321,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2895]) ).
cnf(c_0_4322,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2896]) ).
cnf(c_0_4323,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2897]) ).
cnf(c_0_4324,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_2898]) ).
cnf(c_0_4325,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),X3) = hAPP(hAPP(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_2899]) ).
cnf(c_0_4326,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_2900]) ).
cnf(c_0_4327,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk68_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_4328,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(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_2901]) ).
cnf(c_0_4329,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_2902]) ).
cnf(c_0_4330,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2551]) ).
cnf(c_0_4331,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2903]) ).
cnf(c_0_4332,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2904]) ).
cnf(c_0_4333,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_4334,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_4335,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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2905]) ).
cnf(c_0_4336,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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3),c_Nat_OSuc(X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2906]) ).
cnf(c_0_4337,plain,
c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X2)),c_Transcendental_Ocos(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X2)),c_Transcendental_Osin(X1))),
inference(split_conjunct,[status(thm)],[c_0_2907]) ).
cnf(c_0_4338,plain,
c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Ocos(X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Osin(X2))),
inference(split_conjunct,[status(thm)],[c_0_2908]) ).
cnf(c_0_4339,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),c_Divides_Odiv__class_Odiv(X1,X2,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2909]) ).
cnf(c_0_4340,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Divides_Odiv__class_Odiv(X1,X2,X4))
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2910]) ).
cnf(c_0_4341,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2911]) ).
cnf(c_0_4342,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2912]) ).
cnf(c_0_4343,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_2913]) ).
cnf(c_0_4344,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_2914]) ).
cnf(c_0_4345,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2915]) ).
cnf(c_0_4346,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2916]) ).
cnf(c_0_4347,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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2825]) ).
cnf(c_0_4348,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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2826]) ).
cnf(c_0_4349,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3)),X2))
| ~ hBOOL(hAPP(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_2917]) ).
cnf(c_0_4350,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_4351,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(X1,esk74_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4352,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2918]) ).
cnf(c_0_4353,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,esk72_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4354,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2919]) ).
cnf(c_0_4355,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2920]) ).
cnf(c_0_4356,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2921]) ).
cnf(c_0_4357,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_2922]) ).
cnf(c_0_4358,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2923]) ).
cnf(c_0_4359,plain,
c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Ocos(X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Osin(X2))),
inference(split_conjunct,[status(thm)],[c_0_2924]) ).
cnf(c_0_4360,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2925]) ).
cnf(c_0_4361,plain,
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2926]) ).
cnf(c_0_4362,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2))),
inference(split_conjunct,[status(thm)],[c_0_2927]) ).
cnf(c_0_4363,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk21_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2928]) ).
cnf(c_0_4364,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_2929]) ).
cnf(c_0_4365,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(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_2930]) ).
cnf(c_0_4366,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(X1,esk22_1(X1))),hAPP(X1,esk23_1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2931]) ).
cnf(c_0_4367,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2915]) ).
cnf(c_0_4368,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2916]) ).
cnf(c_0_4369,plain,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_2932]) ).
cnf(c_0_4370,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_2896]) ).
cnf(c_0_4371,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(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_2896]) ).
cnf(c_0_4372,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2933]) ).
cnf(c_0_4373,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2934]) ).
cnf(c_0_4374,plain,
( X3 = esk34_2(X2,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2935]) ).
cnf(c_0_4375,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2661]) ).
cnf(c_0_4376,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(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_2936]) ).
cnf(c_0_4377,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(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_2936]) ).
cnf(c_0_4378,plain,
( X4 = X6
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(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_2937]) ).
cnf(c_0_4379,plain,
hBOOL(hAPP(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_2938]) ).
cnf(c_0_4380,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_2939]) ).
cnf(c_0_4381,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(split_conjunct,[status(thm)],[c_0_2940]) ).
cnf(c_0_4382,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(split_conjunct,[status(thm)],[c_0_2941]) ).
cnf(c_0_4383,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_2942]) ).
cnf(c_0_4384,plain,
hBOOL(hAPP(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_2943]) ).
cnf(c_0_4385,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2944]) ).
cnf(c_0_4386,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_2945]) ).
cnf(c_0_4387,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_2946]) ).
cnf(c_0_4388,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(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_2947]) ).
cnf(c_0_4389,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(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_2948]) ).
cnf(c_0_4390,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(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_2949]) ).
cnf(c_0_4391,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2869]) ).
cnf(c_0_4392,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2870]) ).
cnf(c_0_4393,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2835]) ).
cnf(c_0_4394,plain,
( c_SEQ_Osubseq(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,esk3_1(X1))),hAPP(X1,esk4_1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2950]) ).
cnf(c_0_4395,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2951]) ).
cnf(c_0_4396,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2825]) ).
cnf(c_0_4397,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2826]) ).
cnf(c_0_4398,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2952]) ).
cnf(c_0_4399,plain,
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2953]) ).
cnf(c_0_4400,plain,
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2954]) ).
cnf(c_0_4401,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_2955]) ).
cnf(c_0_4402,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),esk18_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2956]) ).
cnf(c_0_4403,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),esk13_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2581]) ).
cnf(c_0_4404,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk65_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2825]) ).
cnf(c_0_4405,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk64_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2826]) ).
cnf(c_0_4406,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2816]) ).
cnf(c_0_4407,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_2816]) ).
cnf(c_0_4408,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_2957]) ).
cnf(c_0_4409,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_2958]) ).
cnf(c_0_4410,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_2959]) ).
cnf(c_0_4411,plain,
hBOOL(hAPP(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2))),
inference(split_conjunct,[status(thm)],[c_0_2960]) ).
cnf(c_0_4412,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk65_3(X3,X2,X1))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[c_0_2825]) ).
cnf(c_0_4413,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk64_3(X3,X2,X1))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[c_0_2826]) ).
cnf(c_0_4414,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))),
inference(split_conjunct,[status(thm)],[c_0_2961]) ).
cnf(c_0_4415,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
inference(split_conjunct,[status(thm)],[c_0_2962]) ).
cnf(c_0_4416,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_RComplete_Onatfloor(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2944]) ).
cnf(c_0_4417,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2963]) ).
cnf(c_0_4418,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Groups_Oone__class_Oone(X1))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2964]) ).
cnf(c_0_4419,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),c_Groups_Oone__class_Oone(X1))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2965]) ).
cnf(c_0_4420,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4421,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2966]) ).
cnf(c_0_4422,plain,
( c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2967]) ).
cnf(c_0_4423,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_2968]) ).
cnf(c_0_4424,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2969]) ).
cnf(c_0_4425,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2969]) ).
cnf(c_0_4426,plain,
( c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2970]) ).
cnf(c_0_4427,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),esk75_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4428,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))
| ~ hBOOL(hAPP(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_2971]) ).
cnf(c_0_4429,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2972]) ).
cnf(c_0_4430,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2973]) ).
cnf(c_0_4431,plain,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2974]) ).
cnf(c_0_4432,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Ocos(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Osin(X1))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_2975]) ).
cnf(c_0_4433,plain,
( ~ hBOOL(hAPP(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_2976]) ).
cnf(c_0_4434,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_2977]) ).
cnf(c_0_4435,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_2978]) ).
cnf(c_0_4436,plain,
( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(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_4437,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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2980]) ).
cnf(c_0_4438,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2973]) ).
cnf(c_0_4439,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(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_2981]) ).
cnf(c_0_4440,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk35_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2982]) ).
cnf(c_0_4441,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk34_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2935]) ).
cnf(c_0_4442,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2983]) ).
cnf(c_0_4443,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_2984]) ).
cnf(c_0_4444,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_2985]) ).
cnf(c_0_4445,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_2986]) ).
cnf(c_0_4446,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_2987]) ).
cnf(c_0_4447,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2988]) ).
cnf(c_0_4448,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2989]) ).
cnf(c_0_4449,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2990]) ).
cnf(c_0_4450,plain,
( hBOOL(hAPP(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_2955]) ).
cnf(c_0_4451,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(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_2955]) ).
cnf(c_0_4452,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4453,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_2974]) ).
cnf(c_0_4454,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_2969]) ).
cnf(c_0_4455,plain,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2901]) ).
cnf(c_0_4456,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2902]) ).
cnf(c_0_4457,plain,
c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Ocos(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Osin(X2))),
inference(split_conjunct,[status(thm)],[c_0_2991]) ).
cnf(c_0_4458,plain,
c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X2)),c_Transcendental_Osin(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X2)),c_Transcendental_Ocos(X1))),
inference(split_conjunct,[status(thm)],[c_0_2992]) ).
cnf(c_0_4459,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2993]) ).
cnf(c_0_4460,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2994]) ).
cnf(c_0_4461,plain,
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2995]) ).
cnf(c_0_4462,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2996]) ).
cnf(c_0_4463,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2997]) ).
cnf(c_0_4464,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2998]) ).
cnf(c_0_4465,plain,
( X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_2999]) ).
cnf(c_0_4466,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_3000]) ).
cnf(c_0_4467,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2929]) ).
cnf(c_0_4468,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2930]) ).
cnf(c_0_4469,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2871]) ).
cnf(c_0_4470,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2871]) ).
cnf(c_0_4471,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_3001]) ).
cnf(c_0_4472,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_3002]) ).
cnf(c_0_4473,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_3003]) ).
cnf(c_0_4474,plain,
c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Ocos(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Osin(X2))),
inference(split_conjunct,[status(thm)],[c_0_3004]) ).
cnf(c_0_4475,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3005]) ).
cnf(c_0_4476,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(split_conjunct,[status(thm)],[c_0_3006]) ).
cnf(c_0_4477,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(split_conjunct,[status(thm)],[c_0_3007]) ).
cnf(c_0_4478,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
inference(split_conjunct,[status(thm)],[c_0_3008]) ).
cnf(c_0_4479,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ hBOOL(hAPP(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_3009]) ).
cnf(c_0_4480,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3010]) ).
cnf(c_0_4481,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3011]) ).
cnf(c_0_4482,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_3011]) ).
cnf(c_0_4483,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3012]) ).
cnf(c_0_4484,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_3012]) ).
cnf(c_0_4485,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3013]) ).
cnf(c_0_4486,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_3014]) ).
cnf(c_0_4487,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2940]) ).
cnf(c_0_4488,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2941]) ).
cnf(c_0_4489,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ c_SEQ_Oincseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2753]) ).
cnf(c_0_4490,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ c_SEQ_Odecseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2754]) ).
cnf(c_0_4491,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) = c_Groups_Ozero__class_Ozero(X1)
| ~ 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_2884]) ).
cnf(c_0_4492,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3015]) ).
cnf(c_0_4493,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3016]) ).
cnf(c_0_4494,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3017]) ).
cnf(c_0_4495,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3018]) ).
cnf(c_0_4496,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)))),
inference(split_conjunct,[status(thm)],[c_0_3019]) ).
cnf(c_0_4497,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X1,X2)),X3) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3)),X2)),
inference(split_conjunct,[status(thm)],[c_0_3020]) ).
cnf(c_0_4498,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_3021]) ).
cnf(c_0_4499,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_3022]) ).
cnf(c_0_4500,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3023]) ).
cnf(c_0_4501,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| ~ epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2974]) ).
cnf(c_0_4502,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3015]) ).
cnf(c_0_4503,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3017]) ).
cnf(c_0_4504,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk35_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2982]) ).
cnf(c_0_4505,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk34_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2935]) ).
cnf(c_0_4506,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3024]) ).
cnf(c_0_4507,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3025]) ).
cnf(c_0_4508,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3026]) ).
cnf(c_0_4509,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3027]) ).
cnf(c_0_4510,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3028]) ).
cnf(c_0_4511,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3029]) ).
cnf(c_0_4512,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3030]) ).
cnf(c_0_4513,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3031]) ).
cnf(c_0_4514,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_3014]) ).
cnf(c_0_4515,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3032]) ).
cnf(c_0_4516,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X2) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3033]) ).
cnf(c_0_4517,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2955]) ).
cnf(c_0_4518,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3034]) ).
cnf(c_0_4519,plain,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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),X1)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_3035]) ).
cnf(c_0_4520,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_3036]) ).
cnf(c_0_4521,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_3037]) ).
cnf(c_0_4522,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_3038]) ).
cnf(c_0_4523,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_3039]) ).
cnf(c_0_4524,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_3040]) ).
cnf(c_0_4525,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_3041]) ).
cnf(c_0_4526,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ c_SEQ_Osubseq(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2950]) ).
cnf(c_0_4527,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,esk58_1(X1))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3042]) ).
cnf(c_0_4528,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3043]) ).
cnf(c_0_4529,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2993]) ).
cnf(c_0_4530,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_RComplete_Onatfloor(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3044]) ).
cnf(c_0_4531,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_2999]) ).
cnf(c_0_4532,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3045]) ).
cnf(c_0_4533,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3046]) ).
cnf(c_0_4534,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3047]) ).
cnf(c_0_4535,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3048]) ).
cnf(c_0_4536,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3049]) ).
cnf(c_0_4537,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3050]) ).
cnf(c_0_4538,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3051]) ).
cnf(c_0_4539,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3052]) ).
cnf(c_0_4540,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X1))),v_r)),
inference(split_conjunct,[status(thm)],[c_0_3053]) ).
cnf(c_0_4541,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_2955]) ).
cnf(c_0_4542,plain,
( X3 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(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_3054]) ).
cnf(c_0_4543,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3055]) ).
cnf(c_0_4544,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3056]) ).
cnf(c_0_4545,plain,
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X1)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3057]) ).
cnf(c_0_4546,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3058]) ).
cnf(c_0_4547,plain,
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3059]) ).
cnf(c_0_4548,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk58_1(X1)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3042]) ).
cnf(c_0_4549,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),esk21_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2928]) ).
cnf(c_0_4550,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3034]) ).
cnf(c_0_4551,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2996]) ).
cnf(c_0_4552,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2997]) ).
cnf(c_0_4553,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_3060]) ).
cnf(c_0_4554,plain,
( c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Transcendental_Oln(X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3061]) ).
cnf(c_0_4555,plain,
( hAPP(hAPP(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_2936]) ).
cnf(c_0_4556,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ epred1_3(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2974]) ).
cnf(c_0_4557,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2),c_Complex_Ocomplex_OComplex(X3,X4)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X3),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_3062]) ).
cnf(c_0_4558,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_3063]) ).
cnf(c_0_4559,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_3064]) ).
cnf(c_0_4560,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_3065]) ).
cnf(c_0_4561,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3066]) ).
cnf(c_0_4562,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk48_2(X2,X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3067]) ).
cnf(c_0_4563,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_3068]) ).
cnf(c_0_4564,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_3069]) ).
cnf(c_0_4565,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3070]) ).
cnf(c_0_4566,plain,
( hBOOL(hAPP(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_3071]) ).
cnf(c_0_4567,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3072]) ).
cnf(c_0_4568,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X1,X2)),c_Complex_Ocomplex_OComplex(X3,X4)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_3073]) ).
cnf(c_0_4569,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X1,X2)),c_Complex_Orcis(X3,X4)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_3074]) ).
cnf(c_0_4570,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_3075]) ).
cnf(c_0_4571,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3076]) ).
cnf(c_0_4572,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3077]) ).
cnf(c_0_4573,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3078]) ).
cnf(c_0_4574,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3079]) ).
cnf(c_0_4575,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2881]) ).
cnf(c_0_4576,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(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_3080]) ).
cnf(c_0_4577,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(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_3081]) ).
cnf(c_0_4578,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_3082]) ).
cnf(c_0_4579,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3083]) ).
cnf(c_0_4580,plain,
( c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3084]) ).
cnf(c_0_4581,plain,
( c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3085]) ).
cnf(c_0_4582,plain,
c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_3086]) ).
cnf(c_0_4583,plain,
c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_3087]) ).
cnf(c_0_4584,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_3080]) ).
cnf(c_0_4585,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_3088]) ).
cnf(c_0_4586,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(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_3089]) ).
cnf(c_0_4587,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_4588,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4589,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3090]) ).
cnf(c_0_4590,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3091]) ).
cnf(c_0_4591,plain,
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3092]) ).
cnf(c_0_4592,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_3093]) ).
cnf(c_0_4593,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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_3094]) ).
cnf(c_0_4594,plain,
( ~ hBOOL(hAPP(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_3095]) ).
cnf(c_0_4595,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3096]) ).
cnf(c_0_4596,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| c_Transcendental_Oln(X1) != c_Transcendental_Oln(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3097]) ).
cnf(c_0_4597,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3098]) ).
cnf(c_0_4598,plain,
( hBOOL(hAPP(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_2955]) ).
cnf(c_0_4599,plain,
( X3 = X2
| hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2955]) ).
cnf(c_0_4600,plain,
( c_Transcendental_Oln(X1) = c_Transcendental_Oln(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3097]) ).
cnf(c_0_4601,plain,
( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3099]) ).
cnf(c_0_4602,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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3100]) ).
cnf(c_0_4603,plain,
( X2 = X3
| ~ hBOOL(hAPP(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_3101]) ).
cnf(c_0_4604,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_3102]) ).
cnf(c_0_4605,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
inference(split_conjunct,[status(thm)],[c_0_3103]) ).
cnf(c_0_4606,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,esk66_1(X1))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2672]) ).
cnf(c_0_4607,plain,
( c_Transcendental_Ocos(c_Transcendental_Oarccos(X1)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_3104]) ).
cnf(c_0_4608,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3105]) ).
cnf(c_0_4609,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X2) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3106]) ).
cnf(c_0_4610,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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_3054]) ).
cnf(c_0_4611,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk60_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3107]) ).
cnf(c_0_4612,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_3065]) ).
cnf(c_0_4613,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3108]) ).
cnf(c_0_4614,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3109]) ).
cnf(c_0_4615,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_3110]) ).
cnf(c_0_4616,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_3111]) ).
cnf(c_0_4617,plain,
( hBOOL(hAPP(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_2929]) ).
cnf(c_0_4618,plain,
( hBOOL(hAPP(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_2930]) ).
cnf(c_0_4619,plain,
( hAPP(hAPP(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_3112]) ).
cnf(c_0_4620,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3096]) ).
cnf(c_0_4621,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[c_0_3113]) ).
cnf(c_0_4622,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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3114]) ).
cnf(c_0_4623,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hBOOL(hAPP(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_2976]) ).
cnf(c_0_4624,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_3115]) ).
cnf(c_0_4625,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_3116]) ).
cnf(c_0_4626,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_2940]) ).
cnf(c_0_4627,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3117]) ).
cnf(c_0_4628,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3118]) ).
cnf(c_0_4629,plain,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3119]) ).
cnf(c_0_4630,plain,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3120]) ).
cnf(c_0_4631,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3121]) ).
cnf(c_0_4632,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3122]) ).
cnf(c_0_4633,plain,
( X1 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk50_2(X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3123]) ).
cnf(c_0_4634,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3124]) ).
cnf(c_0_4635,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3125]) ).
cnf(c_0_4636,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3090]) ).
cnf(c_0_4637,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3126]) ).
cnf(c_0_4638,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3127]) ).
cnf(c_0_4639,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3128]) ).
cnf(c_0_4640,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3129]) ).
cnf(c_0_4641,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3130]) ).
cnf(c_0_4642,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3131]) ).
cnf(c_0_4643,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3132]) ).
cnf(c_0_4644,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3133]) ).
cnf(c_0_4645,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk21_2(X2,X1)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2928]) ).
cnf(c_0_4646,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,c_Nat_OSuc(X2))))
| ~ c_SEQ_Osubseq(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2890]) ).
cnf(c_0_4647,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_3080]) ).
cnf(c_0_4648,plain,
( X2 = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3134]) ).
cnf(c_0_4649,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3135]) ).
cnf(c_0_4650,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_3136]) ).
cnf(c_0_4651,plain,
hBOOL(hAPP(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_3137]) ).
cnf(c_0_4652,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_3138]) ).
cnf(c_0_4653,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))),
inference(split_conjunct,[status(thm)],[c_0_3139]) ).
cnf(c_0_4654,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_3080]) ).
cnf(c_0_4655,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3140]) ).
cnf(c_0_4656,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3141]) ).
cnf(c_0_4657,plain,
( X1 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3142]) ).
cnf(c_0_4658,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3143]) ).
cnf(c_0_4659,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3144]) ).
cnf(c_0_4660,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3145]) ).
cnf(c_0_4661,plain,
( c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3146]) ).
cnf(c_0_4662,plain,
( c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3147]) ).
cnf(c_0_4663,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3148]) ).
cnf(c_0_4664,plain,
( c_SEQ_Oincseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk15_2(X2,X1)),esk16_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2753]) ).
cnf(c_0_4665,plain,
( c_SEQ_Odecseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk11_2(X2,X1)),esk12_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2754]) ).
cnf(c_0_4666,plain,
( c_SEQ_Omonoseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk5_2(X2,X1)),esk6_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2755]) ).
cnf(c_0_4667,plain,
( c_SEQ_Omonoseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk7_2(X2,X1)),esk8_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2755]) ).
cnf(c_0_4668,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3149]) ).
cnf(c_0_4669,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)
| ~ hBOOL(hAPP(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_3150]) ).
cnf(c_0_4670,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[c_0_3151]) ).
cnf(c_0_4671,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_3080]) ).
cnf(c_0_4672,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3152]) ).
cnf(c_0_4673,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_3153]) ).
cnf(c_0_4674,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3150]) ).
cnf(c_0_4675,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4676,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_3154]) ).
cnf(c_0_4677,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3155]) ).
cnf(c_0_4678,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk60_2(X2,X1)),c_Nat_OSuc(X2)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3107]) ).
cnf(c_0_4679,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),X2) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_3156]) ).
cnf(c_0_4680,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_3080]) ).
cnf(c_0_4681,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3157]) ).
cnf(c_0_4682,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3158]) ).
cnf(c_0_4683,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3159]) ).
cnf(c_0_4684,plain,
( c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3099]) ).
cnf(c_0_4685,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3160]) ).
cnf(c_0_4686,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3161]) ).
cnf(c_0_4687,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3162]) ).
cnf(c_0_4688,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3155]) ).
cnf(c_0_4689,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2955]) ).
cnf(c_0_4690,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_3151]) ).
cnf(c_0_4691,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(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_3163]) ).
cnf(c_0_4692,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)
| ~ hBOOL(hAPP(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_3101]) ).
cnf(c_0_4693,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3164]) ).
cnf(c_0_4694,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3165]) ).
cnf(c_0_4695,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3166]) ).
cnf(c_0_4696,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3167]) ).
cnf(c_0_4697,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3168]) ).
cnf(c_0_4698,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3143]) ).
cnf(c_0_4699,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3144]) ).
cnf(c_0_4700,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3169]) ).
cnf(c_0_4701,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_RComplete_Onatceiling(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3170]) ).
cnf(c_0_4702,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3171]) ).
cnf(c_0_4703,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_3172]) ).
cnf(c_0_4704,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3173]) ).
cnf(c_0_4705,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(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_3174]) ).
cnf(c_0_4706,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3174]) ).
cnf(c_0_4707,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3175]) ).
cnf(c_0_4708,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X2 != c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3123]) ).
cnf(c_0_4709,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| c_Nat_OSuc(X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3176]) ).
cnf(c_0_4710,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4711,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[c_0_3177]) ).
cnf(c_0_4712,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[c_0_3178]) ).
cnf(c_0_4713,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3179]) ).
cnf(c_0_4714,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3180]) ).
cnf(c_0_4715,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3181]) ).
cnf(c_0_4716,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3182]) ).
cnf(c_0_4717,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X4 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3183]) ).
cnf(c_0_4718,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3120]) ).
cnf(c_0_4719,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3184]) ).
cnf(c_0_4720,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3185]) ).
cnf(c_0_4721,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3186]) ).
cnf(c_0_4722,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X4 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3187]) ).
cnf(c_0_4723,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_3188]) ).
cnf(c_0_4724,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_3189]) ).
cnf(c_0_4725,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3190]) ).
cnf(c_0_4726,plain,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3191]) ).
cnf(c_0_4727,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3192]) ).
cnf(c_0_4728,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3193]) ).
cnf(c_0_4729,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3194]) ).
cnf(c_0_4730,plain,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3118]) ).
cnf(c_0_4731,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3195]) ).
cnf(c_0_4732,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3196]) ).
cnf(c_0_4733,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3197]) ).
cnf(c_0_4734,plain,
( X1 = c_Nat_OSuc(X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3198]) ).
cnf(c_0_4735,plain,
( X1 = c_Nat_OSuc(X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3199]) ).
cnf(c_0_4736,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3164]) ).
cnf(c_0_4737,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3165]) ).
cnf(c_0_4738,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3200]) ).
cnf(c_0_4739,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_3201]) ).
cnf(c_0_4740,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_3202]) ).
cnf(c_0_4741,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_3203]) ).
cnf(c_0_4742,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_3204]) ).
cnf(c_0_4743,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_3204]) ).
cnf(c_0_4744,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3190]) ).
cnf(c_0_4745,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3090]) ).
cnf(c_0_4746,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3191]) ).
cnf(c_0_4747,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3205]) ).
cnf(c_0_4748,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3206]) ).
cnf(c_0_4749,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3207]) ).
cnf(c_0_4750,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3208]) ).
cnf(c_0_4751,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3209]) ).
cnf(c_0_4752,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),
inference(split_conjunct,[status(thm)],[c_0_3210]) ).
cnf(c_0_4753,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),
inference(split_conjunct,[status(thm)],[c_0_3211]) ).
cnf(c_0_4754,plain,
hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2)),
inference(split_conjunct,[status(thm)],[c_0_3212]) ).
cnf(c_0_4755,plain,
hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)),
inference(split_conjunct,[status(thm)],[c_0_3213]) ).
cnf(c_0_4756,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| X1 != c_Nat_OSuc(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3067]) ).
cnf(c_0_4757,plain,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3214]) ).
cnf(c_0_4758,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3215]) ).
cnf(c_0_4759,plain,
hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1),hAPP(c_Complex_OIm,X2)),
inference(split_conjunct,[status(thm)],[c_0_3216]) ).
cnf(c_0_4760,plain,
hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1),hAPP(c_Complex_ORe,X2)),
inference(split_conjunct,[status(thm)],[c_0_3217]) ).
cnf(c_0_4761,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3066]) ).
cnf(c_0_4762,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(split_conjunct,[status(thm)],[c_0_3218]) ).
cnf(c_0_4763,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_3134]) ).
cnf(c_0_4764,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3215]) ).
cnf(c_0_4765,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3219]) ).
cnf(c_0_4766,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3220]) ).
cnf(c_0_4767,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3199]) ).
cnf(c_0_4768,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3206]) ).
cnf(c_0_4769,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3221]) ).
cnf(c_0_4770,plain,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_3222]) ).
cnf(c_0_4771,plain,
( hBOOL(hAPP(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_3089]) ).
cnf(c_0_4772,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_3204]) ).
cnf(c_0_4773,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3223]) ).
cnf(c_0_4774,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3224]) ).
cnf(c_0_4775,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3225]) ).
cnf(c_0_4776,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3226]) ).
cnf(c_0_4777,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3227]) ).
cnf(c_0_4778,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3228]) ).
cnf(c_0_4779,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3223]) ).
cnf(c_0_4780,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3229]) ).
cnf(c_0_4781,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3224]) ).
cnf(c_0_4782,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3225]) ).
cnf(c_0_4783,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3230]) ).
cnf(c_0_4784,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3231]) ).
cnf(c_0_4785,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3227]) ).
cnf(c_0_4786,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3228]) ).
cnf(c_0_4787,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_3232]) ).
cnf(c_0_4788,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_3233]) ).
cnf(c_0_4789,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2),
inference(split_conjunct,[status(thm)],[c_0_3234]) ).
cnf(c_0_4790,plain,
( ~ hBOOL(hAPP(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_3235]) ).
cnf(c_0_4791,plain,
( ~ hBOOL(hAPP(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_3236]) ).
cnf(c_0_4792,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3237]) ).
cnf(c_0_4793,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3238]) ).
cnf(c_0_4794,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk17_2(X1,X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3239]) ).
cnf(c_0_4795,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk10_2(X1,X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3240]) ).
cnf(c_0_4796,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3241]) ).
cnf(c_0_4797,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3242]) ).
cnf(c_0_4798,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3243]) ).
cnf(c_0_4799,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_3244]) ).
cnf(c_0_4800,plain,
( c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3245]) ).
cnf(c_0_4801,plain,
( c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3246]) ).
cnf(c_0_4802,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_3247]) ).
cnf(c_0_4803,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_3248]) ).
cnf(c_0_4804,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_3248]) ).
cnf(c_0_4805,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)
| X1 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3249]) ).
cnf(c_0_4806,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,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_3250]) ).
cnf(c_0_4807,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3110]) ).
cnf(c_0_4808,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_3111]) ).
cnf(c_0_4809,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_3251]) ).
cnf(c_0_4810,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3108]) ).
cnf(c_0_4811,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3252]) ).
cnf(c_0_4812,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3253]) ).
cnf(c_0_4813,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3254]) ).
cnf(c_0_4814,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3192]) ).
cnf(c_0_4815,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3255]) ).
cnf(c_0_4816,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3256]) ).
cnf(c_0_4817,plain,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3127]) ).
cnf(c_0_4818,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3257]) ).
cnf(c_0_4819,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3179]) ).
cnf(c_0_4820,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3258]) ).
cnf(c_0_4821,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3259]) ).
cnf(c_0_4822,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(esk48_2(X2,X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3067]) ).
cnf(c_0_4823,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X2),X4)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3260]) ).
cnf(c_0_4824,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3261]) ).
cnf(c_0_4825,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3262]) ).
cnf(c_0_4826,plain,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_3263]) ).
cnf(c_0_4827,plain,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3264]) ).
cnf(c_0_4828,plain,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X2)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_3265]) ).
cnf(c_0_4829,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3124]) ).
cnf(c_0_4830,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3125]) ).
cnf(c_0_4831,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3266]) ).
cnf(c_0_4832,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3267]) ).
cnf(c_0_4833,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3268]) ).
cnf(c_0_4834,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3269]) ).
cnf(c_0_4835,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3270]) ).
cnf(c_0_4836,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2)))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3133]) ).
cnf(c_0_4837,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_3271]) ).
cnf(c_0_4838,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_3272]) ).
cnf(c_0_4839,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk18_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2956]) ).
cnf(c_0_4840,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk13_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2581]) ).
cnf(c_0_4841,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3207]) ).
cnf(c_0_4842,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3273]) ).
cnf(c_0_4843,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3274]) ).
cnf(c_0_4844,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3135]) ).
cnf(c_0_4845,plain,
( hBOOL(hAPP(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_3253]) ).
cnf(c_0_4846,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_3275]) ).
cnf(c_0_4847,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X2)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_3276]) ).
cnf(c_0_4848,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)))),
inference(split_conjunct,[status(thm)],[c_0_3277]) ).
cnf(c_0_4849,plain,
c_Complex_Oexpi(hAPP(hAPP(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_3278]) ).
cnf(c_0_4850,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X1)),
inference(split_conjunct,[status(thm)],[c_0_3279]) ).
cnf(c_0_4851,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X2 = X1
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3280]) ).
cnf(c_0_4852,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_3281]) ).
cnf(c_0_4853,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_3282]) ).
cnf(c_0_4854,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3283]) ).
cnf(c_0_4855,plain,
( X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_Transcendental_Oln(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3284]) ).
cnf(c_0_4856,plain,
( hBOOL(hAPP(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_3163]) ).
cnf(c_0_4857,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_3285]) ).
cnf(c_0_4858,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3286]) ).
cnf(c_0_4859,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3287]) ).
cnf(c_0_4860,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3288]) ).
cnf(c_0_4861,plain,
( c_Transcendental_Oln(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3284]) ).
cnf(c_0_4862,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_3289]) ).
cnf(c_0_4863,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_3290]) ).
cnf(c_0_4864,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_3291]) ).
cnf(c_0_4865,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_3292]) ).
cnf(c_0_4866,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_3293]) ).
cnf(c_0_4867,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3239]) ).
cnf(c_0_4868,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3240]) ).
cnf(c_0_4869,plain,
( X1 = c_Nat_OSuc(esk49_1(X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3294]) ).
cnf(c_0_4870,plain,
hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X1)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(split_conjunct,[status(thm)],[c_0_3295]) ).
cnf(c_0_4871,plain,
hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X1)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(split_conjunct,[status(thm)],[c_0_3296]) ).
cnf(c_0_4872,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = X4
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3297]) ).
cnf(c_0_4873,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != X4 ),
inference(split_conjunct,[status(thm)],[c_0_3297]) ).
cnf(c_0_4874,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != X4 ),
inference(split_conjunct,[status(thm)],[c_0_3298]) ).
cnf(c_0_4875,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = X4
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3298]) ).
cnf(c_0_4876,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) = X4
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3299]) ).
cnf(c_0_4877,plain,
( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4)
| X4 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4) != X3
| ~ class_Rings_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3300]) ).
cnf(c_0_4878,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk38_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2627]) ).
cnf(c_0_4879,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk37_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2628]) ).
cnf(c_0_4880,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk31_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2629]) ).
cnf(c_0_4881,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk30_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2630]) ).
cnf(c_0_4882,plain,
( hBOOL(hAPP(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_3301]) ).
cnf(c_0_4883,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3302]) ).
cnf(c_0_4884,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3303]) ).
cnf(c_0_4885,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Nat_OSuc(X2)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_3304]) ).
cnf(c_0_4886,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1)))),
inference(split_conjunct,[status(thm)],[c_0_3305]) ).
cnf(c_0_4887,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk22_1(X1)),esk23_1(X1)))
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2931]) ).
cnf(c_0_4888,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3306]) ).
cnf(c_0_4889,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3307]) ).
cnf(c_0_4890,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_3308]) ).
cnf(c_0_4891,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_3309]) ).
cnf(c_0_4892,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3237]) ).
cnf(c_0_4893,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oabs__class_Oabs(X1,X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3310]) ).
cnf(c_0_4894,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3190]) ).
cnf(c_0_4895,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3256]) ).
cnf(c_0_4896,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3256]) ).
cnf(c_0_4897,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3127]) ).
cnf(c_0_4898,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3311]) ).
cnf(c_0_4899,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3312]) ).
cnf(c_0_4900,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3313]) ).
cnf(c_0_4901,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3314]) ).
cnf(c_0_4902,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3315]) ).
cnf(c_0_4903,plain,
( c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_3316]) ).
cnf(c_0_4904,plain,
( c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[c_0_3317]) ).
cnf(c_0_4905,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(X2,X1)))
| ~ c_SEQ_Osubseq(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3318]) ).
cnf(c_0_4906,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1))),
inference(split_conjunct,[status(thm)],[c_0_3319]) ).
cnf(c_0_4907,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_3320]) ).
cnf(c_0_4908,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[c_0_3321]) ).
cnf(c_0_4909,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[c_0_3322]) ).
cnf(c_0_4910,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[c_0_3323]) ).
cnf(c_0_4911,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3324]) ).
cnf(c_0_4912,plain,
( hBOOL(hAPP(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_3325]) ).
cnf(c_0_4913,plain,
( hBOOL(hAPP(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_3326]) ).
cnf(c_0_4914,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3327]) ).
cnf(c_0_4915,plain,
( c_SEQ_Oconvergent(X1,c_COMBK(X1,tc_Nat_Onat,X2))
| ~ class_RealVector_Ometric__space(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3328]) ).
cnf(c_0_4916,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3223]) ).
cnf(c_0_4917,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_3329]) ).
cnf(c_0_4918,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3281]) ).
cnf(c_0_4919,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3281]) ).
cnf(c_0_4920,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3224]) ).
cnf(c_0_4921,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3330]) ).
cnf(c_0_4922,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3331]) ).
cnf(c_0_4923,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3228]) ).
cnf(c_0_4924,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_3329]) ).
cnf(c_0_4925,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_3332]) ).
cnf(c_0_4926,plain,
c_Complex_Ocomplex_Ocomplex__case(X1,X2,c_Complex_Ocomplex_OComplex(X3,X4)) = hAPP(hAPP(X2,X3),X4),
inference(split_conjunct,[status(thm)],[c_0_3333]) ).
cnf(c_0_4927,plain,
c_Complex_Ocomplex_Ocomplex__rec(X1,X2,c_Complex_Ocomplex_OComplex(X3,X4)) = hAPP(hAPP(X2,X3),X4),
inference(split_conjunct,[status(thm)],[c_0_3334]) ).
cnf(c_0_4928,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_3247]) ).
cnf(c_0_4929,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_3335]) ).
cnf(c_0_4930,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_3336]) ).
cnf(c_0_4931,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_3337]) ).
cnf(c_0_4932,plain,
( c_SEQ_Osubseq(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk3_1(X1)),esk4_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2950]) ).
cnf(c_0_4933,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_3263]) ).
cnf(c_0_4934,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_3264]) ).
cnf(c_0_4935,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_3338]) ).
cnf(c_0_4936,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_3339]) ).
cnf(c_0_4937,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3340]) ).
cnf(c_0_4938,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Nat_OSuc(X2)),
inference(split_conjunct,[status(thm)],[c_0_3341]) ).
cnf(c_0_4939,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk36_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2589]) ).
cnf(c_0_4940,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk29_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2590]) ).
cnf(c_0_4941,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[c_0_3342]) ).
cnf(c_0_4942,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[c_0_3343]) ).
cnf(c_0_4943,plain,
( hBOOL(hAPP(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_3275]) ).
cnf(c_0_4944,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_3344]) ).
cnf(c_0_4945,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_3345]) ).
cnf(c_0_4946,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_3346]) ).
cnf(c_0_4947,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = X2
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3347]) ).
cnf(c_0_4948,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_3348]) ).
cnf(c_0_4949,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_3349]) ).
cnf(c_0_4950,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_3350]) ).
cnf(c_0_4951,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3351]) ).
cnf(c_0_4952,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3352]) ).
cnf(c_0_4953,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))
| hAPP(hAPP(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_3353]) ).
cnf(c_0_4954,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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3354]) ).
cnf(c_0_4955,plain,
hBOOL(hAPP(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_3355]) ).
cnf(c_0_4956,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(X1))),
inference(split_conjunct,[status(thm)],[c_0_3356]) ).
cnf(c_0_4957,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))),
inference(split_conjunct,[status(thm)],[c_0_3357]) ).
cnf(c_0_4958,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_3290]) ).
cnf(c_0_4959,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_3291]) ).
cnf(c_0_4960,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3358]) ).
cnf(c_0_4961,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_3289]) ).
cnf(c_0_4962,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_3292]) ).
cnf(c_0_4963,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_3293]) ).
cnf(c_0_4964,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_3329]) ).
cnf(c_0_4965,plain,
( hBOOL(hAPP(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_3294]) ).
cnf(c_0_4966,plain,
( hBOOL(hAPP(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_3199]) ).
cnf(c_0_4967,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3359]) ).
cnf(c_0_4968,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_3360]) ).
cnf(c_0_4969,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3353]) ).
cnf(c_0_4970,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(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_3353]) ).
cnf(c_0_4971,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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3354]) ).
cnf(c_0_4972,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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3354]) ).
cnf(c_0_4973,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_3289]) ).
cnf(c_0_4974,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_3292]) ).
cnf(c_0_4975,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_3293]) ).
cnf(c_0_4976,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3302]) ).
cnf(c_0_4977,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3303]) ).
cnf(c_0_4978,plain,
hBOOL(hAPP(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_3361]) ).
cnf(c_0_4979,plain,
hBOOL(hAPP(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_3362]) ).
cnf(c_0_4980,plain,
hBOOL(hAPP(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_3363]) ).
cnf(c_0_4981,plain,
( hBOOL(hAPP(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_3067]) ).
cnf(c_0_4982,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3191]) ).
cnf(c_0_4983,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3119]) ).
cnf(c_0_4984,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3119]) ).
cnf(c_0_4985,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 != X3
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3364]) ).
cnf(c_0_4986,plain,
( c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3246]) ).
cnf(c_0_4987,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_3365]) ).
cnf(c_0_4988,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_3365]) ).
cnf(c_0_4989,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_3366]) ).
cnf(c_0_4990,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_3367]) ).
cnf(c_0_4991,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_3368]) ).
cnf(c_0_4992,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_3369]) ).
cnf(c_0_4993,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_3370]) ).
cnf(c_0_4994,plain,
( hBOOL(hAPP(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_3307]) ).
cnf(c_0_4995,plain,
( hBOOL(hAPP(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_3371]) ).
cnf(c_0_4996,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3206]) ).
cnf(c_0_4997,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_3353]) ).
cnf(c_0_4998,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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3354]) ).
cnf(c_0_4999,plain,
hAPP(c_Complex_ORe,c_Complex_Orcis(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Ocos(X2)),
inference(split_conjunct,[status(thm)],[c_0_3372]) ).
cnf(c_0_5000,plain,
hAPP(c_Complex_OIm,c_Complex_Orcis(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Osin(X2)),
inference(split_conjunct,[status(thm)],[c_0_3373]) ).
cnf(c_0_5001,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3374]) ).
cnf(c_0_5002,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_3375]) ).
cnf(c_0_5003,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_3376]) ).
cnf(c_0_5004,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X1))),
inference(split_conjunct,[status(thm)],[c_0_3377]) ).
cnf(c_0_5005,plain,
hBOOL(hAPP(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_3378]) ).
cnf(c_0_5006,plain,
hBOOL(hAPP(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_3379]) ).
cnf(c_0_5007,plain,
( hBOOL(hAPP(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_3320]) ).
cnf(c_0_5008,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_3376]) ).
cnf(c_0_5009,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk28_0)),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_5010,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk27_0)),
inference(split_conjunct,[status(thm)],[c_0_2820]) ).
cnf(c_0_5011,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk26_0)),
inference(split_conjunct,[status(thm)],[c_0_2821]) ).
cnf(c_0_5012,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk25_0)),
inference(split_conjunct,[status(thm)],[c_0_2822]) ).
cnf(c_0_5013,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(split_conjunct,[status(thm)],[c_0_3380]) ).
cnf(c_0_5014,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_3381]) ).
cnf(c_0_5015,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_3382]) ).
cnf(c_0_5016,plain,
c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(split_conjunct,[status(thm)],[c_0_3383]) ).
cnf(c_0_5017,plain,
( X1 = X2
| hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3384]) ).
cnf(c_0_5018,plain,
( X1 = X2
| hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3385]) ).
cnf(c_0_5019,plain,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3386]) ).
cnf(c_0_5020,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_3387]) ).
cnf(c_0_5021,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_3387]) ).
cnf(c_0_5022,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_3388]) ).
cnf(c_0_5023,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_3388]) ).
cnf(c_0_5024,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3389]) ).
cnf(c_0_5025,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3389]) ).
cnf(c_0_5026,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3225]) ).
cnf(c_0_5027,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3231]) ).
cnf(c_0_5028,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3390]) ).
cnf(c_0_5029,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3227]) ).
cnf(c_0_5030,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_3365]) ).
cnf(c_0_5031,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_3391]) ).
cnf(c_0_5032,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3392]) ).
cnf(c_0_5033,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_3393]) ).
cnf(c_0_5034,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_3394]) ).
cnf(c_0_5035,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_3395]) ).
cnf(c_0_5036,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_3396]) ).
cnf(c_0_5037,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3397]) ).
cnf(c_0_5038,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3398]) ).
cnf(c_0_5039,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_3399]) ).
cnf(c_0_5040,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_3400]) ).
cnf(c_0_5041,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_3401]) ).
cnf(c_0_5042,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_3402]) ).
cnf(c_0_5043,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_3403]) ).
cnf(c_0_5044,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_3404]) ).
cnf(c_0_5045,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_3405]) ).
cnf(c_0_5046,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_3406]) ).
cnf(c_0_5047,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3407]) ).
cnf(c_0_5048,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3408]) ).
cnf(c_0_5049,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3409]) ).
cnf(c_0_5050,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3347]) ).
cnf(c_0_5051,plain,
( hAPP(hAPP(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_3353]) ).
cnf(c_0_5052,plain,
( hAPP(hAPP(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_3353]) ).
cnf(c_0_5053,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(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_3354]) ).
cnf(c_0_5054,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(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_3354]) ).
cnf(c_0_5055,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),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_3410]) ).
cnf(c_0_5056,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_3411]) ).
cnf(c_0_5057,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_3412]) ).
cnf(c_0_5058,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_3346]) ).
cnf(c_0_5059,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_3346]) ).
cnf(c_0_5060,plain,
( hAPP(hAPP(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_3351]) ).
cnf(c_0_5061,plain,
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(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_3352]) ).
cnf(c_0_5062,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3413]) ).
cnf(c_0_5063,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3414]) ).
cnf(c_0_5064,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_3415]) ).
cnf(c_0_5065,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_3416]) ).
cnf(c_0_5066,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_3417]) ).
cnf(c_0_5067,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_3418]) ).
cnf(c_0_5068,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_2968]) ).
cnf(c_0_5069,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_3348]) ).
cnf(c_0_5070,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_3349]) ).
cnf(c_0_5071,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3410]) ).
cnf(c_0_5072,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_3419]) ).
cnf(c_0_5073,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3420]) ).
cnf(c_0_5074,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_3421]) ).
cnf(c_0_5075,plain,
( X2 = hAPP(hAPP(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_3359]) ).
cnf(c_0_5076,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3422]) ).
cnf(c_0_5077,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_3423]) ).
cnf(c_0_5078,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_3424]) ).
cnf(c_0_5079,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_3425]) ).
cnf(c_0_5080,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_3426]) ).
cnf(c_0_5081,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_3427]) ).
cnf(c_0_5082,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3428]) ).
cnf(c_0_5083,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3429]) ).
cnf(c_0_5084,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3430]) ).
cnf(c_0_5085,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_3360]) ).
cnf(c_0_5086,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X1,
inference(split_conjunct,[status(thm)],[c_0_3431]) ).
cnf(c_0_5087,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_3432]) ).
cnf(c_0_5088,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X1),c_Transcendental_Osin(X1))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3433]) ).
cnf(c_0_5089,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_3434]) ).
cnf(c_0_5090,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_3435]) ).
cnf(c_0_5091,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_3436]) ).
cnf(c_0_5092,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_3080]) ).
cnf(c_0_5093,plain,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Osgn__class_Osgn(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3437]) ).
cnf(c_0_5094,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3438]) ).
cnf(c_0_5095,plain,
c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X1),hAPP(c_Complex_OIm,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3439]) ).
cnf(c_0_5096,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_3387]) ).
cnf(c_0_5097,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_3388]) ).
cnf(c_0_5098,plain,
( hAPP(hAPP(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_3389]) ).
cnf(c_0_5099,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3440]) ).
cnf(c_0_5100,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[c_0_3441]) ).
cnf(c_0_5101,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_3360]) ).
cnf(c_0_5102,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_3442]) ).
cnf(c_0_5103,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_3443]) ).
cnf(c_0_5104,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(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_3444]) ).
cnf(c_0_5105,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_3445]) ).
cnf(c_0_5106,plain,
c_Nat_OSuc(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(split_conjunct,[status(thm)],[c_0_3446]) ).
cnf(c_0_5107,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_3447]) ).
cnf(c_0_5108,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3444]) ).
cnf(c_0_5109,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_3448]) ).
cnf(c_0_5110,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_3003]) ).
cnf(c_0_5111,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_2852]) ).
cnf(c_0_5112,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_3381]) ).
cnf(c_0_5113,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_3381]) ).
cnf(c_0_5114,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,X1)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3449]) ).
cnf(c_0_5115,plain,
c_Nat_OSuc(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_3450]) ).
cnf(c_0_5116,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_3451]) ).
cnf(c_0_5117,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_3452]) ).
cnf(c_0_5118,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_3453]) ).
cnf(c_0_5119,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_5120,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_3455]) ).
cnf(c_0_5121,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_2883]) ).
cnf(c_0_5122,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_5123,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_3457]) ).
cnf(c_0_5124,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3458]) ).
cnf(c_0_5125,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_3459]) ).
cnf(c_0_5126,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_3460]) ).
cnf(c_0_5127,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3461]) ).
cnf(c_0_5128,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)) = c_RealDef_Oreal(tc_Nat_Onat,X1),
inference(split_conjunct,[status(thm)],[c_0_3462]) ).
cnf(c_0_5129,plain,
( X1 = X3
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3463]) ).
cnf(c_0_5130,plain,
( X2 = X4
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3463]) ).
cnf(c_0_5131,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_3464]) ).
cnf(c_0_5132,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_SEQ_Odecseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3465]) ).
cnf(c_0_5133,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_SEQ_Oincseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3466]) ).
cnf(c_0_5134,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_3464]) ).
cnf(c_0_5135,plain,
( X1 = X2
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_RealDef_Oreal(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3467]) ).
cnf(c_0_5136,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3468]) ).
cnf(c_0_5137,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3469]) ).
cnf(c_0_5138,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3470]) ).
cnf(c_0_5139,plain,
c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3471]) ).
cnf(c_0_5140,plain,
hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3472]) ).
cnf(c_0_5141,plain,
hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_3473]) ).
cnf(c_0_5142,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_3474]) ).
cnf(c_0_5143,plain,
( class_Orderings_Oord(tc_fun(X1,X2))
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3475]) ).
cnf(c_0_5144,plain,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3476]) ).
cnf(c_0_5145,plain,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3477]) ).
cnf(c_0_5146,plain,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Complex_Ocomplex_OComplex(X3,X4)
| X2 != X4
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3463]) ).
cnf(c_0_5147,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3468]) ).
cnf(c_0_5148,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3469]) ).
cnf(c_0_5149,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3470]) ).
cnf(c_0_5150,plain,
c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3478]) ).
cnf(c_0_5151,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_3474]) ).
cnf(c_0_5152,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3479]) ).
cnf(c_0_5153,plain,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3480]) ).
cnf(c_0_5154,plain,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3481]) ).
cnf(c_0_5155,plain,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Osgn__if(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3482]) ).
cnf(c_0_5156,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3483]) ).
cnf(c_0_5157,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3484]) ).
cnf(c_0_5158,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[c_0_3485]) ).
cnf(c_0_5159,plain,
c_Complex_Ocis(X1) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X1),c_Transcendental_Osin(X1)),
inference(split_conjunct,[status(thm)],[c_0_3486]) ).
cnf(c_0_5160,plain,
( X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3487]) ).
cnf(c_0_5161,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3487]) ).
cnf(c_0_5162,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3488]) ).
cnf(c_0_5163,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3488]) ).
cnf(c_0_5164,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_3489]) ).
cnf(c_0_5165,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_3490]) ).
cnf(c_0_5166,plain,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3487]) ).
cnf(c_0_5167,plain,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| 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_3488]) ).
cnf(c_0_5168,plain,
( c_RealDef_Oreal(tc_Nat_Onat,X1) = c_RealDef_Oreal(tc_Nat_Onat,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3467]) ).
cnf(c_0_5169,plain,
( hAPP(c_Complex_ORe,X1) = hAPP(c_Complex_ORe,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3384]) ).
cnf(c_0_5170,plain,
( hAPP(c_Complex_OIm,X1) = hAPP(c_Complex_OIm,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3384]) ).
cnf(c_0_5171,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3491]) ).
cnf(c_0_5172,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3492]) ).
cnf(c_0_5173,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3493]) ).
cnf(c_0_5174,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3494]) ).
cnf(c_0_5175,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Oii ),
inference(split_conjunct,[status(thm)],[c_0_3495]) ).
cnf(c_0_5176,plain,
( X2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Oii ),
inference(split_conjunct,[status(thm)],[c_0_3495]) ).
cnf(c_0_5177,plain,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Complex_Oii
| X2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3495]) ).
cnf(c_0_5178,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_3496]) ).
cnf(c_0_5179,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_3497]) ).
cnf(c_0_5180,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_3498]) ).
cnf(c_0_5181,plain,
hAPP(c_Complex_ORe,c_Complex_Ocis(X1)) = c_Transcendental_Ocos(X1),
inference(split_conjunct,[status(thm)],[c_0_3499]) ).
cnf(c_0_5182,plain,
hAPP(c_Complex_OIm,c_Complex_Ocis(X1)) = c_Transcendental_Osin(X1),
inference(split_conjunct,[status(thm)],[c_0_3500]) ).
cnf(c_0_5183,plain,
c_Complex_Ocis(X1) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),
inference(split_conjunct,[status(thm)],[c_0_3501]) ).
cnf(c_0_5184,plain,
( c_RealDef_Oreal(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_3493]) ).
cnf(c_0_5185,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_3502]) ).
cnf(c_0_5186,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_3502]) ).
cnf(c_0_5187,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_3503]) ).
cnf(c_0_5188,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_3503]) ).
cnf(c_0_5189,plain,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_3504]) ).
cnf(c_0_5190,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_3505]) ).
cnf(c_0_5191,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_3506]) ).
cnf(c_0_5192,plain,
c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3507]) ).
cnf(c_0_5193,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3508]) ).
cnf(c_0_5194,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3509]) ).
cnf(c_0_5195,plain,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3510]) ).
cnf(c_0_5196,plain,
hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3511]) ).
cnf(c_0_5197,plain,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3512]) ).
cnf(c_0_5198,plain,
hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3513]) ).
cnf(c_0_5199,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3514]) ).
cnf(c_0_5200,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3515]) ).
cnf(c_0_5201,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3516]) ).
cnf(c_0_5202,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3517]) ).
cnf(c_0_5203,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3518]) ).
cnf(c_0_5204,plain,
( class_Groups_Osgn__if(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3519]) ).
cnf(c_0_5205,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3520]) ).
cnf(c_0_5206,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3521]) ).
cnf(c_0_5207,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3522]) ).
cnf(c_0_5208,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3523]) ).
cnf(c_0_5209,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3524]) ).
cnf(c_0_5210,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3525]) ).
cnf(c_0_5211,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3526]) ).
cnf(c_0_5212,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3527]) ).
cnf(c_0_5213,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3528]) ).
cnf(c_0_5214,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3529]) ).
cnf(c_0_5215,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3530]) ).
cnf(c_0_5216,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3531]) ).
cnf(c_0_5217,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3532]) ).
cnf(c_0_5218,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3533]) ).
cnf(c_0_5219,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3534]) ).
cnf(c_0_5220,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3535]) ).
cnf(c_0_5221,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3536]) ).
cnf(c_0_5222,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3537]) ).
cnf(c_0_5223,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3538]) ).
cnf(c_0_5224,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3539]) ).
cnf(c_0_5225,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3540]) ).
cnf(c_0_5226,plain,
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3541]) ).
cnf(c_0_5227,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3542]) ).
cnf(c_0_5228,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3543]) ).
cnf(c_0_5229,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3544]) ).
cnf(c_0_5230,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3545]) ).
cnf(c_0_5231,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3546]) ).
cnf(c_0_5232,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3547]) ).
cnf(c_0_5233,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3548]) ).
cnf(c_0_5234,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3549]) ).
cnf(c_0_5235,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3550]) ).
cnf(c_0_5236,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3551]) ).
cnf(c_0_5237,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3552]) ).
cnf(c_0_5238,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3553]) ).
cnf(c_0_5239,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3554]) ).
cnf(c_0_5240,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3555]) ).
cnf(c_0_5241,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_3556]) ).
cnf(c_0_5242,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3557]) ).
cnf(c_0_5243,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3558]) ).
cnf(c_0_5244,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3559]) ).
cnf(c_0_5245,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3560]) ).
cnf(c_0_5246,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3561]) ).
cnf(c_0_5247,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3562]) ).
cnf(c_0_5248,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3563]) ).
cnf(c_0_5249,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_3564]) ).
cnf(c_0_5250,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3565]) ).
cnf(c_0_5251,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3566]) ).
cnf(c_0_5252,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3567]) ).
cnf(c_0_5253,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3568]) ).
cnf(c_0_5254,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_3569]) ).
cnf(c_0_5255,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3570]) ).
cnf(c_0_5256,plain,
( c_Transcendental_Osin(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_3571]) ).
cnf(c_0_5257,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3572]) ).
cnf(c_0_5258,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3573]) ).
cnf(c_0_5259,plain,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3574]) ).
cnf(c_0_5260,plain,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3575]) ).
cnf(c_0_5261,plain,
( c_Nat_OSuc(X1) = c_Nat_OSuc(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3572]) ).
cnf(c_0_5262,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_3576]) ).
cnf(c_0_5263,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_3577]) ).
cnf(c_0_5264,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3578]) ).
cnf(c_0_5265,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3579]) ).
cnf(c_0_5266,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_3580]) ).
cnf(c_0_5267,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3581]) ).
cnf(c_0_5268,plain,
c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3582]) ).
cnf(c_0_5269,plain,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3583]) ).
cnf(c_0_5270,plain,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3584]) ).
cnf(c_0_5271,plain,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3585]) ).
cnf(c_0_5272,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_3586]) ).
cnf(c_0_5273,plain,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3587]) ).
cnf(c_0_5274,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3588]) ).
cnf(c_0_5275,plain,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3589]) ).
cnf(c_0_5276,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3590]) ).
cnf(c_0_5277,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_3591]) ).
cnf(c_0_5278,plain,
X1 != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_3592]) ).
cnf(c_0_5279,plain,
c_Nat_OSuc(X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_3593]) ).
cnf(c_0_5280,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3594]) ).
cnf(c_0_5281,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3595]) ).
cnf(c_0_5282,plain,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3596]) ).
cnf(c_0_5283,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3597]) ).
cnf(c_0_5284,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3598]) ).
cnf(c_0_5285,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3599]) ).
cnf(c_0_5286,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3600]) ).
cnf(c_0_5287,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3601]) ).
cnf(c_0_5288,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3602]) ).
cnf(c_0_5289,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3603]) ).
cnf(c_0_5290,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3604]) ).
cnf(c_0_5291,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3605]) ).
cnf(c_0_5292,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3606]) ).
cnf(c_0_5293,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3607]) ).
cnf(c_0_5294,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3608]) ).
cnf(c_0_5295,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3609]) ).
cnf(c_0_5296,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3610]) ).
cnf(c_0_5297,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3611]) ).
cnf(c_0_5298,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3612]) ).
cnf(c_0_5299,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3613]) ).
cnf(c_0_5300,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3614]) ).
cnf(c_0_5301,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3615]) ).
cnf(c_0_5302,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3616]) ).
cnf(c_0_5303,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3617]) ).
cnf(c_0_5304,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3618]) ).
cnf(c_0_5305,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3619]) ).
cnf(c_0_5306,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3620]) ).
cnf(c_0_5307,plain,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3621]) ).
cnf(c_0_5308,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3622]) ).
cnf(c_0_5309,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3623]) ).
cnf(c_0_5310,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3624]) ).
cnf(c_0_5311,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3625]) ).
cnf(c_0_5312,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3626]) ).
cnf(c_0_5313,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3627]) ).
cnf(c_0_5314,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3628]) ).
cnf(c_0_5315,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3629]) ).
cnf(c_0_5316,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3630]) ).
cnf(c_0_5317,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3631]) ).
cnf(c_0_5318,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3632]) ).
cnf(c_0_5319,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3633]) ).
cnf(c_0_5320,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3634]) ).
cnf(c_0_5321,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3635]) ).
cnf(c_0_5322,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3636]) ).
cnf(c_0_5323,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3637]) ).
cnf(c_0_5324,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3638]) ).
cnf(c_0_5325,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3639]) ).
cnf(c_0_5326,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3640]) ).
cnf(c_0_5327,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3641]) ).
cnf(c_0_5328,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3642]) ).
cnf(c_0_5329,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3643]) ).
cnf(c_0_5330,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3644]) ).
cnf(c_0_5331,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3645]) ).
cnf(c_0_5332,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3646]) ).
cnf(c_0_5333,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3647]) ).
cnf(c_0_5334,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3648]) ).
cnf(c_0_5335,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3649]) ).
cnf(c_0_5336,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3650]) ).
cnf(c_0_5337,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3651]) ).
cnf(c_0_5338,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3652]) ).
cnf(c_0_5339,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3653]) ).
cnf(c_0_5340,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3654]) ).
cnf(c_0_5341,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3655]) ).
cnf(c_0_5342,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3656]) ).
cnf(c_0_5343,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3657]) ).
cnf(c_0_5344,plain,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3658]) ).
cnf(c_0_5345,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3659]) ).
cnf(c_0_5346,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3660]) ).
cnf(c_0_5347,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3661]) ).
cnf(c_0_5348,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3662]) ).
cnf(c_0_5349,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3663]) ).
cnf(c_0_5350,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3664]) ).
cnf(c_0_5351,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3665]) ).
cnf(c_0_5352,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3666]) ).
cnf(c_0_5353,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3667]) ).
cnf(c_0_5354,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3668]) ).
cnf(c_0_5355,plain,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3669]) ).
cnf(c_0_5356,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3670]) ).
cnf(c_0_5357,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3671]) ).
cnf(c_0_5358,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3672]) ).
cnf(c_0_5359,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3673]) ).
cnf(c_0_5360,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3674]) ).
cnf(c_0_5361,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3675]) ).
cnf(c_0_5362,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3676]) ).
cnf(c_0_5363,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3677]) ).
cnf(c_0_5364,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3678]) ).
cnf(c_0_5365,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3679]) ).
cnf(c_0_5366,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3680]) ).
cnf(c_0_5367,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3681]) ).
cnf(c_0_5368,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3682]) ).
cnf(c_0_5369,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3683]) ).
cnf(c_0_5370,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3684]) ).
cnf(c_0_5371,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3685]) ).
cnf(c_0_5372,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3686]) ).
cnf(c_0_5373,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3687]) ).
cnf(c_0_5374,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3688]) ).
cnf(c_0_5375,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3689]) ).
cnf(c_0_5376,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3690]) ).
cnf(c_0_5377,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3691]) ).
cnf(c_0_5378,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3692]) ).
cnf(c_0_5379,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3693]) ).
cnf(c_0_5380,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3694]) ).
cnf(c_0_5381,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3695]) ).
cnf(c_0_5382,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3696]) ).
cnf(c_0_5383,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3697]) ).
cnf(c_0_5384,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3698]) ).
cnf(c_0_5385,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3699]) ).
cnf(c_0_5386,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[c_0_3700]) ).
cnf(c_0_5387,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[c_0_3701]) ).
cnf(c_0_5388,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[c_0_3702]) ).
cnf(c_0_5389,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3703]) ).
cnf(c_0_5390,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3704]) ).
cnf(c_0_5391,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3705]) ).
cnf(c_0_5392,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3706]) ).
cnf(c_0_5393,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3707]) ).
cnf(c_0_5394,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3708]) ).
cnf(c_0_5395,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3709]) ).
cnf(c_0_5396,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3710]) ).
cnf(c_0_5397,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3711]) ).
cnf(c_0_5398,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3712]) ).
cnf(c_0_5399,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3713]) ).
cnf(c_0_5400,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3714]) ).
cnf(c_0_5401,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3715]) ).
cnf(c_0_5402,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3716]) ).
cnf(c_0_5403,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3717]) ).
cnf(c_0_5404,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3718]) ).
cnf(c_0_5405,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3719]) ).
cnf(c_0_5406,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3720]) ).
cnf(c_0_5407,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3721]) ).
cnf(c_0_5408,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3722]) ).
cnf(c_0_5409,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3723]) ).
cnf(c_0_5410,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3724]) ).
cnf(c_0_5411,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3725]) ).
cnf(c_0_5412,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3726]) ).
cnf(c_0_5413,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3727]) ).
cnf(c_0_5414,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3728]) ).
cnf(c_0_5415,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3729]) ).
cnf(c_0_5416,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3730]) ).
cnf(c_0_5417,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3731]) ).
cnf(c_0_5418,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3732]) ).
cnf(c_0_5419,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3733]) ).
cnf(c_0_5420,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3734]) ).
cnf(c_0_5421,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3735]) ).
cnf(c_0_5422,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3736]) ).
cnf(c_0_5423,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3737]) ).
cnf(c_0_5424,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3738]) ).
cnf(c_0_5425,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3739]) ).
cnf(c_0_5426,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3740]) ).
cnf(c_0_5427,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3741]) ).
cnf(c_0_5428,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3742]) ).
cnf(c_0_5429,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3743]) ).
cnf(c_0_5430,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3744]) ).
cnf(c_0_5431,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3745]) ).
cnf(c_0_5432,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3746]) ).
cnf(c_0_5433,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3747]) ).
cnf(c_0_5434,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3748]) ).
cnf(c_0_5435,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3749]) ).
cnf(c_0_5436,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3750]) ).
cnf(c_0_5437,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3751]) ).
cnf(c_0_5438,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3752]) ).
cnf(c_0_5439,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3753]) ).
cnf(c_0_5440,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3754]) ).
cnf(c_0_5441,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3755]) ).
cnf(c_0_5442,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3756]) ).
cnf(c_0_5443,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3757]) ).
cnf(c_0_5444,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3758]) ).
cnf(c_0_5445,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3759]) ).
cnf(c_0_5446,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3760]) ).
cnf(c_0_5447,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3761]) ).
cnf(c_0_5448,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3762]) ).
cnf(c_0_5449,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3763]) ).
cnf(c_0_5450,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3764]) ).
cnf(c_0_5451,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3765]) ).
cnf(c_0_5452,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3766]) ).
cnf(c_0_5453,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3767]) ).
cnf(c_0_5454,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3768]) ).
cnf(c_0_5455,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3769]) ).
cnf(c_0_5456,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3770]) ).
cnf(c_0_5457,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3771]) ).
cnf(c_0_5458,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3772]) ).
cnf(c_0_5459,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3773]) ).
cnf(c_0_5460,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3774]) ).
cnf(c_0_5461,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3775]) ).
cnf(c_0_5462,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3776]) ).
cnf(c_0_5463,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3777]) ).
cnf(c_0_5464,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3778]) ).
cnf(c_0_5465,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3779]) ).
cnf(c_0_5466,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3780]) ).
cnf(c_0_5467,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3781]) ).
cnf(c_0_5468,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3782]) ).
cnf(c_0_5469,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3783]) ).
cnf(c_0_5470,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3784]) ).
cnf(c_0_5471,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3785]) ).
cnf(c_0_5472,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3786]) ).
cnf(c_0_5473,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3787]) ).
cnf(c_0_5474,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3788]) ).
cnf(c_0_5475,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3789]) ).
cnf(c_0_5476,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3790]) ).
cnf(c_0_5477,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3791]) ).
cnf(c_0_5478,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3792]) ).
cnf(c_0_5479,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3793]) ).
cnf(c_0_5480,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3794]) ).
cnf(c_0_5481,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3795]) ).
cnf(c_0_5482,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_3796]) ).
cnf(c_0_5483,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3797]) ).
cnf(c_0_5484,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3798]) ).
cnf(c_0_5485,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3799]) ).
cnf(c_0_5486,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_3800]) ).
cnf(c_0_5487,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3801]) ).
cnf(c_0_5488,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3802]) ).
cnf(c_0_5489,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3803]) ).
cnf(c_0_5490,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3804]) ).
cnf(c_0_5491,plain,
c_SEQ_Osubseq(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_2543]) ).
cnf(c_0_5492,plain,
c_SEQ_Osubseq(v_ga____),
inference(split_conjunct,[status(thm)],[c_0_3805]) ).
cnf(c_0_5493,plain,
c_SEQ_Osubseq(v_f____),
inference(split_conjunct,[status(thm)],[c_0_3806]) ).
cnf(c_0_5494,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
c_0_3807,
[final] ).
cnf(c_0_5495,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4))
| ~ hBOOL(hAPP(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,esk67_4(X3,X5,X1,X2))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
c_0_3808,
[final] ).
cnf(c_0_5496,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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_3809,
[final] ).
cnf(c_0_5497,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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_3810,
[final] ).
cnf(c_0_5498,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
c_0_3811,
[final] ).
cnf(c_0_5499,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,esk9_0)))),
c_0_3812,
[final] ).
cnf(c_0_5500,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
c_0_3813,
[final] ).
cnf(c_0_5501,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4)),X5)) ),
c_0_3814,
[final] ).
cnf(c_0_5502,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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_3815,
[final] ).
cnf(c_0_5503,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
c_0_3816,
[final] ).
cnf(c_0_5504,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
c_0_3817,
[final] ).
cnf(c_0_5505,plain,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk20_4(X3,X2,X4,X1)))),X3)) ),
c_0_3818,
[final] ).
cnf(c_0_5506,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5))) ),
c_0_3819,
[final] ).
cnf(c_0_5507,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5))) ),
c_0_3820,
[final] ).
cnf(c_0_5508,plain,
( c_SEQ_OBseq(X1,X2)
| ~ c_SEQ_OBseq(X1,c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3821,
[final] ).
cnf(c_0_5509,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),hAPP(hAPP(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_3822,
[final] ).
cnf(c_0_5510,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),hAPP(hAPP(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_3823,
[final] ).
cnf(c_0_5511,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,esk2_4(X4,X3,X2,X1))),hAPP(X4,esk2_4(X4,X3,X2,X1)))) ),
c_0_3824,
[final] ).
cnf(c_0_5512,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),hAPP(hAPP(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_3825,
[final] ).
cnf(c_0_5513,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),hAPP(hAPP(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_3826,
[final] ).
cnf(c_0_5514,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
c_0_3827,
[final] ).
cnf(c_0_5515,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
c_0_3828,
[final] ).
cnf(c_0_5516,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X3),hAPP(X1,X2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2))),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X3),hAPP(X1,X2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2))),X3)),
c_0_3829,
[final] ).
cnf(c_0_5517,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_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_3830,
[final] ).
cnf(c_0_5518,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5))) ),
c_0_3831,
[final] ).
cnf(c_0_5519,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5))) ),
c_0_3832,
[final] ).
cnf(c_0_5520,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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),esk24_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_3833,
[final] ).
cnf(c_0_5521,plain,
( c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X3)
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3834,
[final] ).
cnf(c_0_5522,plain,
( c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X3)
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3835,
[final] ).
cnf(c_0_5523,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5)))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_3836,
[final] ).
cnf(c_0_5524,plain,
( c_SEQ_Oconvergent(X1,c_COMBC(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__field(X1) ),
c_0_3837,
[final] ).
cnf(c_0_5525,plain,
( c_SEQ_Oconvergent(X1,c_COMBC(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3838,
[final] ).
cnf(c_0_5526,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_3839,
[final] ).
cnf(c_0_5527,plain,
( c_SEQ_OBseq(X1,c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3)))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3840,
[final] ).
cnf(c_0_5528,plain,
c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
c_0_3841,
[final] ).
cnf(c_0_5529,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
c_0_3842,
[final] ).
cnf(c_0_5530,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1),hAPP(c_Complex_ORe,X2)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1),hAPP(c_Complex_OIm,X2)))))),
c_0_3843,
[final] ).
cnf(c_0_5531,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X3,X5)),X6))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X6)),X5)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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),X4),X5))),X6)
| ~ class_RealVector_Oreal__field(X1) ),
c_0_3844,
[final] ).
cnf(c_0_5532,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3))) ),
c_0_3845,
[final] ).
cnf(c_0_5533,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X5))) ),
c_0_3846,
[final] ).
cnf(c_0_5534,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_3847,
[final] ).
cnf(c_0_5535,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_3848,
[final] ).
cnf(c_0_5536,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring(X1) ),
c_0_3849,
[final] ).
cnf(c_0_5537,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
c_0_3850,
[final] ).
cnf(c_0_5538,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X6) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X5) ),
c_0_3851,
[final] ).
cnf(c_0_5539,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
c_0_3852,
[final] ).
cnf(c_0_5540,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk44_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk43_3(X2,X1,X4)))),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
c_0_3853,
[final] ).
cnf(c_0_5541,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk40_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk39_3(X2,X1,X4)))),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
c_0_3854,
[final] ).
cnf(c_0_5542,plain,
( hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_3855,
[final] ).
cnf(c_0_5543,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4))),esk46_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk45_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
c_0_3856,
[final] ).
cnf(c_0_5544,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4))),esk42_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk41_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
c_0_3857,
[final] ).
cnf(c_0_5545,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1(X1) ),
c_0_3858,
[final] ).
cnf(c_0_5546,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
c_0_3859,
[final] ).
cnf(c_0_5547,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk46_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk45_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
c_0_3860,
[final] ).
cnf(c_0_5548,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk42_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk41_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
c_0_3861,
[final] ).
cnf(c_0_5549,plain,
( c_SEQ_OBseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk19_3(X2,X3,X1)))),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3862,
[final] ).
cnf(c_0_5550,plain,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk14_3(X2,X1,X3)))),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
c_0_3863,
[final] ).
cnf(c_0_5551,plain,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk57_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
c_0_3864,
[final] ).
cnf(c_0_5552,plain,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk55_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
c_0_3865,
[final] ).
cnf(c_0_5553,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_3866,
[final] ).
cnf(c_0_5554,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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_3867,
[final] ).
cnf(c_0_5555,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),hAPP(hAPP(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,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X4)) ),
c_0_3868,
[final] ).
cnf(c_0_5556,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),hAPP(hAPP(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,hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X1)) ),
c_0_3869,
[final] ).
cnf(c_0_5557,plain,
( hBOOL(hAPP(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))),esk62_1(X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3870,
[final] ).
cnf(c_0_5558,plain,
( hBOOL(hAPP(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))),esk36_1(X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3871,
[final] ).
cnf(c_0_5559,plain,
( hBOOL(hAPP(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))),esk29_1(X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3872,
[final] ).
cnf(c_0_5560,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_3873,
[final] ).
cnf(c_0_5561,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6) ),
c_0_3874,
[final] ).
cnf(c_0_5562,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_OIm,X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_ORe,X2)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),
c_0_3875,
[final] ).
cnf(c_0_5563,plain,
( c_SEQ_Oconvergent(X1,c_COMBB(X1,X1,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3876,
[final] ).
cnf(c_0_5564,plain,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
c_0_3877,
[final] ).
cnf(c_0_5565,plain,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),X5),
c_0_3878,
[final] ).
cnf(c_0_5566,plain,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X4,hAPP(X5,X6)),
c_0_3879,
[final] ).
cnf(c_0_5567,plain,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))) ),
c_0_3880,
[final] ).
cnf(c_0_5568,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,X1))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,X1) ),
c_0_3881,
[final] ).
cnf(c_0_5569,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,X1))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,X1) ),
c_0_3882,
[final] ).
cnf(c_0_5570,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_3883,
[final] ).
cnf(c_0_5571,plain,
hBOOL(hAPP(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,hAPP(hAPP(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_3884,
[final] ).
cnf(c_0_5572,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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_3885,
[final] ).
cnf(c_0_5573,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2)) ),
c_0_3886,
[final] ).
cnf(c_0_5574,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| ~ class_Rings_Oring(X1)
| X4 != hAPP(hAPP(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_3887,
[final] ).
cnf(c_0_5575,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| ~ class_Rings_Oring(X1)
| hAPP(hAPP(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_3888,
[final] ).
cnf(c_0_5576,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X4 != hAPP(hAPP(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_3889,
[final] ).
cnf(c_0_5577,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4) != X5 ),
c_0_3890,
[final] ).
cnf(c_0_5578,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),esk68_3(X3,X2,X1))) ),
c_0_3891,
[final] ).
cnf(c_0_5579,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),esk68_3(X3,X2,X1))) ),
c_0_3892,
[final] ).
cnf(c_0_5580,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_3893,
[final] ).
cnf(c_0_5581,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4)) ),
c_0_3894,
[final] ).
cnf(c_0_5582,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))))),
c_0_3895,
[final] ).
cnf(c_0_5583,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),esk67_4(X3,X5,X1,X2)))
| ~ class_Orderings_Oord(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4)) ),
c_0_3896,
[final] ).
cnf(c_0_5584,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)))),
c_0_3897,
[final] ).
cnf(c_0_5585,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4)) ),
c_0_3898,
[final] ).
cnf(c_0_5586,plain,
( X2 = hAPP(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6) ),
c_0_3899,
[final] ).
cnf(c_0_5587,plain,
( hAPP(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6) ),
c_0_3900,
[final] ).
cnf(c_0_5588,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk59_2(X2,X1))),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
c_0_3901,
[final] ).
cnf(c_0_5589,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X3)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X4))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_3902,
[final] ).
cnf(c_0_5590,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X3))) ),
c_0_3903,
[final] ).
cnf(c_0_5591,plain,
( X3 = hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5) ),
c_0_3904,
[final] ).
cnf(c_0_5592,plain,
( hAPP(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5) ),
c_0_3905,
[final] ).
cnf(c_0_5593,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Rings_Osemiring(X1) ),
c_0_3906,
[final] ).
cnf(c_0_5594,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_3907,
[final] ).
cnf(c_0_5595,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3908,
[final] ).
cnf(c_0_5596,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)),X4))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3909,
[final] ).
cnf(c_0_5597,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),esk71_3(X3,X2,X1))),X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
c_0_3910,
[final] ).
cnf(c_0_5598,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),esk71_3(X3,X2,X1))),X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
c_0_3911,
[final] ).
cnf(c_0_5599,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk59_2(X2,X1)))),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
c_0_3912,
[final] ).
cnf(c_0_5600,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)),X4),
c_0_3913,
[final] ).
cnf(c_0_5601,plain,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X3,X2,X1))),esk73_3(X3,X2,X1)) = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk74_3(X3,X2,X1))),esk75_3(X3,X2,X1)) = X3 ),
c_0_3914,
[final] ).
cnf(c_0_5602,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_3915,
[final] ).
cnf(c_0_5603,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
c_0_3916,
[final] ).
cnf(c_0_5604,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
c_0_3917,
[final] ).
cnf(c_0_5605,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(esk71_3(X3,X2,X1)))))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
c_0_3918,
[final] ).
cnf(c_0_5606,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| ~ class_Rings_Olinordered__ring(X1) ),
c_0_3919,
[final] ).
cnf(c_0_5607,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),hAPP(hAPP(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_3920,
[final] ).
cnf(c_0_5608,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_3921,
[final] ).
cnf(c_0_5609,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(esk71_3(X3,X2,X1)))))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
c_0_3922,
[final] ).
cnf(c_0_5610,plain,
( hBOOL(hAPP(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)),esk63_2(X2,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3923,
[final] ).
cnf(c_0_5611,plain,
( hBOOL(hAPP(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)),esk61_2(X3,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3924,
[final] ).
cnf(c_0_5612,plain,
( hBOOL(hAPP(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)),esk38_2(X3,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3925,
[final] ).
cnf(c_0_5613,plain,
( hBOOL(hAPP(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)),esk37_2(X2,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3926,
[final] ).
cnf(c_0_5614,plain,
( hBOOL(hAPP(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)),esk31_2(X3,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3927,
[final] ).
cnf(c_0_5615,plain,
( hBOOL(hAPP(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)),esk30_2(X2,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_3928,
[final] ).
cnf(c_0_5616,plain,
( hBOOL(hAPP(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_3929,
[final] ).
cnf(c_0_5617,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(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_3930,
[final] ).
cnf(c_0_5618,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Fields_Olinordered__field(X1) ),
c_0_3931,
[final] ).
cnf(c_0_5619,plain,
( hAPP(hAPP(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_3932,
[final] ).
cnf(c_0_5620,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
c_0_3933,
[final] ).
cnf(c_0_5621,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_3934,
[final] ).
cnf(c_0_5622,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))),
c_0_3935,
[final] ).
cnf(c_0_5623,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
c_0_3936,
[final] ).
cnf(c_0_5624,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_3937,
[final] ).
cnf(c_0_5625,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_3938,
[final] ).
cnf(c_0_5626,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(X4))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X2)) ),
c_0_3939,
[final] ).
cnf(c_0_5627,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_3940,
[final] ).
cnf(c_0_5628,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_3941,
[final] ).
cnf(c_0_5629,plain,
( hBOOL(hAPP(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_3942,
[final] ).
cnf(c_0_5630,plain,
( hBOOL(hAPP(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_3943,
[final] ).
cnf(c_0_5631,plain,
( hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_3944,
[final] ).
cnf(c_0_5632,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_3945,
[final] ).
cnf(c_0_5633,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_3946,
[final] ).
cnf(c_0_5634,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_3947,
[final] ).
cnf(c_0_5635,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_3948,
[final] ).
cnf(c_0_5636,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_3949,
[final] ).
cnf(c_0_5637,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_3950,
[final] ).
cnf(c_0_5638,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_3951,
[final] ).
cnf(c_0_5639,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_3952,
[final] ).
cnf(c_0_5640,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_3953,
[final] ).
cnf(c_0_5641,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(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_3954,
[final] ).
cnf(c_0_5642,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3)),X4))
| ~ class_Rings_Olinordered__semidom(X3) ),
c_0_3955,
[final] ).
cnf(c_0_5643,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3)),X4))
| ~ class_Rings_Olinordered__semidom(X3) ),
c_0_3956,
[final] ).
cnf(c_0_5644,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(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_3957,
[final] ).
cnf(c_0_5645,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_3958,
[final] ).
cnf(c_0_5646,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_3959,
[final] ).
cnf(c_0_5647,plain,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X3,X2,X1))),esk73_3(X3,X2,X1)) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_3960,
[final] ).
cnf(c_0_5648,plain,
( X2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)) ),
c_0_3961,
[final] ).
cnf(c_0_5649,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X3,X2,X1)),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk74_3(X3,X2,X1))),esk75_3(X3,X2,X1)) = X3 ),
c_0_3962,
[final] ).
cnf(c_0_5650,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_3963,
[final] ).
cnf(c_0_5651,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_3964,
[final] ).
cnf(c_0_5652,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1)),
c_0_3965,
[final] ).
cnf(c_0_5653,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_3966,
[final] ).
cnf(c_0_5654,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_3967,
[final] ).
cnf(c_0_5655,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_3968,
[final] ).
cnf(c_0_5656,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_3969,
[final] ).
cnf(c_0_5657,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
c_0_3970,
[final] ).
cnf(c_0_5658,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
c_0_3971,
[final] ).
cnf(c_0_5659,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_3972,
[final] ).
cnf(c_0_5660,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_3973,
[final] ).
cnf(c_0_5661,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(esk52_2(X2,X1)))),hAPP(X2,esk52_2(X2,X1)))) ),
c_0_3974,
[final] ).
cnf(c_0_5662,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk66_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_3975,
[final] ).
cnf(c_0_5663,plain,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_3976,
[final] ).
cnf(c_0_5664,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_3977,
[final] ).
cnf(c_0_5665,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_3978,
[final] ).
cnf(c_0_5666,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_3979,
[final] ).
cnf(c_0_5667,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_3980,
[final] ).
cnf(c_0_5668,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_3981,
[final] ).
cnf(c_0_5669,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_3982,
[final] ).
cnf(c_0_5670,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_3983,
[final] ).
cnf(c_0_5671,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(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),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X1,X2)),c_Complex_Ocomplex_OComplex(X3,X4)),
c_0_3984,
[final] ).
cnf(c_0_5672,plain,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X3,X2,X1))),esk73_3(X3,X2,X1)) = X3
| ~ hBOOL(hAPP(X1,esk74_3(X3,X2,X1))) ),
c_0_3985,
[final] ).
cnf(c_0_5673,plain,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk74_3(X3,X2,X1))),esk75_3(X3,X2,X1)) = X3
| ~ hBOOL(hAPP(X1,esk72_3(X3,X2,X1))) ),
c_0_3986,
[final] ).
cnf(c_0_5674,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_3987,
[final] ).
cnf(c_0_5675,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_3988,
[final] ).
cnf(c_0_5676,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
c_0_3989,
[final] ).
cnf(c_0_5677,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(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_3990,
[final] ).
cnf(c_0_5678,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(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_3991,
[final] ).
cnf(c_0_5679,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(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_3992,
[final] ).
cnf(c_0_5680,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(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_3993,
[final] ).
cnf(c_0_5681,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(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_3994,
[final] ).
cnf(c_0_5682,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
c_0_3995,
[final] ).
cnf(c_0_5683,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
c_0_3996,
[final] ).
cnf(c_0_5684,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
c_0_3997,
[final] ).
cnf(c_0_5685,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
c_0_3998,
[final] ).
cnf(c_0_5686,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
c_0_3999,
[final] ).
cnf(c_0_5687,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
c_0_4000,
[final] ).
cnf(c_0_5688,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
c_0_4001,
[final] ).
cnf(c_0_5689,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
c_0_4002,
[final] ).
cnf(c_0_5690,plain,
( X2 = X3
| X4 = X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)) ),
c_0_4003,
[final] ).
cnf(c_0_5691,plain,
( X3 = X5
| X2 = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
c_0_4004,
[final] ).
cnf(c_0_5692,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4005,
[final] ).
cnf(c_0_5693,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4006,
[final] ).
cnf(c_0_5694,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4007,
[final] ).
cnf(c_0_5695,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X3,X2,X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk74_3(X3,X2,X1))),esk75_3(X3,X2,X1)) = X3 ),
c_0_4008,
[final] ).
cnf(c_0_5696,plain,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X3,X2,X1))),esk73_3(X3,X2,X1)) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),esk75_3(X3,X2,X1))) ),
c_0_4009,
[final] ).
cnf(c_0_5697,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4010,
[final] ).
cnf(c_0_5698,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
c_0_4011,
[final] ).
cnf(c_0_5699,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4012,
[final] ).
cnf(c_0_5700,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk51_2(X2,X1))),hAPP(X2,c_Nat_OSuc(esk51_2(X2,X1))))) ),
c_0_4013,
[final] ).
cnf(c_0_5701,plain,
( c_SEQ_OBseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),esk20_4(X4,X2,X3,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_4014,
[final] ).
cnf(c_0_5702,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X3,X2,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4015,
[final] ).
cnf(c_0_5703,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
c_0_4016,
[final] ).
cnf(c_0_5704,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
c_0_4017,
[final] ).
cnf(c_0_5705,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4018,
[final] ).
cnf(c_0_5706,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(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_4019,
[final] ).
cnf(c_0_5707,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_4020,
[final] ).
cnf(c_0_5708,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),esk69_3(X3,X2,X1))),esk70_3(X3,X2,X1)) = X2
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
c_0_4021,
[final] ).
cnf(c_0_5709,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_4022,
[final] ).
cnf(c_0_5710,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(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_4023,
[final] ).
cnf(c_0_5711,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
c_0_4024,
[final] ).
cnf(c_0_5712,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
c_0_4025,
[final] ).
cnf(c_0_5713,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)),X2)) ),
c_0_4026,
[final] ).
cnf(c_0_5714,plain,
( c_RComplete_Onatceiling(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
c_0_4027,
[final] ).
cnf(c_0_5715,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_4028,
[final] ).
cnf(c_0_5716,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),esk69_3(X3,X2,X1))),esk70_3(X3,X2,X1)) = X2 ),
c_0_4029,
[final] ).
cnf(c_0_5717,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4030,
[final] ).
cnf(c_0_5718,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))) ),
c_0_4031,
[final] ).
cnf(c_0_5719,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4032,
[final] ).
cnf(c_0_5720,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
c_0_4033,
[final] ).
cnf(c_0_5721,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__comm__semiring__strict(X1) ),
c_0_4034,
[final] ).
cnf(c_0_5722,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4035,
[final] ).
cnf(c_0_5723,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4036,
[final] ).
cnf(c_0_5724,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
c_0_4037,
[final] ).
cnf(c_0_5725,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
c_0_4038,
[final] ).
cnf(c_0_5726,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
c_0_4039,
[final] ).
cnf(c_0_5727,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Oordered__comm__semiring(X1) ),
c_0_4040,
[final] ).
cnf(c_0_5728,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
c_0_4041,
[final] ).
cnf(c_0_5729,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
c_0_4042,
[final] ).
cnf(c_0_5730,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_4043,
[final] ).
cnf(c_0_5731,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_4044,
[final] ).
cnf(c_0_5732,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4045,
[final] ).
cnf(c_0_5733,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
c_0_4046,
[final] ).
cnf(c_0_5734,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk47_2(X2,X1))),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
c_0_4047,
[final] ).
cnf(c_0_5735,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4048,
[final] ).
cnf(c_0_5736,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4049,
[final] ).
cnf(c_0_5737,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4)) ),
c_0_4050,
[final] ).
cnf(c_0_5738,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4051,
[final] ).
cnf(c_0_5739,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) ),
c_0_4052,
[final] ).
cnf(c_0_5740,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_4053,
[final] ).
cnf(c_0_5741,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4054,
[final] ).
cnf(c_0_5742,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4055,
[final] ).
cnf(c_0_5743,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3)) ),
c_0_4056,
[final] ).
cnf(c_0_5744,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
c_0_4057,
[final] ).
cnf(c_0_5745,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
c_0_4058,
[final] ).
cnf(c_0_5746,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3)) ),
c_0_4059,
[final] ).
cnf(c_0_5747,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4060,
[final] ).
cnf(c_0_5748,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4061,
[final] ).
cnf(c_0_5749,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Rings_Oordered__ring(X1) ),
c_0_4062,
[final] ).
cnf(c_0_5750,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
| ~ class_Rings_Oordered__ring(X1) ),
c_0_4063,
[final] ).
cnf(c_0_5751,plain,
( c_RComplete_Onatfloor(X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
c_0_4064,
[final] ).
cnf(c_0_5752,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
c_0_4065,
[final] ).
cnf(c_0_5753,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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_4066,
[final] ).
cnf(c_0_5754,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
c_0_4067,
[final] ).
cnf(c_0_5755,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
c_0_4068,
[final] ).
cnf(c_0_5756,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
c_0_4069,
[final] ).
cnf(c_0_5757,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
c_0_4070,
[final] ).
cnf(c_0_5758,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
c_0_4071,
[final] ).
cnf(c_0_5759,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X3)) ),
c_0_4072,
[final] ).
cnf(c_0_5760,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,esk72_3(X3,X2,X1))) ),
c_0_4073,
[final] ).
cnf(c_0_5761,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X1)) ),
c_0_4074,
[final] ).
cnf(c_0_5762,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X3,X2,X1)),X2))
| ~ hBOOL(hAPP(X1,esk74_3(X3,X2,X1))) ),
c_0_4075,
[final] ).
cnf(c_0_5763,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
c_0_4076,
[final] ).
cnf(c_0_5764,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2)) ),
c_0_4077,
[final] ).
cnf(c_0_5765,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
c_0_4078,
[final] ).
cnf(c_0_5766,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_4079,
[final] ).
cnf(c_0_5767,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
c_0_4080,
[final] ).
cnf(c_0_5768,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4081,
[final] ).
cnf(c_0_5769,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4082,
[final] ).
cnf(c_0_5770,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk74_3(X3,X2,X1))),esk75_3(X3,X2,X1)) = X3 ),
c_0_4083,
[final] ).
cnf(c_0_5771,plain,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X3,X2,X1))),esk73_3(X3,X2,X1)) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4084,
[final] ).
cnf(c_0_5772,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
c_0_4085,
[final] ).
cnf(c_0_5773,plain,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4086,
[final] ).
cnf(c_0_5774,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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_4087,
[final] ).
cnf(c_0_5775,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
c_0_4088,
[final] ).
cnf(c_0_5776,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4089,
[final] ).
cnf(c_0_5777,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4090,
[final] ).
cnf(c_0_5778,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4091,
[final] ).
cnf(c_0_5779,plain,
( hBOOL(hAPP(X1,X4))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5),X3)) ),
c_0_4092,
[final] ).
cnf(c_0_5780,plain,
( c_SEQ_Oincseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk15_2(X2,X1))),hAPP(X2,esk16_2(X2,X1)))) ),
c_0_4093,
[final] ).
cnf(c_0_5781,plain,
( c_SEQ_Odecseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk12_2(X2,X1))),hAPP(X2,esk11_2(X2,X1)))) ),
c_0_4094,
[final] ).
cnf(c_0_5782,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk5_2(X2,X1))),hAPP(X2,esk6_2(X2,X1)))) ),
c_0_4095,
[final] ).
cnf(c_0_5783,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk8_2(X2,X1))),hAPP(X2,esk7_2(X2,X1)))) ),
c_0_4096,
[final] ).
cnf(c_0_5784,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
c_0_4097,
[final] ).
cnf(c_0_5785,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
c_0_4098,
[final] ).
cnf(c_0_5786,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))) ),
c_0_4099,
[final] ).
cnf(c_0_5787,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4100,
[final] ).
cnf(c_0_5788,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
c_0_4101,
[final] ).
cnf(c_0_5789,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3)) ),
c_0_4102,
[final] ).
cnf(c_0_5790,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
c_0_4103,
[final] ).
cnf(c_0_5791,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
c_0_4104,
[final] ).
cnf(c_0_5792,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
c_0_4105,
[final] ).
cnf(c_0_5793,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4106,
[final] ).
cnf(c_0_5794,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3)) ),
c_0_4107,
[final] ).
cnf(c_0_5795,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
c_0_4108,
[final] ).
cnf(c_0_5796,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
c_0_4109,
[final] ).
cnf(c_0_5797,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
c_0_4110,
[final] ).
cnf(c_0_5798,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4111,
[final] ).
cnf(c_0_5799,plain,
( hBOOL(hAPP(X1,X4))
| ~ epred1_3(X1,X2,X3)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
c_0_4112,
[final] ).
cnf(c_0_5800,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_4113,
[final] ).
cnf(c_0_5801,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4114,
[final] ).
cnf(c_0_5802,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4115,
[final] ).
cnf(c_0_5803,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(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_4116,
[final] ).
cnf(c_0_5804,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(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_4117,
[final] ).
cnf(c_0_5805,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X3)) ),
c_0_4118,
[final] ).
cnf(c_0_5806,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
c_0_4119,
[final] ).
cnf(c_0_5807,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
c_0_4120,
[final] ).
cnf(c_0_5808,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
c_0_4121,
[final] ).
cnf(c_0_5809,plain,
( hBOOL(hAPP(X1,X4))
| ~ epred1_3(X1,X2,X3)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4122,
[final] ).
cnf(c_0_5810,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X3,X2,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),esk75_3(X3,X2,X1))) ),
c_0_4123,
[final] ).
cnf(c_0_5811,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
c_0_4124,
[final] ).
cnf(c_0_5812,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
c_0_4125,
[final] ).
cnf(c_0_5813,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
c_0_4126,
[final] ).
cnf(c_0_5814,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4)) ),
c_0_4127,
[final] ).
cnf(c_0_5815,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
c_0_4128,
[final] ).
cnf(c_0_5816,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
c_0_4129,
[final] ).
cnf(c_0_5817,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
c_0_4130,
[final] ).
cnf(c_0_5818,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4)) ),
c_0_4131,
[final] ).
cnf(c_0_5819,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_OIm,X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_ORe,X2))) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),
c_0_4132,
[final] ).
cnf(c_0_5820,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4133,
[final] ).
cnf(c_0_5821,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4134,
[final] ).
cnf(c_0_5822,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4135,
[final] ).
cnf(c_0_5823,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
c_0_4136,
[final] ).
cnf(c_0_5824,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4137,
[final] ).
cnf(c_0_5825,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
c_0_4138,
[final] ).
cnf(c_0_5826,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
c_0_4139,
[final] ).
cnf(c_0_5827,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
c_0_4140,
[final] ).
cnf(c_0_5828,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
c_0_4141,
[final] ).
cnf(c_0_5829,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4142,
[final] ).
cnf(c_0_5830,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
c_0_4143,
[final] ).
cnf(c_0_5831,plain,
( epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,esk72_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,esk74_3(X3,X2,X1))) ),
c_0_4144,
[final] ).
cnf(c_0_5832,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
c_0_4145,
[final] ).
cnf(c_0_5833,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
c_0_4146,
[final] ).
cnf(c_0_5834,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
c_0_4147,
[final] ).
cnf(c_0_5835,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
c_0_4148,
[final] ).
cnf(c_0_5836,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4149,
[final] ).
cnf(c_0_5837,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4150,
[final] ).
cnf(c_0_5838,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4151,
[final] ).
cnf(c_0_5839,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5840,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_4153,
[final] ).
cnf(c_0_5841,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)) ),
c_0_4154,
[final] ).
cnf(c_0_5842,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk70_3(X3,X2,X1)),X3))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
c_0_4155,
[final] ).
cnf(c_0_5843,plain,
( ~ hBOOL(hAPP(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_4156,
[final] ).
cnf(c_0_5844,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_4157,
[final] ).
cnf(c_0_5845,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_4158,
[final] ).
cnf(c_0_5846,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) ),
c_0_4159,
[final] ).
cnf(c_0_5847,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4160,
[final] ).
cnf(c_0_5848,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
c_0_4161,
[final] ).
cnf(c_0_5849,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4162,
[final] ).
cnf(c_0_5850,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4163,
[final] ).
cnf(c_0_5851,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4164,
[final] ).
cnf(c_0_5852,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
c_0_4165,
[final] ).
cnf(c_0_5853,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4166,
[final] ).
cnf(c_0_5854,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
c_0_4167,
[final] ).
cnf(c_0_5855,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
c_0_4168,
[final] ).
cnf(c_0_5856,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
c_0_4169,
[final] ).
cnf(c_0_5857,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
c_0_4170,
[final] ).
cnf(c_0_5858,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
c_0_4171,
[final] ).
cnf(c_0_5859,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
c_0_4172,
[final] ).
cnf(c_0_5860,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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
c_0_4173,
[final] ).
cnf(c_0_5861,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
c_0_4174,
[final] ).
cnf(c_0_5862,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X5)),hAPP(X2,X6)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X6))
| ~ c_SEQ_Omonoseq(X1,X2) ),
c_0_4175,
[final] ).
cnf(c_0_5863,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk70_3(X3,X2,X1)),X3)) ),
c_0_4176,
[final] ).
cnf(c_0_5864,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,esk74_3(X3,X2,X1))) ),
c_0_4177,
[final] ).
cnf(c_0_5865,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3)) ),
c_0_4178,
[final] ).
cnf(c_0_5866,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X3)) ),
c_0_4179,
[final] ).
cnf(c_0_5867,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
c_0_4180,
[final] ).
cnf(c_0_5868,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
c_0_4181,
[final] ).
cnf(c_0_5869,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
c_0_4182,
[final] ).
cnf(c_0_5870,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
c_0_4183,
[final] ).
cnf(c_0_5871,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
c_0_4184,
[final] ).
cnf(c_0_5872,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
c_0_4185,
[final] ).
cnf(c_0_5873,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
c_0_4186,
[final] ).
cnf(c_0_5874,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
c_0_4187,
[final] ).
cnf(c_0_5875,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
c_0_4188,
[final] ).
cnf(c_0_5876,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 != X4 ),
c_0_4189,
[final] ).
cnf(c_0_5877,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X5 ),
c_0_4190,
[final] ).
cnf(c_0_5878,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 != X4 ),
c_0_4191,
[final] ).
cnf(c_0_5879,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X5 ),
c_0_4192,
[final] ).
cnf(c_0_5880,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),esk75_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,esk72_3(X3,X2,X1))) ),
c_0_4193,
[final] ).
cnf(c_0_5881,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_4194,
[final] ).
cnf(c_0_5882,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_4195,
[final] ).
cnf(c_0_5883,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4196,
[final] ).
cnf(c_0_5884,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2)),X1))) ),
c_0_4197,
[final] ).
cnf(c_0_5885,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk33_0))),
c_0_4198,
[final] ).
cnf(c_0_5886,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk32_0))),
c_0_4199,
[final] ).
cnf(c_0_5887,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk28_0))),
c_0_4200,
[final] ).
cnf(c_0_5888,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk27_0))),
c_0_4201,
[final] ).
cnf(c_0_5889,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk26_0))),
c_0_4202,
[final] ).
cnf(c_0_5890,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk25_0))),
c_0_4203,
[final] ).
cnf(c_0_5891,plain,
( hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
c_0_4204,
[final] ).
cnf(c_0_5892,plain,
( hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4205,
[final] ).
cnf(c_0_5893,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ),
c_0_4206,
[final] ).
cnf(c_0_5894,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
c_0_4207,
[final] ).
cnf(c_0_5895,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(X1,esk65_3(X3,X2,X1))) ),
c_0_4208,
[final] ).
cnf(c_0_5896,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(X1,esk64_3(X3,X2,X1))) ),
c_0_4209,
[final] ).
cnf(c_0_5897,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_4210,
[final] ).
cnf(c_0_5898,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_4211,
[final] ).
cnf(c_0_5899,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_4212,
[final] ).
cnf(c_0_5900,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_4213,
[final] ).
cnf(c_0_5901,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk56_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
c_0_4214,
[final] ).
cnf(c_0_5902,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk54_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
c_0_4215,
[final] ).
cnf(c_0_5903,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
c_0_4216,
[final] ).
cnf(c_0_5904,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(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,X2,X1))) ),
c_0_4217,
[final] ).
cnf(c_0_5905,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))) ),
c_0_4218,
[final] ).
cnf(c_0_5906,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
c_0_4219,
[final] ).
cnf(c_0_5907,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
c_0_4220,
[final] ).
cnf(c_0_5908,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))) ),
c_0_4221,
[final] ).
cnf(c_0_5909,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))) ),
c_0_4222,
[final] ).
cnf(c_0_5910,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,esk69_3(X3,X2,X1))) ),
c_0_4223,
[final] ).
cnf(c_0_5911,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,esk65_3(X3,X2,X1))) ),
c_0_4224,
[final] ).
cnf(c_0_5912,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,esk64_3(X3,X2,X1))) ),
c_0_4225,
[final] ).
cnf(c_0_5913,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4226,
[final] ).
cnf(c_0_5914,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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,X2,X1))) ),
c_0_4227,
[final] ).
cnf(c_0_5915,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4)) ),
c_0_4228,
[final] ).
cnf(c_0_5916,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4229,
[final] ).
cnf(c_0_5917,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X2)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2))) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))),X2)),
c_0_4230,
[final] ).
cnf(c_0_5918,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1) ),
c_0_4231,
[final] ).
cnf(c_0_5919,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4232,
[final] ).
cnf(c_0_5920,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4233,
[final] ).
cnf(c_0_5921,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4234,
[final] ).
cnf(c_0_5922,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
c_0_4235,
[final] ).
cnf(c_0_5923,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
c_0_4236,
[final] ).
cnf(c_0_5924,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,esk71_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
c_0_4237,
[final] ).
cnf(c_0_5925,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4238,
[final] ).
cnf(c_0_5926,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
c_0_4239,
[final] ).
cnf(c_0_5927,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
c_0_4240,
[final] ).
cnf(c_0_5928,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
c_0_4241,
[final] ).
cnf(c_0_5929,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
c_0_4242,
[final] ).
cnf(c_0_5930,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4243,
[final] ).
cnf(c_0_5931,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4244,
[final] ).
cnf(c_0_5932,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4245,
[final] ).
cnf(c_0_5933,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4246,
[final] ).
cnf(c_0_5934,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4247,
[final] ).
cnf(c_0_5935,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ),
c_0_4248,
[final] ).
cnf(c_0_5936,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ),
c_0_4249,
[final] ).
cnf(c_0_5937,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X2))
| ~ hBOOL(hAPP(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_4250,
[final] ).
cnf(c_0_5938,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Fields_Ofield(X1) ),
c_0_4251,
[final] ).
cnf(c_0_5939,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),esk75_3(X3,X2,X1))) ),
c_0_4252,
[final] ).
cnf(c_0_5940,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
c_0_4253,
[final] ).
cnf(c_0_5941,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,esk73_3(X3,X2,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4254,
[final] ).
cnf(c_0_5942,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Ominus__class_Ominus(X1,X3,X5))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_4255,
[final] ).
cnf(c_0_5943,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
c_0_4256,
[final] ).
cnf(c_0_5944,plain,
( c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
c_0_4257,
[final] ).
cnf(c_0_5945,plain,
( hAPP(hAPP(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_4258,
[final] ).
cnf(c_0_5946,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,esk69_3(X3,X2,X1))) ),
c_0_4259,
[final] ).
cnf(c_0_5947,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4260,
[final] ).
cnf(c_0_5948,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_4261,
[final] ).
cnf(c_0_5949,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_RealVector_Oreal__normed__field(X1) ),
c_0_4262,
[final] ).
cnf(c_0_5950,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
c_0_4263,
[final] ).
cnf(c_0_5951,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_4264,
[final] ).
cnf(c_0_5952,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring(X1) ),
c_0_4265,
[final] ).
cnf(c_0_5953,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4266,
[final] ).
cnf(c_0_5954,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4267,
[final] ).
cnf(c_0_5955,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4268,
[final] ).
cnf(c_0_5956,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4269,
[final] ).
cnf(c_0_5957,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_4270,
[final] ).
cnf(c_0_5958,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,esk71_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
c_0_4271,
[final] ).
cnf(c_0_5959,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
c_0_4272,
[final] ).
cnf(c_0_5960,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
c_0_4273,
[final] ).
cnf(c_0_5961,plain,
hBOOL(hAPP(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_4274,
[final] ).
cnf(c_0_5962,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
c_0_4275,
[final] ).
cnf(c_0_5963,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4276,
[final] ).
cnf(c_0_5964,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__ring(X1) ),
c_0_4277,
[final] ).
cnf(c_0_5965,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4278,
[final] ).
cnf(c_0_5966,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
c_0_4279,
[final] ).
cnf(c_0_5967,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2))) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),
c_0_4280,
[final] ).
cnf(c_0_5968,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(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_4281,
[final] ).
cnf(c_0_5969,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(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_4282,
[final] ).
cnf(c_0_5970,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))) ),
c_0_4283,
[final] ).
cnf(c_0_5971,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))) ),
c_0_4284,
[final] ).
cnf(c_0_5972,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))) ),
c_0_4285,
[final] ).
cnf(c_0_5973,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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
c_0_4286,
[final] ).
cnf(c_0_5974,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
c_0_4287,
[final] ).
cnf(c_0_5975,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
c_0_4288,
[final] ).
cnf(c_0_5976,plain,
( ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3)) ),
c_0_4289,
[final] ).
cnf(c_0_5977,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4290,
[final] ).
cnf(c_0_5978,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4291,
[final] ).
cnf(c_0_5979,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4292,
[final] ).
cnf(c_0_5980,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4293,
[final] ).
cnf(c_0_5981,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
c_0_4294,
[final] ).
cnf(c_0_5982,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
c_0_4295,
[final] ).
cnf(c_0_5983,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)))),
c_0_4296,
[final] ).
cnf(c_0_5984,plain,
( c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4297,
[final] ).
cnf(c_0_5985,plain,
( c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
c_0_4298,
[final] ).
cnf(c_0_5986,plain,
( c_Nat_OSuc(hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4299,
[final] ).
cnf(c_0_5987,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4300,
[final] ).
cnf(c_0_5988,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4301,
[final] ).
cnf(c_0_5989,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
c_0_4302,
[final] ).
cnf(c_0_5990,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
c_0_4303,
[final] ).
cnf(c_0_5991,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(X3))),hAPP(X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4)),hAPP(X2,c_Nat_OSuc(X4))))
| ~ class_Orderings_Oorder(X1)
| ~ c_SEQ_Omonoseq(X1,X2) ),
c_0_4304,
[final] ).
cnf(c_0_5992,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
c_0_4305,
[final] ).
cnf(c_0_5993,plain,
( hBOOL(hAPP(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,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
c_0_4306,
[final] ).
cnf(c_0_5994,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4307,
[final] ).
cnf(c_0_5995,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(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_4308,
[final] ).
cnf(c_0_5996,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4309,
[final] ).
cnf(c_0_5997,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
c_0_4310,
[final] ).
cnf(c_0_5998,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
c_0_4311,
[final] ).
cnf(c_0_5999,plain,
( c_SEQ_Osubseq(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,esk53_1(X1))),hAPP(X1,c_Nat_OSuc(esk53_1(X1))))) ),
c_0_4312,
[final] ).
cnf(c_0_6000,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
c_0_4313,
[final] ).
cnf(c_0_6001,plain,
( hBOOL(hAPP(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,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4314,
[final] ).
cnf(c_0_6002,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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4315,
[final] ).
cnf(c_0_6003,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4316,
[final] ).
cnf(c_0_6004,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
c_0_4317,
[final] ).
cnf(c_0_6005,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4318,
[final] ).
cnf(c_0_6006,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4319,
[final] ).
cnf(c_0_6007,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4320,
[final] ).
cnf(c_0_6008,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4321,
[final] ).
cnf(c_0_6009,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4322,
[final] ).
cnf(c_0_6010,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4323,
[final] ).
cnf(c_0_6011,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3),
c_0_4324,
[final] ).
cnf(c_0_6012,plain,
hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),X3),
c_0_4325,
[final] ).
cnf(c_0_6013,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3),
c_0_4326,
[final] ).
cnf(c_0_6014,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk68_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3)) ),
c_0_4327,
[final] ).
cnf(c_0_6015,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(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_4328,
[final] ).
cnf(c_0_6016,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_4329,
[final] ).
cnf(c_0_6017,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4)) ),
c_0_4330,
[final] ).
cnf(c_0_6018,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| ~ class_Orderings_Oord(X1) ),
c_0_4331,
[final] ).
cnf(c_0_6019,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| ~ class_Orderings_Oord(X1) ),
c_0_4332,
[final] ).
cnf(c_0_6020,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4333,
[final] ).
cnf(c_0_6021,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
c_0_4334,
[final] ).
cnf(c_0_6022,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4335,
[final] ).
cnf(c_0_6023,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
c_0_4336,
[final] ).
cnf(c_0_6024,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X2)),c_Transcendental_Ocos(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X2)),c_Transcendental_Osin(X1))) = c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
c_0_4337,
[final] ).
cnf(c_0_6025,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Ocos(X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Osin(X2))) = c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
c_0_4338,
[final] ).
cnf(c_0_6026,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),c_Divides_Odiv__class_Odiv(X1,X2,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_4339,
[final] ).
cnf(c_0_6027,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Divides_Odiv__class_Odiv(X1,X2,X4))
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_4340,
[final] ).
cnf(c_0_6028,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_4341,
[final] ).
cnf(c_0_6029,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ class_RealVector_Oreal__normed__field(X1) ),
c_0_4342,
[final] ).
cnf(c_0_6030,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_4343,
[final] ).
cnf(c_0_6031,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_4344,
[final] ).
cnf(c_0_6032,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
c_0_4345,
[final] ).
cnf(c_0_6033,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
c_0_4346,
[final] ).
cnf(c_0_6034,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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
c_0_4347,
[final] ).
cnf(c_0_6035,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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
c_0_4348,
[final] ).
cnf(c_0_6036,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3)),X2))
| ~ hBOOL(hAPP(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_4349,
[final] ).
cnf(c_0_6037,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
c_0_4350,
[final] ).
cnf(c_0_6038,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(X1,esk74_3(X3,X2,X1))) ),
c_0_4351,
[final] ).
cnf(c_0_6039,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4352,
[final] ).
cnf(c_0_6040,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,esk72_3(X3,X2,X1))) ),
c_0_4353,
[final] ).
cnf(c_0_6041,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4354,
[final] ).
cnf(c_0_6042,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4355,
[final] ).
cnf(c_0_6043,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4356,
[final] ).
cnf(c_0_6044,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_4357,
[final] ).
cnf(c_0_6045,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4358,
[final] ).
cnf(c_0_6046,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Ocos(X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Osin(X2))) = c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),
c_0_4359,
[final] ).
cnf(c_0_6047,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X1)) ),
c_0_4360,
[final] ).
cnf(c_0_6048,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4361,
[final] ).
cnf(c_0_6049,plain,
c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2),
c_0_4362,
[final] ).
cnf(c_0_6050,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk21_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_4363,
[final] ).
cnf(c_0_6051,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_4364,
[final] ).
cnf(c_0_6052,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(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_4365,
[final] ).
cnf(c_0_6053,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(X1,esk22_1(X1))),hAPP(X1,esk23_1(X1)))) ),
c_0_4366,
[final] ).
cnf(c_0_6054,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
c_0_4367,
[final] ).
cnf(c_0_6055,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
c_0_4368,
[final] ).
cnf(c_0_6056,plain,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4369,
[final] ).
cnf(c_0_6057,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_4370,
[final] ).
cnf(c_0_6058,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(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_4371,
[final] ).
cnf(c_0_6059,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_4372,
[final] ).
cnf(c_0_6060,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4373,
[final] ).
cnf(c_0_6061,plain,
( X3 = esk34_2(X2,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
c_0_4374,
[final] ).
cnf(c_0_6062,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1) ),
c_0_4375,
[final] ).
cnf(c_0_6063,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(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_4376,
[final] ).
cnf(c_0_6064,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(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_4377,
[final] ).
cnf(c_0_6065,plain,
( X4 = X6
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(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_4378,
[final] ).
cnf(c_0_6066,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),c_Nat_OSuc(X1))),
c_0_4379,
[final] ).
cnf(c_0_6067,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ),
c_0_4380,
[final] ).
cnf(c_0_6068,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
c_0_4381,
[final] ).
cnf(c_0_6069,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
c_0_4382,
[final] ).
cnf(c_0_6070,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),X1)),
c_0_4383,
[final] ).
cnf(c_0_6071,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X1)),
c_0_4384,
[final] ).
cnf(c_0_6072,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
c_0_4385,
[final] ).
cnf(c_0_6073,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_4386,
[final] ).
cnf(c_0_6074,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_4387,
[final] ).
cnf(c_0_6075,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4388,
[final] ).
cnf(c_0_6076,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4389,
[final] ).
cnf(c_0_6077,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4390,
[final] ).
cnf(c_0_6078,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
c_0_4391,
[final] ).
cnf(c_0_6079,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
c_0_4392,
[final] ).
cnf(c_0_6080,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4)) ),
c_0_4393,
[final] ).
cnf(c_0_6081,plain,
( c_SEQ_Osubseq(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,esk3_1(X1))),hAPP(X1,esk4_1(X1)))) ),
c_0_4394,
[final] ).
cnf(c_0_6082,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
c_0_4395,
[final] ).
cnf(c_0_6083,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4) ),
c_0_4396,
[final] ).
cnf(c_0_6084,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4) ),
c_0_4397,
[final] ).
cnf(c_0_6085,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
c_0_4398,
[final] ).
cnf(c_0_6086,plain,
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
c_0_4399,
[final] ).
cnf(c_0_6087,plain,
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
c_0_4400,
[final] ).
cnf(c_0_6088,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_4401,
[final] ).
cnf(c_0_6089,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),esk18_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
c_0_4402,
[final] ).
cnf(c_0_6090,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),esk13_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
c_0_4403,
[final] ).
cnf(c_0_6091,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk65_3(X3,X2,X1)) = X2 ),
c_0_4404,
[final] ).
cnf(c_0_6092,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk64_3(X3,X2,X1)) = X2 ),
c_0_4405,
[final] ).
cnf(c_0_6093,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4406,
[final] ).
cnf(c_0_6094,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
c_0_4407,
[final] ).
cnf(c_0_6095,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),
c_0_4408,
[final] ).
cnf(c_0_6096,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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
c_0_4409,
[final] ).
cnf(c_0_6097,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
c_0_4410,
[final] ).
cnf(c_0_6098,plain,
hBOOL(hAPP(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2))),
c_0_4411,
[final] ).
cnf(c_0_6099,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk65_3(X3,X2,X1)) = X2
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
c_0_4412,
[final] ).
cnf(c_0_6100,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk64_3(X3,X2,X1)) = X2
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
c_0_4413,
[final] ).
cnf(c_0_6101,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))),
c_0_4414,
[final] ).
cnf(c_0_6102,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
c_0_4415,
[final] ).
cnf(c_0_6103,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_RComplete_Onatfloor(X1))) ),
c_0_4416,
[final] ).
cnf(c_0_6104,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4417,
[final] ).
cnf(c_0_6105,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Groups_Oone__class_Oone(X1))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_4418,
[final] ).
cnf(c_0_6106,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),c_Groups_Oone__class_Oone(X1))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_4419,
[final] ).
cnf(c_0_6107,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk73_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4420,
[final] ).
cnf(c_0_6108,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
c_0_4421,
[final] ).
cnf(c_0_6109,plain,
( c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4422,
[final] ).
cnf(c_0_6110,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_4423,
[final] ).
cnf(c_0_6111,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4424,
[final] ).
cnf(c_0_6112,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4425,
[final] ).
cnf(c_0_6113,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)) = c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4426,
[final] ).
cnf(c_0_6114,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),esk75_3(X3,X2,X1))) ),
c_0_4427,
[final] ).
cnf(c_0_6115,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4428,
[final] ).
cnf(c_0_6116,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4429,
[final] ).
cnf(c_0_6117,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
c_0_4430,
[final] ).
cnf(c_0_6118,plain,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))) ),
c_0_4431,
[final] ).
cnf(c_0_6119,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Ocos(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Osin(X1))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_4432,
[final] ).
cnf(c_0_6120,plain,
( ~ hBOOL(hAPP(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_6121,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_4434,
[final] ).
cnf(c_0_6122,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_4435,
[final] ).
cnf(c_0_6123,plain,
( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4436,
[final] ).
cnf(c_0_6124,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
c_0_4437,
[final] ).
cnf(c_0_6125,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2)) ),
c_0_4438,
[final] ).
cnf(c_0_6126,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4439,
[final] ).
cnf(c_0_6127,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk35_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
c_0_4440,
[final] ).
cnf(c_0_6128,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk34_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
c_0_4441,
[final] ).
cnf(c_0_6129,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Rings_Odivision__ring(X1) ),
c_0_4442,
[final] ).
cnf(c_0_6130,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_4443,
[final] ).
cnf(c_0_6131,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_4444,
[final] ).
cnf(c_0_6132,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_4445,
[final] ).
cnf(c_0_6133,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_4446,
[final] ).
cnf(c_0_6134,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4447,
[final] ).
cnf(c_0_6135,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4448,
[final] ).
cnf(c_0_6136,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
c_0_4449,
[final] ).
cnf(c_0_6137,plain,
( hBOOL(hAPP(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_4450,
[final] ).
cnf(c_0_6138,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_4451,
[final] ).
cnf(c_0_6139,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4452,
[final] ).
cnf(c_0_6140,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
c_0_4453,
[final] ).
cnf(c_0_6141,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_4454,
[final] ).
cnf(c_0_6142,plain,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
c_0_4455,
[final] ).
cnf(c_0_6143,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
c_0_4456,
[final] ).
cnf(c_0_6144,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Ocos(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Osin(X2))) = c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
c_0_4457,
[final] ).
cnf(c_0_6145,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X2)),c_Transcendental_Osin(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X2)),c_Transcendental_Ocos(X1))) = c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
c_0_4458,
[final] ).
cnf(c_0_6146,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4459,
[final] ).
cnf(c_0_6147,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
c_0_4460,
[final] ).
cnf(c_0_6148,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
c_0_4461,
[final] ).
cnf(c_0_6149,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
c_0_4462,
[final] ).
cnf(c_0_6150,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
c_0_4463,
[final] ).
cnf(c_0_6151,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_4464,
[final] ).
cnf(c_0_6152,plain,
( X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_4465,
[final] ).
cnf(c_0_6153,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4466,
[final] ).
cnf(c_0_6154,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4467,
[final] ).
cnf(c_0_6155,plain,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4468,
[final] ).
cnf(c_0_6156,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4469,
[final] ).
cnf(c_0_6157,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
c_0_4470,
[final] ).
cnf(c_0_6158,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_4471,
[final] ).
cnf(c_0_6159,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_4472,
[final] ).
cnf(c_0_6160,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_4473,
[final] ).
cnf(c_0_6161,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Ocos(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Osin(X2))) = c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),
c_0_4474,
[final] ).
cnf(c_0_6162,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_4475,
[final] ).
cnf(c_0_6163,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
c_0_4476,
[final] ).
cnf(c_0_6164,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
c_0_4477,
[final] ).
cnf(c_0_6165,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
c_0_4478,
[final] ).
cnf(c_0_6166,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4479,
[final] ).
cnf(c_0_6167,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4480,
[final] ).
cnf(c_0_6168,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
c_0_4481,
[final] ).
cnf(c_0_6169,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X5)) ),
c_0_4482,
[final] ).
cnf(c_0_6170,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
c_0_4483,
[final] ).
cnf(c_0_6171,plain,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X5)) ),
c_0_4484,
[final] ).
cnf(c_0_6172,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4485,
[final] ).
cnf(c_0_6173,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
c_0_4486,
[final] ).
cnf(c_0_6174,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
c_0_4487,
[final] ).
cnf(c_0_6175,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
c_0_4488,
[final] ).
cnf(c_0_6176,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ c_SEQ_Oincseq(X1,X2) ),
c_0_4489,
[final] ).
cnf(c_0_6177,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ c_SEQ_Odecseq(X1,X2) ),
c_0_4490,
[final] ).
cnf(c_0_6178,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4491,
[final] ).
cnf(c_0_6179,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
c_0_4492,
[final] ).
cnf(c_0_6180,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
c_0_4493,
[final] ).
cnf(c_0_6181,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
c_0_4494,
[final] ).
cnf(c_0_6182,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
c_0_4495,
[final] ).
cnf(c_0_6183,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)))),
c_0_4496,
[final] ).
cnf(c_0_6184,plain,
c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3)),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X1,X2)),X3),
c_0_4497,
[final] ).
cnf(c_0_6185,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_4498,
[final] ).
cnf(c_0_6186,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_4499,
[final] ).
cnf(c_0_6187,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_4500,
[final] ).
cnf(c_0_6188,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| ~ epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4501,
[final] ).
cnf(c_0_6189,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
c_0_4502,
[final] ).
cnf(c_0_6190,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
c_0_4503,
[final] ).
cnf(c_0_6191,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk35_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
c_0_4504,
[final] ).
cnf(c_0_6192,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk34_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
c_0_4505,
[final] ).
cnf(c_0_6193,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4506,
[final] ).
cnf(c_0_6194,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
c_0_4507,
[final] ).
cnf(c_0_6195,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
c_0_4508,
[final] ).
cnf(c_0_6196,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4509,
[final] ).
cnf(c_0_6197,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4510,
[final] ).
cnf(c_0_6198,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
c_0_4511,
[final] ).
cnf(c_0_6199,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
c_0_4512,
[final] ).
cnf(c_0_6200,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4513,
[final] ).
cnf(c_0_6201,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
c_0_4514,
[final] ).
cnf(c_0_6202,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4515,
[final] ).
cnf(c_0_6203,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X2) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4516,
[final] ).
cnf(c_0_6204,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
c_0_4517,
[final] ).
cnf(c_0_6205,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2))) ),
c_0_4518,
[final] ).
cnf(c_0_6206,plain,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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),X1)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X2),X1),
c_0_4519,
[final] ).
cnf(c_0_6207,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),
c_0_4520,
[final] ).
cnf(c_0_6208,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_4521,
[final] ).
cnf(c_0_6209,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_4522,
[final] ).
cnf(c_0_6210,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_4523,
[final] ).
cnf(c_0_6211,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_4524,
[final] ).
cnf(c_0_6212,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
c_0_4525,
[final] ).
cnf(c_0_6213,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ c_SEQ_Osubseq(X1) ),
c_0_4526,
[final] ).
cnf(c_0_6214,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,esk58_1(X1))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4527,
[final] ).
cnf(c_0_6215,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4528,
[final] ).
cnf(c_0_6216,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4529,
[final] ).
cnf(c_0_6217,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_RComplete_Onatfloor(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)) ),
c_0_4530,
[final] ).
cnf(c_0_6218,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| X2 != X3 ),
c_0_4531,
[final] ).
cnf(c_0_6219,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4532,
[final] ).
cnf(c_0_6220,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_4533,
[final] ).
cnf(c_0_6221,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4534,
[final] ).
cnf(c_0_6222,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_4535,
[final] ).
cnf(c_0_6223,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4536,
[final] ).
cnf(c_0_6224,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_4537,
[final] ).
cnf(c_0_6225,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4538,
[final] ).
cnf(c_0_6226,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_4539,
[final] ).
cnf(c_0_6227,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X1))),v_r)),
c_0_4540,
[final] ).
cnf(c_0_6228,plain,
( X3 = X2
| hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_4541,
[final] ).
cnf(c_0_6229,plain,
( X3 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(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_4542,
[final] ).
cnf(c_0_6230,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3)) ),
c_0_4543,
[final] ).
cnf(c_0_6231,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
c_0_4544,
[final] ).
cnf(c_0_6232,plain,
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X1)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4545,
[final] ).
cnf(c_0_6233,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4546,
[final] ).
cnf(c_0_6234,plain,
( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4547,
[final] ).
cnf(c_0_6235,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk58_1(X1)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4548,
[final] ).
cnf(c_0_6236,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),esk21_2(X2,X1))) ),
c_0_4549,
[final] ).
cnf(c_0_6237,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
c_0_4550,
[final] ).
cnf(c_0_6238,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4551,
[final] ).
cnf(c_0_6239,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4552,
[final] ).
cnf(c_0_6240,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_4553,
[final] ).
cnf(c_0_6241,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Transcendental_Oln(X1)) = c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4554,
[final] ).
cnf(c_0_6242,plain,
( hAPP(hAPP(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_4555,
[final] ).
cnf(c_0_6243,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ epred1_3(X1,X3,X2) ),
c_0_4556,
[final] ).
cnf(c_0_6244,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X3),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2),c_Complex_Ocomplex_OComplex(X3,X4)),
c_0_4557,
[final] ).
cnf(c_0_6245,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_4558,
[final] ).
cnf(c_0_6246,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_4559,
[final] ).
cnf(c_0_6247,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_4560,
[final] ).
cnf(c_0_6248,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
c_0_4561,
[final] ).
cnf(c_0_6249,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk48_2(X2,X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
c_0_4562,
[final] ).
cnf(c_0_6250,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_4563,
[final] ).
cnf(c_0_6251,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_4564,
[final] ).
cnf(c_0_6252,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_4565,
[final] ).
cnf(c_0_6253,plain,
( hBOOL(hAPP(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_4566,
[final] ).
cnf(c_0_6254,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))
| ~ class_Rings_Olinordered__semidom(X1) ),
c_0_4567,
[final] ).
cnf(c_0_6255,plain,
c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X1,X2)),c_Complex_Ocomplex_OComplex(X3,X4)),
c_0_4568,
[final] ).
cnf(c_0_6256,plain,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X1,X2)),c_Complex_Orcis(X3,X4)),
c_0_4569,
[final] ).
cnf(c_0_6257,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_4570,
[final] ).
cnf(c_0_6258,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4571,
[final] ).
cnf(c_0_6259,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X3)) ),
c_0_4572,
[final] ).
cnf(c_0_6260,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
c_0_4573,
[final] ).
cnf(c_0_6261,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3)) ),
c_0_4574,
[final] ).
cnf(c_0_6262,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
c_0_4575,
[final] ).
cnf(c_0_6263,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4576,
[final] ).
cnf(c_0_6264,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4577,
[final] ).
cnf(c_0_6265,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_4578,
[final] ).
cnf(c_0_6266,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4579,
[final] ).
cnf(c_0_6267,plain,
( c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4580,
[final] ).
cnf(c_0_6268,plain,
( c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4581,
[final] ).
cnf(c_0_6269,plain,
c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X2)),X1)),
c_0_4582,
[final] ).
cnf(c_0_6270,plain,
c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X2)),X1)),
c_0_4583,
[final] ).
cnf(c_0_6271,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4584,
[final] ).
cnf(c_0_6272,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4585,
[final] ).
cnf(c_0_6273,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(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_4586,
[final] ).
cnf(c_0_6274,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4587,
[final] ).
cnf(c_0_6275,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4588,
[final] ).
cnf(c_0_6276,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
c_0_4589,
[final] ).
cnf(c_0_6277,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4590,
[final] ).
cnf(c_0_6278,plain,
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4591,
[final] ).
cnf(c_0_6279,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X3),
c_0_4592,
[final] ).
cnf(c_0_6280,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
c_0_4593,
[final] ).
cnf(c_0_6281,plain,
( ~ hBOOL(hAPP(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_4594,
[final] ).
cnf(c_0_6282,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1))) ),
c_0_4595,
[final] ).
cnf(c_0_6283,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| c_Transcendental_Oln(X1) != c_Transcendental_Oln(X2) ),
c_0_4596,
[final] ).
cnf(c_0_6284,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
c_0_4597,
[final] ).
cnf(c_0_6285,plain,
( hBOOL(hAPP(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_4598,
[final] ).
cnf(c_0_6286,plain,
( X3 = X2
| hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_4599,
[final] ).
cnf(c_0_6287,plain,
( c_Transcendental_Oln(X1) = c_Transcendental_Oln(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| X1 != X2 ),
c_0_4600,
[final] ).
cnf(c_0_6288,plain,
( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4601,
[final] ).
cnf(c_0_6289,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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4602,
[final] ).
cnf(c_0_6290,plain,
( X2 = X3
| ~ hBOOL(hAPP(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_4603,
[final] ).
cnf(c_0_6291,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
c_0_4604,
[final] ).
cnf(c_0_6292,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
c_0_4605,
[final] ).
cnf(c_0_6293,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,esk66_1(X1))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4606,
[final] ).
cnf(c_0_6294,plain,
( c_Transcendental_Ocos(c_Transcendental_Oarccos(X1)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
c_0_4607,
[final] ).
cnf(c_0_6295,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4608,
[final] ).
cnf(c_0_6296,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X2) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
c_0_4609,
[final] ).
cnf(c_0_6297,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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| X3 != X4 ),
c_0_4610,
[final] ).
cnf(c_0_6298,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk60_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4611,
[final] ).
cnf(c_0_6299,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_4612,
[final] ).
cnf(c_0_6300,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2)),X1)) ),
c_0_4613,
[final] ).
cnf(c_0_6301,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4614,
[final] ).
cnf(c_0_6302,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
c_0_4615,
[final] ).
cnf(c_0_6303,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
c_0_4616,
[final] ).
cnf(c_0_6304,plain,
( hBOOL(hAPP(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_4617,
[final] ).
cnf(c_0_6305,plain,
( hBOOL(hAPP(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_4618,
[final] ).
cnf(c_0_6306,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4619,
[final] ).
cnf(c_0_6307,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4620,
[final] ).
cnf(c_0_6308,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
c_0_4621,
[final] ).
cnf(c_0_6309,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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4622,
[final] ).
cnf(c_0_6310,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hBOOL(hAPP(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_4623,
[final] ).
cnf(c_0_6311,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),
c_0_4624,
[final] ).
cnf(c_0_6312,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),
c_0_4625,
[final] ).
cnf(c_0_6313,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| X1 != X2 ),
c_0_4626,
[final] ).
cnf(c_0_6314,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4627,
[final] ).
cnf(c_0_6315,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
c_0_4628,
[final] ).
cnf(c_0_6316,plain,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
c_0_4629,
[final] ).
cnf(c_0_6317,plain,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
c_0_4630,
[final] ).
cnf(c_0_6318,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
c_0_4631,
[final] ).
cnf(c_0_6319,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| ~ class_Orderings_Oorder(X3) ),
c_0_4632,
[final] ).
cnf(c_0_6320,plain,
( c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk50_2(X1,X2))) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
c_0_4633,
[final] ).
cnf(c_0_6321,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
c_0_4634,
[final] ).
cnf(c_0_6322,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
c_0_4635,
[final] ).
cnf(c_0_6323,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
c_0_4636,
[final] ).
cnf(c_0_6324,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4637,
[final] ).
cnf(c_0_6325,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
c_0_4638,
[final] ).
cnf(c_0_6326,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4639,
[final] ).
cnf(c_0_6327,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4640,
[final] ).
cnf(c_0_6328,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4641,
[final] ).
cnf(c_0_6329,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_4642,
[final] ).
cnf(c_0_6330,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4643,
[final] ).
cnf(c_0_6331,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2))) ),
c_0_4644,
[final] ).
cnf(c_0_6332,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk21_2(X2,X1)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_4645,
[final] ).
cnf(c_0_6333,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,c_Nat_OSuc(X2))))
| ~ c_SEQ_Osubseq(X1) ),
c_0_4646,
[final] ).
cnf(c_0_6334,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
c_0_4647,
[final] ).
cnf(c_0_6335,plain,
( X2 = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
c_0_4648,
[final] ).
cnf(c_0_6336,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
c_0_4649,
[final] ).
cnf(c_0_6337,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
c_0_4650,
[final] ).
cnf(c_0_6338,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))),
c_0_4651,
[final] ).
cnf(c_0_6339,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
c_0_4652,
[final] ).
cnf(c_0_6340,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))),
c_0_4653,
[final] ).
cnf(c_0_6341,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
c_0_4654,
[final] ).
cnf(c_0_6342,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
c_0_4655,
[final] ).
cnf(c_0_6343,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4656,
[final] ).
cnf(c_0_6344,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4657,
[final] ).
cnf(c_0_6345,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
c_0_4658,
[final] ).
cnf(c_0_6346,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
c_0_4659,
[final] ).
cnf(c_0_6347,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
c_0_4660,
[final] ).
cnf(c_0_6348,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3)) = c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
c_0_4661,
[final] ).
cnf(c_0_6349,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3)) = c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4662,
[final] ).
cnf(c_0_6350,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4663,
[final] ).
cnf(c_0_6351,plain,
( c_SEQ_Oincseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk15_2(X2,X1)),esk16_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
c_0_4664,
[final] ).
cnf(c_0_6352,plain,
( c_SEQ_Odecseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk11_2(X2,X1)),esk12_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
c_0_4665,
[final] ).
cnf(c_0_6353,plain,
( c_SEQ_Omonoseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk5_2(X2,X1)),esk6_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
c_0_4666,
[final] ).
cnf(c_0_6354,plain,
( c_SEQ_Omonoseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk7_2(X2,X1)),esk8_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
c_0_4667,
[final] ).
cnf(c_0_6355,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(X1),X2),X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
c_0_4668,
[final] ).
cnf(c_0_6356,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3 ),
c_0_4669,
[final] ).
cnf(c_0_6357,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
c_0_4670,
[final] ).
cnf(c_0_6358,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
c_0_4671,
[final] ).
cnf(c_0_6359,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_4672,
[final] ).
cnf(c_0_6360,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_4673,
[final] ).
cnf(c_0_6361,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) ),
c_0_4674,
[final] ).
cnf(c_0_6362,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4675,
[final] ).
cnf(c_0_6363,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_4676,
[final] ).
cnf(c_0_6364,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
c_0_4677,
[final] ).
cnf(c_0_6365,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk60_2(X2,X1)),c_Nat_OSuc(X2)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4678,
[final] ).
cnf(c_0_6366,plain,
c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),X2),
c_0_4679,
[final] ).
cnf(c_0_6367,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
c_0_4680,
[final] ).
cnf(c_0_6368,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
c_0_4681,
[final] ).
cnf(c_0_6369,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4682,
[final] ).
cnf(c_0_6370,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
c_0_4683,
[final] ).
cnf(c_0_6371,plain,
( c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4684,
[final] ).
cnf(c_0_6372,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
c_0_4685,
[final] ).
cnf(c_0_6373,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
c_0_4686,
[final] ).
cnf(c_0_6374,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4687,
[final] ).
cnf(c_0_6375,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
c_0_4688,
[final] ).
cnf(c_0_6376,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
c_0_4689,
[final] ).
cnf(c_0_6377,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
c_0_4690,
[final] ).
cnf(c_0_6378,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(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_4691,
[final] ).
cnf(c_0_6379,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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 != X3 ),
c_0_4692,
[final] ).
cnf(c_0_6380,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
c_0_4693,
[final] ).
cnf(c_0_6381,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
c_0_4694,
[final] ).
cnf(c_0_6382,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
c_0_4695,
[final] ).
cnf(c_0_6383,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
c_0_4696,
[final] ).
cnf(c_0_6384,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
c_0_4697,
[final] ).
cnf(c_0_6385,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4698,
[final] ).
cnf(c_0_6386,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4699,
[final] ).
cnf(c_0_6387,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4700,
[final] ).
cnf(c_0_6388,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_RComplete_Onatceiling(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
c_0_4701,
[final] ).
cnf(c_0_6389,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
c_0_4702,
[final] ).
cnf(c_0_6390,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_4703,
[final] ).
cnf(c_0_6391,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4704,
[final] ).
cnf(c_0_6392,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)) ),
c_0_4705,
[final] ).
cnf(c_0_6393,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
c_0_4706,
[final] ).
cnf(c_0_6394,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
c_0_4707,
[final] ).
cnf(c_0_6395,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X2 != c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) ),
c_0_4708,
[final] ).
cnf(c_0_6396,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| c_Nat_OSuc(X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4709,
[final] ).
cnf(c_0_6397,plain,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
c_0_4710,
[final] ).
cnf(c_0_6398,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
c_0_4711,
[final] ).
cnf(c_0_6399,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
c_0_4712,
[final] ).
cnf(c_0_6400,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 != X2 ),
c_0_4713,
[final] ).
cnf(c_0_6401,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
c_0_4714,
[final] ).
cnf(c_0_6402,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
c_0_4715,
[final] ).
cnf(c_0_6403,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Oord(X1) ),
c_0_4716,
[final] ).
cnf(c_0_6404,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X4 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_4717,
[final] ).
cnf(c_0_6405,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 != X2 ),
c_0_4718,
[final] ).
cnf(c_0_6406,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
c_0_4719,
[final] ).
cnf(c_0_6407,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
c_0_4720,
[final] ).
cnf(c_0_6408,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Oord(X1) ),
c_0_4721,
[final] ).
cnf(c_0_6409,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X4 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_4722,
[final] ).
cnf(c_0_6410,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_4723,
[final] ).
cnf(c_0_6411,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_4724,
[final] ).
cnf(c_0_6412,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
c_0_4725,
[final] ).
cnf(c_0_6413,plain,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
c_0_4726,
[final] ).
cnf(c_0_6414,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
c_0_4727,
[final] ).
cnf(c_0_6415,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_4728,
[final] ).
cnf(c_0_6416,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_4729,
[final] ).
cnf(c_0_6417,plain,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
c_0_4730,
[final] ).
cnf(c_0_6418,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
c_0_4731,
[final] ).
cnf(c_0_6419,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_4732,
[final] ).
cnf(c_0_6420,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_4733,
[final] ).
cnf(c_0_6421,plain,
( X1 = c_Nat_OSuc(X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
c_0_4734,
[final] ).
cnf(c_0_6422,plain,
( X1 = c_Nat_OSuc(X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
c_0_4735,
[final] ).
cnf(c_0_6423,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4736,
[final] ).
cnf(c_0_6424,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4737,
[final] ).
cnf(c_0_6425,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4738,
[final] ).
cnf(c_0_6426,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_4739,
[final] ).
cnf(c_0_6427,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_4740,
[final] ).
cnf(c_0_6428,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_4741,
[final] ).
cnf(c_0_6429,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_4742,
[final] ).
cnf(c_0_6430,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_4743,
[final] ).
cnf(c_0_6431,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
c_0_4744,
[final] ).
cnf(c_0_6432,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
c_0_4745,
[final] ).
cnf(c_0_6433,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
c_0_4746,
[final] ).
cnf(c_0_6434,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4747,
[final] ).
cnf(c_0_6435,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
c_0_4748,
[final] ).
cnf(c_0_6436,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
c_0_4749,
[final] ).
cnf(c_0_6437,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
c_0_4750,
[final] ).
cnf(c_0_6438,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
c_0_4751,
[final] ).
cnf(c_0_6439,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
c_0_4752,
[final] ).
cnf(c_0_6440,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
c_0_4753,
[final] ).
cnf(c_0_6441,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2)),
c_0_4754,
[final] ).
cnf(c_0_6442,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2)),
c_0_4755,
[final] ).
cnf(c_0_6443,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| X1 != c_Nat_OSuc(X3) ),
c_0_4756,
[final] ).
cnf(c_0_6444,plain,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4757,
[final] ).
cnf(c_0_6445,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
c_0_4758,
[final] ).
cnf(c_0_6446,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1),hAPP(c_Complex_OIm,X2)) = hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),
c_0_4759,
[final] ).
cnf(c_0_6447,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1),hAPP(c_Complex_ORe,X2)) = hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),
c_0_4760,
[final] ).
cnf(c_0_6448,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4761,
[final] ).
cnf(c_0_6449,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
c_0_4762,
[final] ).
cnf(c_0_6450,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != X1 ),
c_0_4763,
[final] ).
cnf(c_0_6451,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4764,
[final] ).
cnf(c_0_6452,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4765,
[final] ).
cnf(c_0_6453,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4766,
[final] ).
cnf(c_0_6454,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4767,
[final] ).
cnf(c_0_6455,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4768,
[final] ).
cnf(c_0_6456,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4769,
[final] ).
cnf(c_0_6457,plain,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
c_0_4770,
[final] ).
cnf(c_0_6458,plain,
( hBOOL(hAPP(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_4771,
[final] ).
cnf(c_0_6459,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_4772,
[final] ).
cnf(c_0_6460,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
c_0_4773,
[final] ).
cnf(c_0_6461,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4774,
[final] ).
cnf(c_0_6462,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4775,
[final] ).
cnf(c_0_6463,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4776,
[final] ).
cnf(c_0_6464,plain,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
c_0_4777,
[final] ).
cnf(c_0_6465,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
c_0_4778,
[final] ).
cnf(c_0_6466,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
c_0_4779,
[final] ).
cnf(c_0_6467,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4780,
[final] ).
cnf(c_0_6468,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4781,
[final] ).
cnf(c_0_6469,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4782,
[final] ).
cnf(c_0_6470,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4783,
[final] ).
cnf(c_0_6471,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4784,
[final] ).
cnf(c_0_6472,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
c_0_4785,
[final] ).
cnf(c_0_6473,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
c_0_4786,
[final] ).
cnf(c_0_6474,plain,
hAPP(hAPP(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_4787,
[final] ).
cnf(c_0_6475,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2),
c_0_4788,
[final] ).
cnf(c_0_6476,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2),
c_0_4789,
[final] ).
cnf(c_0_6477,plain,
( ~ hBOOL(hAPP(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_4790,
[final] ).
cnf(c_0_6478,plain,
( ~ hBOOL(hAPP(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_4791,
[final] ).
cnf(c_0_6479,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
c_0_4792,
[final] ).
cnf(c_0_6480,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4793,
[final] ).
cnf(c_0_6481,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk17_2(X1,X2)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4794,
[final] ).
cnf(c_0_6482,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk10_2(X1,X2)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4795,
[final] ).
cnf(c_0_6483,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_4796,
[final] ).
cnf(c_0_6484,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_4797,
[final] ).
cnf(c_0_6485,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4798,
[final] ).
cnf(c_0_6486,plain,
hAPP(hAPP(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_4799,
[final] ).
cnf(c_0_6487,plain,
( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Nat__Transfer_Otsub(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
c_0_4800,
[final] ).
cnf(c_0_6488,plain,
( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Nat__Transfer_Otsub(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
c_0_4801,
[final] ).
cnf(c_0_6489,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_4802,
[final] ).
cnf(c_0_6490,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_4803,
[final] ).
cnf(c_0_6491,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_4804,
[final] ).
cnf(c_0_6492,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)
| c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)) != X1 ),
c_0_4805,
[final] ).
cnf(c_0_6493,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
c_0_4806,
[final] ).
cnf(c_0_6494,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4807,
[final] ).
cnf(c_0_6495,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
c_0_4808,
[final] ).
cnf(c_0_6496,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_4809,
[final] ).
cnf(c_0_6497,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4810,
[final] ).
cnf(c_0_6498,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4811,
[final] ).
cnf(c_0_6499,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4812,
[final] ).
cnf(c_0_6500,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
c_0_4813,
[final] ).
cnf(c_0_6501,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
c_0_4814,
[final] ).
cnf(c_0_6502,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4815,
[final] ).
cnf(c_0_6503,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_4816,
[final] ).
cnf(c_0_6504,plain,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4817,
[final] ).
cnf(c_0_6505,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4818,
[final] ).
cnf(c_0_6506,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4819,
[final] ).
cnf(c_0_6507,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_4820,
[final] ).
cnf(c_0_6508,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4821,
[final] ).
cnf(c_0_6509,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(esk48_2(X2,X1)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
c_0_4822,
[final] ).
cnf(c_0_6510,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X2),X4)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
c_0_4823,
[final] ).
cnf(c_0_6511,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
c_0_4824,
[final] ).
cnf(c_0_6512,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
c_0_4825,
[final] ).
cnf(c_0_6513,plain,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4) ),
c_0_4826,
[final] ).
cnf(c_0_6514,plain,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3) ),
c_0_4827,
[final] ).
cnf(c_0_6515,plain,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X2)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
c_0_4828,
[final] ).
cnf(c_0_6516,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4829,
[final] ).
cnf(c_0_6517,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4830,
[final] ).
cnf(c_0_6518,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4831,
[final] ).
cnf(c_0_6519,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4832,
[final] ).
cnf(c_0_6520,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4833,
[final] ).
cnf(c_0_6521,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4834,
[final] ).
cnf(c_0_6522,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_4835,
[final] ).
cnf(c_0_6523,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2)))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_4836,
[final] ).
cnf(c_0_6524,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_4837,
[final] ).
cnf(c_0_6525,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_4838,
[final] ).
cnf(c_0_6526,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk18_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
c_0_4839,
[final] ).
cnf(c_0_6527,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk13_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
c_0_4840,
[final] ).
cnf(c_0_6528,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| X1 != X2 ),
c_0_4841,
[final] ).
cnf(c_0_6529,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_4842,
[final] ).
cnf(c_0_6530,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
c_0_4843,
[final] ).
cnf(c_0_6531,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
c_0_4844,
[final] ).
cnf(c_0_6532,plain,
( hBOOL(hAPP(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_4845,
[final] ).
cnf(c_0_6533,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
c_0_4846,
[final] ).
cnf(c_0_6534,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X2)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),
c_0_4847,
[final] ).
cnf(c_0_6535,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)))),
c_0_4848,
[final] ).
cnf(c_0_6536,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X2)) = c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2)),
c_0_4849,
[final] ).
cnf(c_0_6537,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X1)),
c_0_4850,
[final] ).
cnf(c_0_6538,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X2 = X1
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1)) ),
c_0_4851,
[final] ).
cnf(c_0_6539,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| X2 = X1 ),
c_0_4852,
[final] ).
cnf(c_0_6540,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| X2 = X1 ),
c_0_4853,
[final] ).
cnf(c_0_6541,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_4854,
[final] ).
cnf(c_0_6542,plain,
( X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_Transcendental_Oln(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_4855,
[final] ).
cnf(c_0_6543,plain,
( hBOOL(hAPP(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_4856,
[final] ).
cnf(c_0_6544,plain,
c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),
c_0_4857,
[final] ).
cnf(c_0_6545,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
c_0_4858,
[final] ).
cnf(c_0_6546,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
c_0_4859,
[final] ).
cnf(c_0_6547,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
c_0_4860,
[final] ).
cnf(c_0_6548,plain,
( c_Transcendental_Oln(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
c_0_4861,
[final] ).
cnf(c_0_6549,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_4862,
[final] ).
cnf(c_0_6550,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_4863,
[final] ).
cnf(c_0_6551,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_4864,
[final] ).
cnf(c_0_6552,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_4865,
[final] ).
cnf(c_0_6553,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_4866,
[final] ).
cnf(c_0_6554,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
c_0_4867,
[final] ).
cnf(c_0_6555,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
c_0_4868,
[final] ).
cnf(c_0_6556,plain,
( c_Nat_OSuc(esk49_1(X1)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4869,
[final] ).
cnf(c_0_6557,plain,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) = hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X1)),
c_0_4870,
[final] ).
cnf(c_0_6558,plain,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) = hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X1)),
c_0_4871,
[final] ).
cnf(c_0_6559,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = X4
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2) ),
c_0_4872,
[final] ).
cnf(c_0_6560,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != X4 ),
c_0_4873,
[final] ).
cnf(c_0_6561,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != X4 ),
c_0_4874,
[final] ).
cnf(c_0_6562,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = X4
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2) ),
c_0_4875,
[final] ).
cnf(c_0_6563,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) = X4
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_4876,
[final] ).
cnf(c_0_6564,plain,
( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4)
| X4 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4) != X3
| ~ class_Rings_Odivision__ring(X2) ),
c_0_4877,
[final] ).
cnf(c_0_6565,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk38_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4878,
[final] ).
cnf(c_0_6566,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk37_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4879,
[final] ).
cnf(c_0_6567,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk31_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4880,
[final] ).
cnf(c_0_6568,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk30_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4881,
[final] ).
cnf(c_0_6569,plain,
( hBOOL(hAPP(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_4882,
[final] ).
cnf(c_0_6570,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
c_0_4883,
[final] ).
cnf(c_0_6571,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3) ),
c_0_4884,
[final] ).
cnf(c_0_6572,plain,
c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Nat_OSuc(X2)),
c_0_4885,
[final] ).
cnf(c_0_6573,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1)))),
c_0_4886,
[final] ).
cnf(c_0_6574,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk22_1(X1)),esk23_1(X1)))
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1) ),
c_0_4887,
[final] ).
cnf(c_0_6575,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_4888,
[final] ).
cnf(c_0_6576,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
c_0_4889,
[final] ).
cnf(c_0_6577,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X2) = X1,
c_0_4890,
[final] ).
cnf(c_0_6578,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X1) = X2,
c_0_4891,
[final] ).
cnf(c_0_6579,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Oone__class_Oone(X1) ),
c_0_4892,
[final] ).
cnf(c_0_6580,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oabs__class_Oabs(X1,X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_4893,
[final] ).
cnf(c_0_6581,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
c_0_4894,
[final] ).
cnf(c_0_6582,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
c_0_4895,
[final] ).
cnf(c_0_6583,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
c_0_4896,
[final] ).
cnf(c_0_6584,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
c_0_4897,
[final] ).
cnf(c_0_6585,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
c_0_4898,
[final] ).
cnf(c_0_6586,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
c_0_4899,
[final] ).
cnf(c_0_6587,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X2),X1))
| ~ class_Orderings_Oorder(X3) ),
c_0_4900,
[final] ).
cnf(c_0_6588,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = X2
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4901,
[final] ).
cnf(c_0_6589,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4902,
[final] ).
cnf(c_0_6590,plain,
( c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
c_0_4903,
[final] ).
cnf(c_0_6591,plain,
( c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
c_0_4904,
[final] ).
cnf(c_0_6592,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(X2,X1)))
| ~ c_SEQ_Osubseq(X2) ),
c_0_4905,
[final] ).
cnf(c_0_6593,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1))),
c_0_4906,
[final] ).
cnf(c_0_6594,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
c_0_4907,
[final] ).
cnf(c_0_6595,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
c_0_4908,
[final] ).
cnf(c_0_6596,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
c_0_4909,
[final] ).
cnf(c_0_6597,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
c_0_4910,
[final] ).
cnf(c_0_6598,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
c_0_4911,
[final] ).
cnf(c_0_6599,plain,
( hBOOL(hAPP(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_4912,
[final] ).
cnf(c_0_6600,plain,
( hBOOL(hAPP(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_4913,
[final] ).
cnf(c_0_6601,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
c_0_4914,
[final] ).
cnf(c_0_6602,plain,
( c_SEQ_Oconvergent(X1,c_COMBK(X1,tc_Nat_Onat,X2))
| ~ class_RealVector_Ometric__space(X1) ),
c_0_4915,
[final] ).
cnf(c_0_6603,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X1 != X2 ),
c_0_4916,
[final] ).
cnf(c_0_6604,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_4917,
[final] ).
cnf(c_0_6605,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4918,
[final] ).
cnf(c_0_6606,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
c_0_4919,
[final] ).
cnf(c_0_6607,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
c_0_4920,
[final] ).
cnf(c_0_6608,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
c_0_4921,
[final] ).
cnf(c_0_6609,plain,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
c_0_4922,
[final] ).
cnf(c_0_6610,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| X1 != X2 ),
c_0_4923,
[final] ).
cnf(c_0_6611,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_4924,
[final] ).
cnf(c_0_6612,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X3,
c_0_4925,
[final] ).
cnf(c_0_6613,plain,
c_Complex_Ocomplex_Ocomplex__case(X1,X2,c_Complex_Ocomplex_OComplex(X3,X4)) = hAPP(hAPP(X2,X3),X4),
c_0_4926,
[final] ).
cnf(c_0_6614,plain,
c_Complex_Ocomplex_Ocomplex__rec(X1,X2,c_Complex_Ocomplex_OComplex(X3,X4)) = hAPP(hAPP(X2,X3),X4),
c_0_4927,
[final] ).
cnf(c_0_6615,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_4928,
[final] ).
cnf(c_0_6616,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X1)),
c_0_4929,
[final] ).
cnf(c_0_6617,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X1)),
c_0_4930,
[final] ).
cnf(c_0_6618,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_4931,
[final] ).
cnf(c_0_6619,plain,
( c_SEQ_Osubseq(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk3_1(X1)),esk4_1(X1))) ),
c_0_4932,
[final] ).
cnf(c_0_6620,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 != X4 ),
c_0_4933,
[final] ).
cnf(c_0_6621,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X3 != X4 ),
c_0_4934,
[final] ).
cnf(c_0_6622,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)),
c_0_4935,
[final] ).
cnf(c_0_6623,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_4936,
[final] ).
cnf(c_0_6624,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_4937,
[final] ).
cnf(c_0_6625,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Nat_OSuc(X2)),
c_0_4938,
[final] ).
cnf(c_0_6626,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk36_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4939,
[final] ).
cnf(c_0_6627,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk29_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_4940,
[final] ).
cnf(c_0_6628,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
c_0_4941,
[final] ).
cnf(c_0_6629,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
c_0_4942,
[final] ).
cnf(c_0_6630,plain,
( hBOOL(hAPP(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_4943,
[final] ).
cnf(c_0_6631,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_4944,
[final] ).
cnf(c_0_6632,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_4945,
[final] ).
cnf(c_0_6633,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_4946,
[final] ).
cnf(c_0_6634,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = X2
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != c_Groups_Oone__class_Oone(X1) ),
c_0_4947,
[final] ).
cnf(c_0_6635,plain,
( X2 = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4948,
[final] ).
cnf(c_0_6636,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_4949,
[final] ).
cnf(c_0_6637,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_4950,
[final] ).
cnf(c_0_6638,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4951,
[final] ).
cnf(c_0_6639,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_4952,
[final] ).
cnf(c_0_6640,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))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4953,
[final] ).
cnf(c_0_6641,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))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4954,
[final] ).
cnf(c_0_6642,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(X1))),
c_0_4955,
[final] ).
cnf(c_0_6643,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(X1))),
c_0_4956,
[final] ).
cnf(c_0_6644,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))),
c_0_4957,
[final] ).
cnf(c_0_6645,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_4958,
[final] ).
cnf(c_0_6646,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_4959,
[final] ).
cnf(c_0_6647,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_4960,
[final] ).
cnf(c_0_6648,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_4961,
[final] ).
cnf(c_0_6649,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_4962,
[final] ).
cnf(c_0_6650,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_4963,
[final] ).
cnf(c_0_6651,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_4964,
[final] ).
cnf(c_0_6652,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 != c_Nat_OSuc(X2) ),
c_0_4965,
[final] ).
cnf(c_0_6653,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| X1 != c_Nat_OSuc(X2) ),
c_0_4966,
[final] ).
cnf(c_0_6654,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2) != X3 ),
c_0_4967,
[final] ).
cnf(c_0_6655,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_4968,
[final] ).
cnf(c_0_6656,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4969,
[final] ).
cnf(c_0_6657,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4970,
[final] ).
cnf(c_0_6658,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4971,
[final] ).
cnf(c_0_6659,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4972,
[final] ).
cnf(c_0_6660,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_4973,
[final] ).
cnf(c_0_6661,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_4974,
[final] ).
cnf(c_0_6662,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_4975,
[final] ).
cnf(c_0_6663,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)
| X2 != X3 ),
c_0_4976,
[final] ).
cnf(c_0_6664,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)
| X1 != X3 ),
c_0_4977,
[final] ).
cnf(c_0_6665,plain,
hBOOL(hAPP(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_4978,
[final] ).
cnf(c_0_6666,plain,
hBOOL(hAPP(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_4979,
[final] ).
cnf(c_0_6667,plain,
hBOOL(hAPP(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_4980,
[final] ).
cnf(c_0_6668,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_4981,
[final] ).
cnf(c_0_6669,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
c_0_4982,
[final] ).
cnf(c_0_6670,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
c_0_4983,
[final] ).
cnf(c_0_6671,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
c_0_4984,
[final] ).
cnf(c_0_6672,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 != X3
| ~ class_Orderings_Opreorder(X1) ),
c_0_4985,
[final] ).
cnf(c_0_6673,plain,
( c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
c_0_4986,
[final] ).
cnf(c_0_6674,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_4987,
[final] ).
cnf(c_0_6675,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_4988,
[final] ).
cnf(c_0_6676,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1),
c_0_4989,
[final] ).
cnf(c_0_6677,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_4990,
[final] ).
cnf(c_0_6678,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_4991,
[final] ).
cnf(c_0_6679,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_4992,
[final] ).
cnf(c_0_6680,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
c_0_4993,
[final] ).
cnf(c_0_6681,plain,
( hBOOL(hAPP(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_4994,
[final] ).
cnf(c_0_6682,plain,
( hBOOL(hAPP(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_4995,
[final] ).
cnf(c_0_6683,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| X1 != X2 ),
c_0_4996,
[final] ).
cnf(c_0_6684,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4997,
[final] ).
cnf(c_0_6685,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
c_0_4998,
[final] ).
cnf(c_0_6686,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Ocos(X2)) = hAPP(c_Complex_ORe,c_Complex_Orcis(X1,X2)),
c_0_4999,
[final] ).
cnf(c_0_6687,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Osin(X2)) = hAPP(c_Complex_OIm,c_Complex_Orcis(X1,X2)),
c_0_5000,
[final] ).
cnf(c_0_6688,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_5001,
[final] ).
cnf(c_0_6689,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_5002,
[final] ).
cnf(c_0_6690,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_5003,
[final] ).
cnf(c_0_6691,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X1))),
c_0_5004,
[final] ).
cnf(c_0_6692,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
c_0_5005,
[final] ).
cnf(c_0_6693,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
c_0_5006,
[final] ).
cnf(c_0_6694,plain,
( hBOOL(hAPP(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_5007,
[final] ).
cnf(c_0_6695,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_5008,
[final] ).
cnf(c_0_6696,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk28_0)),
c_0_5009,
[final] ).
cnf(c_0_6697,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk27_0)),
c_0_5010,
[final] ).
cnf(c_0_6698,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk26_0)),
c_0_5011,
[final] ).
cnf(c_0_6699,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk25_0)),
c_0_5012,
[final] ).
cnf(c_0_6700,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
c_0_5013,
[final] ).
cnf(c_0_6701,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_5014,
[final] ).
cnf(c_0_6702,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_5015,
[final] ).
cnf(c_0_6703,plain,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1),
c_0_5016,
[final] ).
cnf(c_0_6704,plain,
( X1 = X2
| hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2) ),
c_0_5017,
[final] ).
cnf(c_0_6705,plain,
( X1 = X2
| hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2) ),
c_0_5018,
[final] ).
cnf(c_0_6706,plain,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_5019,
[final] ).
cnf(c_0_6707,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_5020,
[final] ).
cnf(c_0_6708,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_5021,
[final] ).
cnf(c_0_6709,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_5022,
[final] ).
cnf(c_0_6710,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_5023,
[final] ).
cnf(c_0_6711,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5024,
[final] ).
cnf(c_0_6712,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5025,
[final] ).
cnf(c_0_6713,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
c_0_5026,
[final] ).
cnf(c_0_6714,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
c_0_5027,
[final] ).
cnf(c_0_6715,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
c_0_5028,
[final] ).
cnf(c_0_6716,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| X1 != X2 ),
c_0_5029,
[final] ).
cnf(c_0_6717,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_5030,
[final] ).
cnf(c_0_6718,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_5031,
[final] ).
cnf(c_0_6719,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2 ),
c_0_5032,
[final] ).
cnf(c_0_6720,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_5033,
[final] ).
cnf(c_0_6721,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X1)),
c_0_5034,
[final] ).
cnf(c_0_6722,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
c_0_5035,
[final] ).
cnf(c_0_6723,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X1)),
c_0_5036,
[final] ).
cnf(c_0_6724,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_5037,
[final] ).
cnf(c_0_6725,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
c_0_5038,
[final] ).
cnf(c_0_6726,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_5039,
[final] ).
cnf(c_0_6727,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_5040,
[final] ).
cnf(c_0_6728,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_5041,
[final] ).
cnf(c_0_6729,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_5042,
[final] ).
cnf(c_0_6730,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_5043,
[final] ).
cnf(c_0_6731,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_5044,
[final] ).
cnf(c_0_6732,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_5045,
[final] ).
cnf(c_0_6733,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_5046,
[final] ).
cnf(c_0_6734,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5047,
[final] ).
cnf(c_0_6735,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_5048,
[final] ).
cnf(c_0_6736,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Groups_Omonoid__add(X1) ),
c_0_5049,
[final] ).
cnf(c_0_6737,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1)
| X3 != X2 ),
c_0_5050,
[final] ).
cnf(c_0_6738,plain,
( hAPP(hAPP(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_5051,
[final] ).
cnf(c_0_6739,plain,
( hAPP(hAPP(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_5052,
[final] ).
cnf(c_0_6740,plain,
( hAPP(hAPP(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_5053,
[final] ).
cnf(c_0_6741,plain,
( hAPP(hAPP(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_5054,
[final] ).
cnf(c_0_6742,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5055,
[final] ).
cnf(c_0_6743,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_5056,
[final] ).
cnf(c_0_6744,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_5057,
[final] ).
cnf(c_0_6745,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_5058,
[final] ).
cnf(c_0_6746,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_5059,
[final] ).
cnf(c_0_6747,plain,
( hAPP(hAPP(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_5060,
[final] ).
cnf(c_0_6748,plain,
( hAPP(hAPP(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_5061,
[final] ).
cnf(c_0_6749,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_5062,
[final] ).
cnf(c_0_6750,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
c_0_5063,
[final] ).
cnf(c_0_6751,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_5064,
[final] ).
cnf(c_0_6752,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_5065,
[final] ).
cnf(c_0_6753,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_5066,
[final] ).
cnf(c_0_6754,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_5067,
[final] ).
cnf(c_0_6755,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_5068,
[final] ).
cnf(c_0_6756,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 != X3 ),
c_0_5069,
[final] ).
cnf(c_0_6757,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_5070,
[final] ).
cnf(c_0_6758,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
c_0_5071,
[final] ).
cnf(c_0_6759,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
c_0_5072,
[final] ).
cnf(c_0_6760,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
c_0_5073,
[final] ).
cnf(c_0_6761,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
c_0_5074,
[final] ).
cnf(c_0_6762,plain,
( hAPP(hAPP(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_5075,
[final] ).
cnf(c_0_6763,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Odivision__ring(X1) ),
c_0_5076,
[final] ).
cnf(c_0_6764,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_5077,
[final] ).
cnf(c_0_6765,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_5078,
[final] ).
cnf(c_0_6766,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_5079,
[final] ).
cnf(c_0_6767,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
c_0_5080,
[final] ).
cnf(c_0_6768,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_5081,
[final] ).
cnf(c_0_6769,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5082,
[final] ).
cnf(c_0_6770,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_5083,
[final] ).
cnf(c_0_6771,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Omonoid__add(X1) ),
c_0_5084,
[final] ).
cnf(c_0_6772,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_5085,
[final] ).
cnf(c_0_6773,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X1,
c_0_5086,
[final] ).
cnf(c_0_6774,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
c_0_5087,
[final] ).
cnf(c_0_6775,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X1),c_Transcendental_Osin(X1))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_5088,
[final] ).
cnf(c_0_6776,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_5089,
[final] ).
cnf(c_0_6777,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_5090,
[final] ).
cnf(c_0_6778,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
c_0_5091,
[final] ).
cnf(c_0_6779,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
c_0_5092,
[final] ).
cnf(c_0_6780,plain,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Osgn__class_Osgn(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5093,
[final] ).
cnf(c_0_6781,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_5094,
[final] ).
cnf(c_0_6782,plain,
c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X1),hAPP(c_Complex_OIm,X1)) = X1,
c_0_5095,
[final] ).
cnf(c_0_6783,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_5096,
[final] ).
cnf(c_0_6784,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_5097,
[final] ).
cnf(c_0_6785,plain,
( hAPP(hAPP(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_5098,
[final] ).
cnf(c_0_6786,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_5099,
[final] ).
cnf(c_0_6787,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
c_0_5100,
[final] ).
cnf(c_0_6788,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_5101,
[final] ).
cnf(c_0_6789,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_5102,
[final] ).
cnf(c_0_6790,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_5103,
[final] ).
cnf(c_0_6791,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(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_5104,
[final] ).
cnf(c_0_6792,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
c_0_5105,
[final] ).
cnf(c_0_6793,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = c_Nat_OSuc(X1),
c_0_5106,
[final] ).
cnf(c_0_6794,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5107,
[final] ).
cnf(c_0_6795,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_5108,
[final] ).
cnf(c_0_6796,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_5109,
[final] ).
cnf(c_0_6797,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_5110,
[final] ).
cnf(c_0_6798,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_5111,
[final] ).
cnf(c_0_6799,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_5112,
[final] ).
cnf(c_0_6800,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_5113,
[final] ).
cnf(c_0_6801,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,X1)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1) ),
c_0_5114,
[final] ).
cnf(c_0_6802,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_OSuc(X1),
c_0_5115,
[final] ).
cnf(c_0_6803,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = X1,
c_0_5116,
[final] ).
cnf(c_0_6804,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) = X1,
c_0_5117,
[final] ).
cnf(c_0_6805,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
c_0_5118,
[final] ).
cnf(c_0_6806,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
c_0_5119,
[final] ).
cnf(c_0_6807,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
c_0_5120,
[final] ).
cnf(c_0_6808,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5121,
[final] ).
cnf(c_0_6809,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_5122,
[final] ).
cnf(c_0_6810,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
c_0_5123,
[final] ).
cnf(c_0_6811,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
c_0_5124,
[final] ).
cnf(c_0_6812,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
c_0_5125,
[final] ).
cnf(c_0_6813,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
c_0_5126,
[final] ).
cnf(c_0_6814,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
c_0_5127,
[final] ).
cnf(c_0_6815,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)) = c_RealDef_Oreal(tc_Nat_Onat,X1),
c_0_5128,
[final] ).
cnf(c_0_6816,plain,
( X1 = X3
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
c_0_5129,
[final] ).
cnf(c_0_6817,plain,
( X2 = X4
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
c_0_5130,
[final] ).
cnf(c_0_6818,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_5131,
[final] ).
cnf(c_0_6819,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_SEQ_Odecseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
c_0_5132,
[final] ).
cnf(c_0_6820,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_SEQ_Oincseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
c_0_5133,
[final] ).
cnf(c_0_6821,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_5134,
[final] ).
cnf(c_0_6822,plain,
( X1 = X2
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_RealDef_Oreal(tc_Nat_Onat,X2) ),
c_0_5135,
[final] ).
cnf(c_0_6823,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5136,
[final] ).
cnf(c_0_6824,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5137,
[final] ).
cnf(c_0_6825,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5138,
[final] ).
cnf(c_0_6826,plain,
c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5139,
[final] ).
cnf(c_0_6827,plain,
hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X1,X2)) = X1,
c_0_5140,
[final] ).
cnf(c_0_6828,plain,
hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X1,X2)) = X2,
c_0_5141,
[final] ).
cnf(c_0_6829,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_5142,
[final] ).
cnf(c_0_6830,plain,
( class_Orderings_Oord(tc_fun(X1,X2))
| ~ class_Orderings_Oord(X2) ),
c_0_5143,
[final] ).
cnf(c_0_6831,plain,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
c_0_5144,
[final] ).
cnf(c_0_6832,plain,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
c_0_5145,
[final] ).
cnf(c_0_6833,plain,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Complex_Ocomplex_OComplex(X3,X4)
| X2 != X4
| X1 != X3 ),
c_0_5146,
[final] ).
cnf(c_0_6834,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5147,
[final] ).
cnf(c_0_6835,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5148,
[final] ).
cnf(c_0_6836,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5149,
[final] ).
cnf(c_0_6837,plain,
c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5150,
[final] ).
cnf(c_0_6838,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_5151,
[final] ).
cnf(c_0_6839,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_5152,
[final] ).
cnf(c_0_6840,plain,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
c_0_5153,
[final] ).
cnf(c_0_6841,plain,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
c_0_5154,
[final] ).
cnf(c_0_6842,plain,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Osgn__if(X1) ),
c_0_5155,
[final] ).
cnf(c_0_6843,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5156,
[final] ).
cnf(c_0_6844,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
c_0_5157,
[final] ).
cnf(c_0_6845,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)) = c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),
c_0_5158,
[final] ).
cnf(c_0_6846,plain,
c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X1),c_Transcendental_Osin(X1)) = c_Complex_Ocis(X1),
c_0_5159,
[final] ).
cnf(c_0_6847,plain,
( X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
c_0_5160,
[final] ).
cnf(c_0_6848,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
c_0_5161,
[final] ).
cnf(c_0_6849,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_5162,
[final] ).
cnf(c_0_6850,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_5163,
[final] ).
cnf(c_0_6851,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_5164,
[final] ).
cnf(c_0_6852,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_5165,
[final] ).
cnf(c_0_6853,plain,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
c_0_5166,
[final] ).
cnf(c_0_6854,plain,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_5167,
[final] ).
cnf(c_0_6855,plain,
( c_RealDef_Oreal(tc_Nat_Onat,X1) = c_RealDef_Oreal(tc_Nat_Onat,X2)
| X1 != X2 ),
c_0_5168,
[final] ).
cnf(c_0_6856,plain,
( hAPP(c_Complex_ORe,X1) = hAPP(c_Complex_ORe,X2)
| X1 != X2 ),
c_0_5169,
[final] ).
cnf(c_0_6857,plain,
( hAPP(c_Complex_OIm,X1) = hAPP(c_Complex_OIm,X2)
| X1 != X2 ),
c_0_5170,
[final] ).
cnf(c_0_6858,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
c_0_5171,
[final] ).
cnf(c_0_6859,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
c_0_5172,
[final] ).
cnf(c_0_6860,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_5173,
[final] ).
cnf(c_0_6861,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_5174,
[final] ).
cnf(c_0_6862,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Oii ),
c_0_5175,
[final] ).
cnf(c_0_6863,plain,
( X2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Oii ),
c_0_5176,
[final] ).
cnf(c_0_6864,plain,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Complex_Oii
| X2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_5177,
[final] ).
cnf(c_0_6865,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
c_0_5178,
[final] ).
cnf(c_0_6866,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_5179,
[final] ).
cnf(c_0_6867,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_5180,
[final] ).
cnf(c_0_6868,plain,
hAPP(c_Complex_ORe,c_Complex_Ocis(X1)) = c_Transcendental_Ocos(X1),
c_0_5181,
[final] ).
cnf(c_0_6869,plain,
hAPP(c_Complex_OIm,c_Complex_Ocis(X1)) = c_Transcendental_Osin(X1),
c_0_5182,
[final] ).
cnf(c_0_6870,plain,
c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = c_Complex_Ocis(X1),
c_0_5183,
[final] ).
cnf(c_0_6871,plain,
( c_RealDef_Oreal(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
c_0_5184,
[final] ).
cnf(c_0_6872,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Oone(X1)
| c_Groups_Oone__class_Oone(X1) != X2 ),
c_0_5185,
[final] ).
cnf(c_0_6873,plain,
( c_Groups_Oone__class_Oone(X1) = X2
| ~ class_Groups_Oone(X1)
| X2 != c_Groups_Oone__class_Oone(X1) ),
c_0_5186,
[final] ).
cnf(c_0_6874,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
c_0_5187,
[final] ).
cnf(c_0_6875,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| ~ class_Groups_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
c_0_5188,
[final] ).
cnf(c_0_6876,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Complex_Oii,
c_0_5189,
[final] ).
cnf(c_0_6877,plain,
( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1) ),
c_0_5190,
[final] ).
cnf(c_0_6878,plain,
( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1) ),
c_0_5191,
[final] ).
cnf(c_0_6879,plain,
c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_5192,
[final] ).
cnf(c_0_6880,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_5193,
[final] ).
cnf(c_0_6881,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_5194,
[final] ).
cnf(c_0_6882,plain,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_5195,
[final] ).
cnf(c_0_6883,plain,
hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_5196,
[final] ).
cnf(c_0_6884,plain,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_5197,
[final] ).
cnf(c_0_6885,plain,
hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_5198,
[final] ).
cnf(c_0_6886,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5199,
[final] ).
cnf(c_0_6887,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
c_0_5200,
[final] ).
cnf(c_0_6888,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
c_0_5201,
[final] ).
cnf(c_0_6889,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5202,
[final] ).
cnf(c_0_6890,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
c_0_5203,
[final] ).
cnf(c_0_6891,plain,
( class_Groups_Osgn__if(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5204,
[final] ).
cnf(c_0_6892,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5205,
[final] ).
cnf(c_0_6893,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5206,
[final] ).
cnf(c_0_6894,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5207,
[final] ).
cnf(c_0_6895,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5208,
[final] ).
cnf(c_0_6896,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_5209,
[final] ).
cnf(c_0_6897,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5210,
[final] ).
cnf(c_0_6898,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_5211,
[final] ).
cnf(c_0_6899,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
c_0_5212,
[final] ).
cnf(c_0_6900,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5213,
[final] ).
cnf(c_0_6901,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5214,
[final] ).
cnf(c_0_6902,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5215,
[final] ).
cnf(c_0_6903,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5216,
[final] ).
cnf(c_0_6904,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5217,
[final] ).
cnf(c_0_6905,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
c_0_5218,
[final] ).
cnf(c_0_6906,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5219,
[final] ).
cnf(c_0_6907,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
c_0_5220,
[final] ).
cnf(c_0_6908,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5221,
[final] ).
cnf(c_0_6909,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5222,
[final] ).
cnf(c_0_6910,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5223,
[final] ).
cnf(c_0_6911,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_5224,
[final] ).
cnf(c_0_6912,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
c_0_5225,
[final] ).
cnf(c_0_6913,plain,
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5226,
[final] ).
cnf(c_0_6914,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5227,
[final] ).
cnf(c_0_6915,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
c_0_5228,
[final] ).
cnf(c_0_6916,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
c_0_5229,
[final] ).
cnf(c_0_6917,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5230,
[final] ).
cnf(c_0_6918,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5231,
[final] ).
cnf(c_0_6919,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5232,
[final] ).
cnf(c_0_6920,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
c_0_5233,
[final] ).
cnf(c_0_6921,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5234,
[final] ).
cnf(c_0_6922,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5235,
[final] ).
cnf(c_0_6923,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5236,
[final] ).
cnf(c_0_6924,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
c_0_5237,
[final] ).
cnf(c_0_6925,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5238,
[final] ).
cnf(c_0_6926,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5239,
[final] ).
cnf(c_0_6927,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
c_0_5240,
[final] ).
cnf(c_0_6928,plain,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
c_0_5241,
[final] ).
cnf(c_0_6929,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5242,
[final] ).
cnf(c_0_6930,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5243,
[final] ).
cnf(c_0_6931,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5244,
[final] ).
cnf(c_0_6932,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5245,
[final] ).
cnf(c_0_6933,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5246,
[final] ).
cnf(c_0_6934,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5247,
[final] ).
cnf(c_0_6935,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5248,
[final] ).
cnf(c_0_6936,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5249,
[final] ).
cnf(c_0_6937,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
c_0_5250,
[final] ).
cnf(c_0_6938,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
c_0_5251,
[final] ).
cnf(c_0_6939,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
c_0_5252,
[final] ).
cnf(c_0_6940,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
c_0_5253,
[final] ).
cnf(c_0_6941,plain,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
c_0_5254,
[final] ).
cnf(c_0_6942,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
c_0_5255,
[final] ).
cnf(c_0_6943,plain,
( c_Transcendental_Osin(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
c_0_5256,
[final] ).
cnf(c_0_6944,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
c_0_5257,
[final] ).
cnf(c_0_6945,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
c_0_5258,
[final] ).
cnf(c_0_6946,plain,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_5259,
[final] ).
cnf(c_0_6947,plain,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_5260,
[final] ).
cnf(c_0_6948,plain,
( c_Nat_OSuc(X1) = c_Nat_OSuc(X2)
| X1 != X2 ),
c_0_5261,
[final] ).
cnf(c_0_6949,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5262,
[final] ).
cnf(c_0_6950,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5263,
[final] ).
cnf(c_0_6951,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5264,
[final] ).
cnf(c_0_6952,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5265,
[final] ).
cnf(c_0_6953,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5266,
[final] ).
cnf(c_0_6954,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5267,
[final] ).
cnf(c_0_6955,plain,
c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_5268,
[final] ).
cnf(c_0_6956,plain,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_5269,
[final] ).
cnf(c_0_6957,plain,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
c_0_5270,
[final] ).
cnf(c_0_6958,plain,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_5271,
[final] ).
cnf(c_0_6959,plain,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
c_0_5272,
[final] ).
cnf(c_0_6960,plain,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
c_0_5273,
[final] ).
cnf(c_0_6961,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5274,
[final] ).
cnf(c_0_6962,plain,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
c_0_5275,
[final] ).
cnf(c_0_6963,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
c_0_5276,
[final] ).
cnf(c_0_6964,plain,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
c_0_5277,
[final] ).
cnf(c_0_6965,plain,
c_Nat_OSuc(X1) != X1,
c_0_5278,
[final] ).
cnf(c_0_6966,plain,
c_Nat_OSuc(X1) != X1,
c_0_5279,
[final] ).
cnf(c_0_6967,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
c_0_5280,
[final] ).
cnf(c_0_6968,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_5281,
[final] ).
cnf(c_0_6969,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
c_0_5282,
[final] ).
cnf(c_0_6970,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
c_0_5283,
[final] ).
cnf(c_0_6971,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
c_0_5284,
[final] ).
cnf(c_0_6972,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
c_0_5285,
[final] ).
cnf(c_0_6973,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
c_0_5286,
[final] ).
cnf(c_0_6974,plain,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_5287,
[final] ).
cnf(c_0_6975,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
c_0_5288,
[final] ).
cnf(c_0_6976,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
c_0_5289,
[final] ).
cnf(c_0_6977,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
c_0_5290,
[final] ).
cnf(c_0_6978,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
c_0_5291,
[final] ).
cnf(c_0_6979,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
c_0_5292,
[final] ).
cnf(c_0_6980,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
c_0_5293,
[final] ).
cnf(c_0_6981,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
c_0_5294,
[final] ).
cnf(c_0_6982,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_5295,
[final] ).
cnf(c_0_6983,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
c_0_5296,
[final] ).
cnf(c_0_6984,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_5297,
[final] ).
cnf(c_0_6985,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
c_0_5298,
[final] ).
cnf(c_0_6986,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_5299,
[final] ).
cnf(c_0_6987,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
c_0_5300,
[final] ).
cnf(c_0_6988,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
c_0_5301,
[final] ).
cnf(c_0_6989,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_5302,
[final] ).
cnf(c_0_6990,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_5303,
[final] ).
cnf(c_0_6991,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_5304,
[final] ).
cnf(c_0_6992,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_5305,
[final] ).
cnf(c_0_6993,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_5306,
[final] ).
cnf(c_0_6994,plain,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
c_0_5307,
[final] ).
cnf(c_0_6995,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_5308,
[final] ).
cnf(c_0_6996,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
c_0_5309,
[final] ).
cnf(c_0_6997,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_5310,
[final] ).
cnf(c_0_6998,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_5311,
[final] ).
cnf(c_0_6999,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
c_0_5312,
[final] ).
cnf(c_0_7000,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
c_0_5313,
[final] ).
cnf(c_0_7001,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_5314,
[final] ).
cnf(c_0_7002,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_5315,
[final] ).
cnf(c_0_7003,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_5316,
[final] ).
cnf(c_0_7004,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
c_0_5317,
[final] ).
cnf(c_0_7005,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
c_0_5318,
[final] ).
cnf(c_0_7006,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
c_0_5319,
[final] ).
cnf(c_0_7007,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
c_0_5320,
[final] ).
cnf(c_0_7008,plain,
class_Groups_Oone(tc_RealDef_Oreal),
c_0_5321,
[final] ).
cnf(c_0_7009,plain,
class_Rings_Oring(tc_RealDef_Oreal),
c_0_5322,
[final] ).
cnf(c_0_7010,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
c_0_5323,
[final] ).
cnf(c_0_7011,plain,
class_Power_Opower(tc_RealDef_Oreal),
c_0_5324,
[final] ).
cnf(c_0_7012,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
c_0_5325,
[final] ).
cnf(c_0_7013,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
c_0_5326,
[final] ).
cnf(c_0_7014,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
c_0_5327,
[final] ).
cnf(c_0_7015,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
c_0_5328,
[final] ).
cnf(c_0_7016,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
c_0_5329,
[final] ).
cnf(c_0_7017,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
c_0_5330,
[final] ).
cnf(c_0_7018,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
c_0_5331,
[final] ).
cnf(c_0_7019,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
c_0_5332,
[final] ).
cnf(c_0_7020,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
c_0_5333,
[final] ).
cnf(c_0_7021,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
c_0_5334,
[final] ).
cnf(c_0_7022,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
c_0_5335,
[final] ).
cnf(c_0_7023,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
c_0_5336,
[final] ).
cnf(c_0_7024,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
c_0_5337,
[final] ).
cnf(c_0_7025,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
c_0_5338,
[final] ).
cnf(c_0_7026,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
c_0_5339,
[final] ).
cnf(c_0_7027,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
c_0_5340,
[final] ).
cnf(c_0_7028,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
c_0_5341,
[final] ).
cnf(c_0_7029,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
c_0_5342,
[final] ).
cnf(c_0_7030,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
c_0_5343,
[final] ).
cnf(c_0_7031,plain,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
c_0_5344,
[final] ).
cnf(c_0_7032,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
c_0_5345,
[final] ).
cnf(c_0_7033,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
c_0_5346,
[final] ).
cnf(c_0_7034,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
c_0_5347,
[final] ).
cnf(c_0_7035,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
c_0_5348,
[final] ).
cnf(c_0_7036,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
c_0_5349,
[final] ).
cnf(c_0_7037,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
c_0_5350,
[final] ).
cnf(c_0_7038,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
c_0_5351,
[final] ).
cnf(c_0_7039,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
c_0_5352,
[final] ).
cnf(c_0_7040,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
c_0_5353,
[final] ).
cnf(c_0_7041,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
c_0_5354,
[final] ).
cnf(c_0_7042,plain,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
c_0_5355,
[final] ).
cnf(c_0_7043,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
c_0_5356,
[final] ).
cnf(c_0_7044,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
c_0_5357,
[final] ).
cnf(c_0_7045,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
c_0_5358,
[final] ).
cnf(c_0_7046,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
c_0_5359,
[final] ).
cnf(c_0_7047,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
c_0_5360,
[final] ).
cnf(c_0_7048,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
c_0_5361,
[final] ).
cnf(c_0_7049,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
c_0_5362,
[final] ).
cnf(c_0_7050,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
c_0_5363,
[final] ).
cnf(c_0_7051,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
c_0_5364,
[final] ).
cnf(c_0_7052,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
c_0_5365,
[final] ).
cnf(c_0_7053,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
c_0_5366,
[final] ).
cnf(c_0_7054,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
c_0_5367,
[final] ).
cnf(c_0_7055,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
c_0_5368,
[final] ).
cnf(c_0_7056,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
c_0_5369,
[final] ).
cnf(c_0_7057,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_5370,
[final] ).
cnf(c_0_7058,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
c_0_5371,
[final] ).
cnf(c_0_7059,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
c_0_5372,
[final] ).
cnf(c_0_7060,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
c_0_5373,
[final] ).
cnf(c_0_7061,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
c_0_5374,
[final] ).
cnf(c_0_7062,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
c_0_5375,
[final] ).
cnf(c_0_7063,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
c_0_5376,
[final] ).
cnf(c_0_7064,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
c_0_5377,
[final] ).
cnf(c_0_7065,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
c_0_5378,
[final] ).
cnf(c_0_7066,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
c_0_5379,
[final] ).
cnf(c_0_7067,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
c_0_5380,
[final] ).
cnf(c_0_7068,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
c_0_5381,
[final] ).
cnf(c_0_7069,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
c_0_5382,
[final] ).
cnf(c_0_7070,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
c_0_5383,
[final] ).
cnf(c_0_7071,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
c_0_5384,
[final] ).
cnf(c_0_7072,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
c_0_5385,
[final] ).
cnf(c_0_7073,plain,
class_Orderings_Oord(tc_HOL_Obool),
c_0_5386,
[final] ).
cnf(c_0_7074,plain,
class_Orderings_Oorder(tc_HOL_Obool),
c_0_5387,
[final] ).
cnf(c_0_7075,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
c_0_5388,
[final] ).
cnf(c_0_7076,plain,
class_Groups_Oone(tc_Nat_Onat),
c_0_5389,
[final] ).
cnf(c_0_7077,plain,
class_Groups_Ozero(tc_Nat_Onat),
c_0_5390,
[final] ).
cnf(c_0_7078,plain,
class_Power_Opower(tc_Nat_Onat),
c_0_5391,
[final] ).
cnf(c_0_7079,plain,
class_Orderings_Oord(tc_Nat_Onat),
c_0_5392,
[final] ).
cnf(c_0_7080,plain,
class_Rings_Osemiring(tc_Nat_Onat),
c_0_5393,
[final] ).
cnf(c_0_7081,plain,
class_Orderings_Oorder(tc_Nat_Onat),
c_0_5394,
[final] ).
cnf(c_0_7082,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
c_0_5395,
[final] ).
cnf(c_0_7083,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
c_0_5396,
[final] ).
cnf(c_0_7084,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
c_0_5397,
[final] ).
cnf(c_0_7085,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
c_0_5398,
[final] ).
cnf(c_0_7086,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
c_0_5399,
[final] ).
cnf(c_0_7087,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
c_0_5400,
[final] ).
cnf(c_0_7088,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
c_0_5401,
[final] ).
cnf(c_0_7089,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
c_0_5402,
[final] ).
cnf(c_0_7090,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
c_0_5403,
[final] ).
cnf(c_0_7091,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
c_0_5404,
[final] ).
cnf(c_0_7092,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
c_0_5405,
[final] ).
cnf(c_0_7093,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
c_0_5406,
[final] ).
cnf(c_0_7094,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
c_0_5407,
[final] ).
cnf(c_0_7095,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
c_0_5408,
[final] ).
cnf(c_0_7096,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
c_0_5409,
[final] ).
cnf(c_0_7097,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
c_0_5410,
[final] ).
cnf(c_0_7098,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
c_0_5411,
[final] ).
cnf(c_0_7099,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
c_0_5412,
[final] ).
cnf(c_0_7100,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
c_0_5413,
[final] ).
cnf(c_0_7101,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
c_0_5414,
[final] ).
cnf(c_0_7102,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
c_0_5415,
[final] ).
cnf(c_0_7103,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
c_0_5416,
[final] ).
cnf(c_0_7104,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
c_0_5417,
[final] ).
cnf(c_0_7105,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
c_0_5418,
[final] ).
cnf(c_0_7106,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
c_0_5419,
[final] ).
cnf(c_0_7107,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
c_0_5420,
[final] ).
cnf(c_0_7108,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
c_0_5421,
[final] ).
cnf(c_0_7109,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
c_0_5422,
[final] ).
cnf(c_0_7110,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
c_0_5423,
[final] ).
cnf(c_0_7111,plain,
class_Groups_Oone(tc_Int_Oint),
c_0_5424,
[final] ).
cnf(c_0_7112,plain,
class_Rings_Oring(tc_Int_Oint),
c_0_5425,
[final] ).
cnf(c_0_7113,plain,
class_Groups_Ozero(tc_Int_Oint),
c_0_5426,
[final] ).
cnf(c_0_7114,plain,
class_Power_Opower(tc_Int_Oint),
c_0_5427,
[final] ).
cnf(c_0_7115,plain,
class_Rings_Oring__1(tc_Int_Oint),
c_0_5428,
[final] ).
cnf(c_0_7116,plain,
class_Groups_Osgn__if(tc_Int_Oint),
c_0_5429,
[final] ).
cnf(c_0_7117,plain,
class_Orderings_Oord(tc_Int_Oint),
c_0_5430,
[final] ).
cnf(c_0_7118,plain,
class_Rings_Osemiring(tc_Int_Oint),
c_0_5431,
[final] ).
cnf(c_0_7119,plain,
class_Orderings_Oorder(tc_Int_Oint),
c_0_5432,
[final] ).
cnf(c_0_7120,plain,
class_Rings_Omult__zero(tc_Int_Oint),
c_0_5433,
[final] ).
cnf(c_0_7121,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
c_0_5434,
[final] ).
cnf(c_0_7122,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
c_0_5435,
[final] ).
cnf(c_0_7123,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
c_0_5436,
[final] ).
cnf(c_0_7124,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
c_0_5437,
[final] ).
cnf(c_0_7125,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
c_0_5438,
[final] ).
cnf(c_0_7126,plain,
class_Orderings_Olinorder(tc_Int_Oint),
c_0_5439,
[final] ).
cnf(c_0_7127,plain,
class_Orderings_Opreorder(tc_Int_Oint),
c_0_5440,
[final] ).
cnf(c_0_7128,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
c_0_5441,
[final] ).
cnf(c_0_7129,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
c_0_5442,
[final] ).
cnf(c_0_7130,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
c_0_5443,
[final] ).
cnf(c_0_7131,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
c_0_5444,
[final] ).
cnf(c_0_7132,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
c_0_5445,
[final] ).
cnf(c_0_7133,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
c_0_5446,
[final] ).
cnf(c_0_7134,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
c_0_5447,
[final] ).
cnf(c_0_7135,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
c_0_5448,
[final] ).
cnf(c_0_7136,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
c_0_5449,
[final] ).
cnf(c_0_7137,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
c_0_5450,
[final] ).
cnf(c_0_7138,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
c_0_5451,
[final] ).
cnf(c_0_7139,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
c_0_5452,
[final] ).
cnf(c_0_7140,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
c_0_5453,
[final] ).
cnf(c_0_7141,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
c_0_5454,
[final] ).
cnf(c_0_7142,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
c_0_5455,
[final] ).
cnf(c_0_7143,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
c_0_5456,
[final] ).
cnf(c_0_7144,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
c_0_5457,
[final] ).
cnf(c_0_7145,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
c_0_5458,
[final] ).
cnf(c_0_7146,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
c_0_5459,
[final] ).
cnf(c_0_7147,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
c_0_5460,
[final] ).
cnf(c_0_7148,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
c_0_5461,
[final] ).
cnf(c_0_7149,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
c_0_5462,
[final] ).
cnf(c_0_7150,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
c_0_5463,
[final] ).
cnf(c_0_7151,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
c_0_5464,
[final] ).
cnf(c_0_7152,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
c_0_5465,
[final] ).
cnf(c_0_7153,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
c_0_5466,
[final] ).
cnf(c_0_7154,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
c_0_5467,
[final] ).
cnf(c_0_7155,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
c_0_5468,
[final] ).
cnf(c_0_7156,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
c_0_5469,
[final] ).
cnf(c_0_7157,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
c_0_5470,
[final] ).
cnf(c_0_7158,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
c_0_5471,
[final] ).
cnf(c_0_7159,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
c_0_5472,
[final] ).
cnf(c_0_7160,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
c_0_5473,
[final] ).
cnf(c_0_7161,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
c_0_5474,
[final] ).
cnf(c_0_7162,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
c_0_5475,
[final] ).
cnf(c_0_7163,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
c_0_5476,
[final] ).
cnf(c_0_7164,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
c_0_5477,
[final] ).
cnf(c_0_7165,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
c_0_5478,
[final] ).
cnf(c_0_7166,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
c_0_5479,
[final] ).
cnf(c_0_7167,plain,
class_Rings_Oidom(tc_Int_Oint),
c_0_5480,
[final] ).
cnf(c_0_7168,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
c_0_5481,
[final] ).
cnf(c_0_7169,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
c_0_5482,
[final] ).
cnf(c_0_7170,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
c_0_5483,
[final] ).
cnf(c_0_7171,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
c_0_5484,
[final] ).
cnf(c_0_7172,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
c_0_5485,
[final] ).
cnf(c_0_7173,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
c_0_5486,
[final] ).
cnf(c_0_7174,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
c_0_5487,
[final] ).
cnf(c_0_7175,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_5488,
[final] ).
cnf(c_0_7176,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_5489,
[final] ).
cnf(c_0_7177,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
c_0_5490,
[final] ).
cnf(c_0_7178,plain,
c_SEQ_Osubseq(esk9_0),
c_0_5491,
[final] ).
cnf(c_0_7179,plain,
c_SEQ_Osubseq(v_ga____),
c_0_5492,
[final] ).
cnf(c_0_7180,plain,
c_SEQ_Osubseq(v_f____),
c_0_5493,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_5494_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5494_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5495_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4))
| ~ hBOOL(hAPP(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_esk67_4(X3,X5,X1,X2))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_1,axiom,
( ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4))
| ~ hBOOL(hAPP(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_esk67_4(X3,X5,X1,X2))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_2,axiom,
( ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4))
| ~ hBOOL(hAPP(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_esk67_4(X3,X5,X1,X2))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4))
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)))))
| ~ hBOOL(hAPP(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_esk67_4(X3,X5,X1,X2))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_4,axiom,
( ~ hBOOL(hAPP(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_esk67_4(X3,X5,X1,X2))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4))
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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_5495]) ).
cnf(c_0_5496_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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_5496]) ).
cnf(c_0_5496_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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_5496]) ).
cnf(c_0_5496_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5497_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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_5497]) ).
cnf(c_0_5497_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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_5497]) ).
cnf(c_0_5497_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5498_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5501_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(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_5501]) ).
cnf(c_0_5502_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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_5502]) ).
cnf(c_0_5502_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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_5502]) ).
cnf(c_0_5502_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(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_5502]) ).
cnf(c_0_5503_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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_5503]) ).
cnf(c_0_5504_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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_5504]) ).
cnf(c_0_5505_0,axiom,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk20_4(X3,X2,X4,X1)))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OBseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk20_4(X3,X2,X4,X1)))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk20_4(X3,X2,X4,X1)))),X3))
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5506_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(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_5506]) ).
cnf(c_0_5506_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(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_5506]) ).
cnf(c_0_5506_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5507_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(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_5507]) ).
cnf(c_0_5507_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(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_5507]) ).
cnf(c_0_5507_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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_5507]) ).
cnf(c_0_5508_0,axiom,
( c_SEQ_OBseq(X1,X2)
| ~ c_SEQ_OBseq(X1,c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_1,axiom,
( ~ c_SEQ_OBseq(X1,c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3)))
| c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_2,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3)))
| c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5509_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),hAPP(hAPP(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_5509]) ).
cnf(c_0_5509_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),hAPP(hAPP(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_5509]) ).
cnf(c_0_5509_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),hAPP(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5510_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),hAPP(hAPP(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_5510]) ).
cnf(c_0_5510_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),hAPP(hAPP(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_5510]) ).
cnf(c_0_5510_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),hAPP(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5511_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,sk1_esk2_4(X4,X3,X2,X1))),hAPP(X4,sk1_esk2_4(X4,X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_1,axiom,
( ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,sk1_esk2_4(X4,X3,X2,X1))),hAPP(X4,sk1_esk2_4(X4,X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,sk1_esk2_4(X4,X3,X2,X1))),hAPP(X4,sk1_esk2_4(X4,X3,X2,X1))))
| ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5512_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),hAPP(hAPP(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_5512]) ).
cnf(c_0_5512_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),hAPP(hAPP(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_5512]) ).
cnf(c_0_5512_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(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_5512]) ).
cnf(c_0_5513_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),hAPP(hAPP(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_5513]) ).
cnf(c_0_5513_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),hAPP(hAPP(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_5513]) ).
cnf(c_0_5513_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(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_5513]) ).
cnf(c_0_5514_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5514_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5)),X6)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5514_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(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_5514]) ).
cnf(c_0_5515_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5)),X6)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(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_5515]) ).
cnf(c_0_5517_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_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_5517]) ).
cnf(c_0_5517_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_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_5517]) ).
cnf(c_0_5518_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(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_5518]) ).
cnf(c_0_5518_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(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_5518]) ).
cnf(c_0_5518_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(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_5518]) ).
cnf(c_0_5519_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(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_5519]) ).
cnf(c_0_5519_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(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_5519]) ).
cnf(c_0_5519_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),hAPP(hAPP(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_5519]) ).
cnf(c_0_5520_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_esk24_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_5520]) ).
cnf(c_0_5520_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_esk24_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_5520]) ).
cnf(c_0_5520_2,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_esk24_2(X2,X1)),X2))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_5520]) ).
cnf(c_0_5521_0,axiom,
( c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X3)
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5521]) ).
cnf(c_0_5521_1,axiom,
( ~ c_SEQ_Oconvergent(X1,X3)
| c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5521]) ).
cnf(c_0_5521_2,axiom,
( ~ c_SEQ_Oconvergent(X1,X2)
| ~ c_SEQ_Oconvergent(X1,X3)
| c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5521]) ).
cnf(c_0_5521_3,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ c_SEQ_Oconvergent(X1,X3)
| c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5521]) ).
cnf(c_0_5522_0,axiom,
( c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X3)
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5522_1,axiom,
( ~ c_SEQ_Oconvergent(X1,X3)
| c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5522_2,axiom,
( ~ c_SEQ_Oconvergent(X1,X2)
| ~ c_SEQ_Oconvergent(X1,X3)
| c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(X1),X2),X3))
| ~ 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_SEQ_Oconvergent(X1,X2)
| ~ c_SEQ_Oconvergent(X1,X3)
| c_SEQ_Oconvergent(X1,c_COMBS(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5523_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5)))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5523]) ).
cnf(c_0_5523_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))) ),
inference(literals_permutation,[status(thm)],[c_0_5523]) ).
cnf(c_0_5524_0,axiom,
( c_SEQ_Oconvergent(X1,c_COMBC(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5524_1,axiom,
( ~ c_SEQ_Oconvergent(X1,X2)
| c_SEQ_Oconvergent(X1,c_COMBC(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5524_2,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_SEQ_Oconvergent(X1,X2)
| c_SEQ_Oconvergent(X1,c_COMBC(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5525_0,axiom,
( c_SEQ_Oconvergent(X1,c_COMBC(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X2)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5525_1,axiom,
( ~ c_SEQ_Oconvergent(X1,X2)
| c_SEQ_Oconvergent(X1,c_COMBC(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5525_2,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_Oconvergent(X1,X2)
| c_SEQ_Oconvergent(X1,c_COMBC(tc_Nat_Onat,X1,X1,c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5526_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_5526]) ).
cnf(c_0_5526_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_5526]) ).
cnf(c_0_5527_0,axiom,
( c_SEQ_OBseq(X1,c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3)))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5527_1,axiom,
( ~ c_SEQ_OBseq(X1,X2)
| c_SEQ_OBseq(X1,c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5527_2,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2)
| c_SEQ_OBseq(X1,c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5531_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X3,X5)),X6))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X6)),X5)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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),X4),X5))),X6)
| ~ class_RealVector_Oreal__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_1,axiom,
( ~ class_RealVector_Oreal__field(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X3,X5)),X6))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X6)),X5)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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),X4),X5))),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5532_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5)),hAPP(hAPP(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_5532]) ).
cnf(c_0_5532_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5)),hAPP(hAPP(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_5532]) ).
cnf(c_0_5532_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5)),hAPP(hAPP(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_5532]) ).
cnf(c_0_5532_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5)),hAPP(hAPP(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_5532]) ).
cnf(c_0_5532_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5533_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4)),hAPP(hAPP(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_5533]) ).
cnf(c_0_5533_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4)),hAPP(hAPP(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_5533]) ).
cnf(c_0_5533_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4)),hAPP(hAPP(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_5533]) ).
cnf(c_0_5533_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4)),hAPP(hAPP(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_5533]) ).
cnf(c_0_5533_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5534_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5535_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5536_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5536_1,axiom,
( ~ class_Rings_Olinordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5537_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5537_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5538_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X6) != hAPP(hAPP(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_5538]) ).
cnf(c_0_5538_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X6) != hAPP(hAPP(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_5538]) ).
cnf(c_0_5538_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X6) != hAPP(hAPP(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_5538]) ).
cnf(c_0_5538_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X6) != hAPP(hAPP(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_5538]) ).
cnf(c_0_5538_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X6) != hAPP(hAPP(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_5538]) ).
cnf(c_0_5538_5,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X6) != hAPP(hAPP(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_5538]) ).
cnf(c_0_5538_6,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X6) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5538]) ).
cnf(c_0_5540_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk44_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk43_3(X2,X1,X4)))),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk44_2(X2,X1)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk43_3(X2,X1,X4)))),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk43_3(X2,X1,X4)))),X4))
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk44_2(X2,X1)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk43_3(X2,X1,X4)))),X4))
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk44_2(X2,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5541_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk40_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk39_3(X2,X1,X4)))),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk40_2(X2,X1)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk39_3(X2,X1,X4)))),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk39_3(X2,X1,X4)))),X4))
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk40_2(X2,X1)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk39_3(X2,X1,X4)))),X4))
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk40_2(X2,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5542_0,axiom,
( hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_5542]) ).
cnf(c_0_5542_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(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)))
| hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_5542]) ).
cnf(c_0_5542_2,axiom,
( hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_5542]) ).
cnf(c_0_5542_3,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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)))
| hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(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_5542]) ).
cnf(c_0_5542_4,axiom,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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)))
| hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(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_5542]) ).
cnf(c_0_5543_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4))),sk1_esk46_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk45_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5543]) ).
cnf(c_0_5543_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4))),sk1_esk46_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk45_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5543]) ).
cnf(c_0_5543_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk45_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4))),sk1_esk46_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5543]) ).
cnf(c_0_5544_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4))),sk1_esk42_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk41_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5544_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4))),sk1_esk42_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk41_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5544_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk41_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X4))),sk1_esk42_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5545_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5545_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5545_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5545_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5545_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5545_5,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| ~ class_Rings_Olinordered__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5545_6,axiom,
( ~ class_Rings_Olinordered__semiring__1(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5546_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X6))
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_5,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))
| ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_6,axiom,
( ~ class_Rings_Olinordered__semiring__1__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != c_Groups_Oone__class_Oone(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5547_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk46_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk45_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5547]) ).
cnf(c_0_5547_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk46_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk45_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5547]) ).
cnf(c_0_5547_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk45_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk46_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5547]) ).
cnf(c_0_5548_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk42_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk41_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5548_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk42_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk41_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5548_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk41_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk42_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5549_0,axiom,
( c_SEQ_OBseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk19_3(X2,X3,X1)))),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk19_3(X2,X3,X1)))),X3))
| c_SEQ_OBseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk19_3(X2,X3,X1)))),X3))
| c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_3,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk19_3(X2,X3,X1)))),X3))
| c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5550_0,axiom,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk14_3(X2,X1,X3)))),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OBseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk14_3(X2,X1,X3)))),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk14_3(X2,X1,X3)))),X3))
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OBseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk14_3(X2,X1,X3)))),X3))
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5551_0,axiom,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk57_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OBseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk57_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk57_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5552_0,axiom,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk55_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OBseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk55_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,sk1_esk55_3(X2,X1,X3)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5553_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5554_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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_5554]) ).
cnf(c_0_5554_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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_5554]) ).
cnf(c_0_5554_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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_5554]) ).
cnf(c_0_5554_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(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_5554]) ).
cnf(c_0_5555_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),hAPP(hAPP(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,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5555_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X4))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),hAPP(hAPP(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,hAPP(hAPP(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_5555]) ).
cnf(c_0_5556_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),hAPP(hAPP(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,hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X1))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),hAPP(hAPP(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,hAPP(hAPP(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_5556]) ).
cnf(c_0_5557_0,axiom,
( hBOOL(hAPP(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_esk62_1(X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5557_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(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_esk62_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5558_0,axiom,
( hBOOL(hAPP(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_esk36_1(X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5558_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(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_esk36_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5559_0,axiom,
( hBOOL(hAPP(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_esk29_1(X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5559_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(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_esk29_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5560_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))
| ~ 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_5560]) ).
cnf(c_0_5560_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5560_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5560_3,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5561_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5) != hAPP(hAPP(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_5561]) ).
cnf(c_0_5561_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5) != hAPP(hAPP(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_5561]) ).
cnf(c_0_5561_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5) != hAPP(hAPP(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_5561]) ).
cnf(c_0_5561_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5) != hAPP(hAPP(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_5561]) ).
cnf(c_0_5561_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5) != hAPP(hAPP(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_5561]) ).
cnf(c_0_5561_5,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5) != hAPP(hAPP(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_5561]) ).
cnf(c_0_5561_6,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1)),X5) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X6)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X6),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5563_0,axiom,
( c_SEQ_Oconvergent(X1,c_COMBB(X1,X1,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_SEQ_Oconvergent(X1,X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_1,axiom,
( ~ c_SEQ_Oconvergent(X1,X3)
| c_SEQ_Oconvergent(X1,c_COMBB(X1,X1,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_2,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_Oconvergent(X1,X3)
| c_SEQ_Oconvergent(X1,c_COMBB(X1,X1,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5567_0,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),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_5567]) ).
cnf(c_0_5568_0,axiom,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,X1))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5568_1,axiom,
( ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,X1)
| c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5569_0,axiom,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,X1))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5569_1,axiom,
( ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,X1)
| c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5570_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5570_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5572_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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_5572]) ).
cnf(c_0_5572_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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_5572]) ).
cnf(c_0_5573_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5574_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| ~ class_Rings_Oring(X1)
| X4 != hAPP(hAPP(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_5574]) ).
cnf(c_0_5574_1,axiom,
( ~ class_Rings_Oring(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| X4 != hAPP(hAPP(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_5574]) ).
cnf(c_0_5574_2,axiom,
( X4 != hAPP(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5574]) ).
cnf(c_0_5575_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| ~ class_Rings_Oring(X1)
| hAPP(hAPP(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_5575]) ).
cnf(c_0_5575_1,axiom,
( ~ class_Rings_Oring(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| hAPP(hAPP(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_5575]) ).
cnf(c_0_5575_2,axiom,
( hAPP(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5576_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X4 != hAPP(hAPP(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_5576]) ).
cnf(c_0_5576_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)
| X4 != hAPP(hAPP(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_5576]) ).
cnf(c_0_5576_2,axiom,
( X4 != hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4) = hAPP(hAPP(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_5576]) ).
cnf(c_0_5577_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5577]) ).
cnf(c_0_5577_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)
| hAPP(hAPP(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_5577]) ).
cnf(c_0_5577_2,axiom,
( hAPP(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = hAPP(hAPP(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_5577]) ).
cnf(c_0_5578_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),sk1_esk68_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5578]) ).
cnf(c_0_5578_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),sk1_esk68_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5578]) ).
cnf(c_0_5578_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),sk1_esk68_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5578]) ).
cnf(c_0_5578_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),sk1_esk68_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5578]) ).
cnf(c_0_5579_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),sk1_esk68_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5579_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),sk1_esk68_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5579_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),sk1_esk68_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5579_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4))),sk1_esk68_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5580_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5580]) ).
cnf(c_0_5580_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5580]) ).
cnf(c_0_5581_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5581_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5581_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4))
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5583_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),sk1_esk67_4(X3,X5,X1,X2)))
| ~ class_Orderings_Oord(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5583_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),sk1_esk67_4(X3,X5,X1,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5583_2,axiom,
( ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),sk1_esk67_4(X3,X5,X1,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5583_3,axiom,
( ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),sk1_esk67_4(X3,X5,X1,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5583_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),X4))
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X5),sk1_esk67_4(X3,X5,X1,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4))),hAPP(hAPP(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_5583]) ).
cnf(c_0_5585_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5585_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5585_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),X4))
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5586_0,axiom,
( X2 = hAPP(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5586]) ).
cnf(c_0_5586_1,axiom,
( ~ class_Rings_Oring(X1)
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5)),X6)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5586]) ).
cnf(c_0_5586_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6)
| ~ class_Rings_Oring(X1)
| X2 = hAPP(hAPP(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_5586]) ).
cnf(c_0_5587_0,axiom,
( hAPP(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5587_1,axiom,
( ~ class_Rings_Oring(X1)
| hAPP(hAPP(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
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5587_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)
| ~ class_Rings_Oring(X1)
| hAPP(hAPP(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_5587]) ).
cnf(c_0_5588_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sk1_esk59_2(X2,X1))),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5588_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sk1_esk59_2(X2,X1))),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5588_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sk1_esk59_2(X2,X1))),X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5589_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X3)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X4))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5589_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X3)),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X4))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5589_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X3)),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5589_3,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X3)),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5590_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(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_5590]) ).
cnf(c_0_5590_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(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_5590]) ).
cnf(c_0_5590_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(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_5590]) ).
cnf(c_0_5590_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(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_5590]) ).
cnf(c_0_5591_0,axiom,
( X3 = hAPP(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3) != hAPP(hAPP(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_5591]) ).
cnf(c_0_5591_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4)),X5)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3) != hAPP(hAPP(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_5591]) ).
cnf(c_0_5591_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X4)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5591]) ).
cnf(c_0_5592_0,axiom,
( hAPP(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) != hAPP(hAPP(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_5592]) ).
cnf(c_0_5592_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4) = X5
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) != hAPP(hAPP(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_5592]) ).
cnf(c_0_5592_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3)),X4) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_5592]) ).
cnf(c_0_5593_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Rings_Osemiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5593]) ).
cnf(c_0_5593_1,axiom,
( ~ class_Rings_Osemiring(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5593]) ).
cnf(c_0_5594_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(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_5594]) ).
cnf(c_0_5594_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_5594]) ).
cnf(c_0_5594_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5594]) ).
cnf(c_0_5594_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5594]) ).
cnf(c_0_5595_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| ~ hBOOL(hAPP(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_5595]) ).
cnf(c_0_5595_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_5595]) ).
cnf(c_0_5595_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| hBOOL(hAPP(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_5595]) ).
cnf(c_0_5595_3,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| hBOOL(hAPP(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_5595]) ).
cnf(c_0_5596_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| ~ hBOOL(hAPP(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_5596]) ).
cnf(c_0_5596_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X5)))
| ~ hBOOL(hAPP(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_5596]) ).
cnf(c_0_5596_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X5)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5596]) ).
cnf(c_0_5596_3,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3)),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5596]) ).
cnf(c_0_5597_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk71_3(X3,X2,X1))),X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5597]) ).
cnf(c_0_5597_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk71_3(X3,X2,X1))),X2))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5597]) ).
cnf(c_0_5597_2,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk71_3(X3,X2,X1))),X2))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5597]) ).
cnf(c_0_5598_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk71_3(X3,X2,X1))),X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5598_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk71_3(X3,X2,X1))),X2))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5598_2,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk71_3(X3,X2,X1))),X2))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5599_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk59_2(X2,X1)))),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5599]) ).
cnf(c_0_5599_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk59_2(X2,X1)))),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5599]) ).
cnf(c_0_5599_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk59_2(X2,X1)))),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5599]) ).
cnf(c_0_5601_0,axiom,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5601_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5601_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5602_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5602]) ).
cnf(c_0_5602_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5602]) ).
cnf(c_0_5603_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5603]) ).
cnf(c_0_5603_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5603]) ).
cnf(c_0_5603_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5603]) ).
cnf(c_0_5604_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5604_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5604_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5605_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(sk1_esk71_3(X3,X2,X1)))))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5605]) ).
cnf(c_0_5605_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(sk1_esk71_3(X3,X2,X1)))))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5605]) ).
cnf(c_0_5605_2,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(sk1_esk71_3(X3,X2,X1)))))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5605]) ).
cnf(c_0_5606_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5606_1,axiom,
( ~ class_Rings_Olinordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5607_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),hAPP(hAPP(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_5607]) ).
cnf(c_0_5607_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))),hAPP(hAPP(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_5607]) ).
cnf(c_0_5608_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5608_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5609_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(sk1_esk71_3(X3,X2,X1)))))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5609]) ).
cnf(c_0_5609_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(sk1_esk71_3(X3,X2,X1)))))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5609]) ).
cnf(c_0_5609_2,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(sk1_esk71_3(X3,X2,X1)))))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5609]) ).
cnf(c_0_5610_0,axiom,
( hBOOL(hAPP(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_esk63_2(X2,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5610]) ).
cnf(c_0_5610_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(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_esk63_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5610]) ).
cnf(c_0_5611_0,axiom,
( hBOOL(hAPP(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_esk61_2(X3,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5611]) ).
cnf(c_0_5611_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(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_esk61_2(X3,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5611]) ).
cnf(c_0_5612_0,axiom,
( hBOOL(hAPP(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_esk38_2(X3,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5612]) ).
cnf(c_0_5612_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(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_esk38_2(X3,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5612]) ).
cnf(c_0_5613_0,axiom,
( hBOOL(hAPP(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_esk37_2(X2,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5613]) ).
cnf(c_0_5613_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(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_esk37_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5613]) ).
cnf(c_0_5614_0,axiom,
( hBOOL(hAPP(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_esk31_2(X3,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5614]) ).
cnf(c_0_5614_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(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_esk31_2(X3,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5614]) ).
cnf(c_0_5615_0,axiom,
( hBOOL(hAPP(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_esk30_2(X2,X1))))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5615]) ).
cnf(c_0_5615_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(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_esk30_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5615]) ).
cnf(c_0_5616_0,axiom,
( hBOOL(hAPP(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_5616]) ).
cnf(c_0_5616_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(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_5616]) ).
cnf(c_0_5617_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(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,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5618_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5618_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5618_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ class_Fields_Olinordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5618_4,axiom,
( ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5619_0,axiom,
( hAPP(hAPP(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_5619]) ).
cnf(c_0_5619_1,axiom,
( ~ class_Rings_Oring(X1)
| hAPP(hAPP(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_5619]) ).
cnf(c_0_5620_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_4,axiom,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5621_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5621]) ).
cnf(c_0_5621_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(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_5621]) ).
cnf(c_0_5621_2,axiom,
( ~ hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5621_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5623_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5623]) ).
cnf(c_0_5623_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5623]) ).
cnf(c_0_5624_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_5624]) ).
cnf(c_0_5624_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_5624]) ).
cnf(c_0_5624_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(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_5624]) ).
cnf(c_0_5624_3,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5624]) ).
cnf(c_0_5625_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_5625]) ).
cnf(c_0_5625_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_5625]) ).
cnf(c_0_5625_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(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_5625]) ).
cnf(c_0_5625_3,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5626_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(X4))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_1,axiom,
( ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(X4))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(X4))))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Nat_OSuc(X4))))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5627_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5627_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5628_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5628_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5629_0,axiom,
( hBOOL(hAPP(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_5629]) ).
cnf(c_0_5629_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(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_5629]) ).
cnf(c_0_5630_0,axiom,
( hBOOL(hAPP(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_5630]) ).
cnf(c_0_5630_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| hBOOL(hAPP(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_5630]) ).
cnf(c_0_5631_0,axiom,
( hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5631_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5632_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5632]) ).
cnf(c_0_5632_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(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_5632]) ).
cnf(c_0_5632_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5632]) ).
cnf(c_0_5632_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5632]) ).
cnf(c_0_5633_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_5633]) ).
cnf(c_0_5633_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(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_5633]) ).
cnf(c_0_5633_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5633_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5634_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_5634]) ).
cnf(c_0_5634_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(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_5634]) ).
cnf(c_0_5634_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5634_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5635_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_5635]) ).
cnf(c_0_5635_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(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_5635]) ).
cnf(c_0_5635_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5635_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5636_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_5636]) ).
cnf(c_0_5636_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(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_5636]) ).
cnf(c_0_5636_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Rings_Olinordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5636_3,axiom,
( ~ class_Rings_Olinordered__semiring(X1)
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5637_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_5637]) ).
cnf(c_0_5637_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(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_5637]) ).
cnf(c_0_5637_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5637]) ).
cnf(c_0_5637_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5637]) ).
cnf(c_0_5638_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(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_5638]) ).
cnf(c_0_5638_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(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_5638]) ).
cnf(c_0_5638_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Rings_Olinordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5638]) ).
cnf(c_0_5638_3,axiom,
( ~ class_Rings_Olinordered__semiring(X1)
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5638]) ).
cnf(c_0_5639_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5639]) ).
cnf(c_0_5639_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5639]) ).
cnf(c_0_5639_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(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_5639]) ).
cnf(c_0_5639_3,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5639]) ).
cnf(c_0_5640_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5640]) ).
cnf(c_0_5640_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5640]) ).
cnf(c_0_5640_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(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_5640]) ).
cnf(c_0_5640_3,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5640]) ).
cnf(c_0_5641_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(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_5641]) ).
cnf(c_0_5641_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(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_5641]) ).
cnf(c_0_5641_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ hBOOL(hAPP(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_5641]) ).
cnf(c_0_5641_3,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5641]) ).
cnf(c_0_5642_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_5642]) ).
cnf(c_0_5642_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_5642]) ).
cnf(c_0_5642_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3)),X4))
| ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5642]) ).
cnf(c_0_5642_3,axiom,
( ~ class_Rings_Olinordered__semidom(X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3)),X4))
| ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5642]) ).
cnf(c_0_5643_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_5643]) ).
cnf(c_0_5643_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_5643]) ).
cnf(c_0_5643_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3)),X4))
| ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5643]) ).
cnf(c_0_5643_3,axiom,
( ~ class_Rings_Olinordered__semidom(X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3)),X4))
| ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5643]) ).
cnf(c_0_5644_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(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_5644]) ).
cnf(c_0_5644_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(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_5644]) ).
cnf(c_0_5644_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ hBOOL(hAPP(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_5644]) ).
cnf(c_0_5644_3,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5644]) ).
cnf(c_0_5645_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5645]) ).
cnf(c_0_5645_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5645]) ).
cnf(c_0_5645_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(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_5645]) ).
cnf(c_0_5645_3,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5645]) ).
cnf(c_0_5646_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5646]) ).
cnf(c_0_5646_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5646]) ).
cnf(c_0_5646_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(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_5646]) ).
cnf(c_0_5646_3,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5647_0,axiom,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5648_0,axiom,
( X2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5649_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5650_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5650]) ).
cnf(c_0_5650_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5650]) ).
cnf(c_0_5650_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5650]) ).
cnf(c_0_5650_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5651_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5651]) ).
cnf(c_0_5651_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5651]) ).
cnf(c_0_5651_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5651]) ).
cnf(c_0_5651_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5651]) ).
cnf(c_0_5653_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5653]) ).
cnf(c_0_5653_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5653]) ).
cnf(c_0_5653_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5653]) ).
cnf(c_0_5653_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5653]) ).
cnf(c_0_5653_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5653]) ).
cnf(c_0_5653_5,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5653]) ).
cnf(c_0_5654_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5654]) ).
cnf(c_0_5654_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5654]) ).
cnf(c_0_5654_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5654]) ).
cnf(c_0_5654_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5654]) ).
cnf(c_0_5654_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5654]) ).
cnf(c_0_5654_5,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5654]) ).
cnf(c_0_5655_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5655]) ).
cnf(c_0_5655_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5655]) ).
cnf(c_0_5655_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5655]) ).
cnf(c_0_5655_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5655]) ).
cnf(c_0_5655_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5655]) ).
cnf(c_0_5655_5,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5655]) ).
cnf(c_0_5656_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5656]) ).
cnf(c_0_5656_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5656]) ).
cnf(c_0_5656_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5656]) ).
cnf(c_0_5656_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5656]) ).
cnf(c_0_5656_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5656]) ).
cnf(c_0_5656_5,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5656]) ).
cnf(c_0_5657_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5657_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5657_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5657_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5657_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5657]) ).
cnf(c_0_5657_5,axiom,
( ~ class_Rings_Oordered__semiring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5657]) ).
cnf(c_0_5658_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5658]) ).
cnf(c_0_5658_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5658]) ).
cnf(c_0_5658_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5658]) ).
cnf(c_0_5658_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5658]) ).
cnf(c_0_5658_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5658]) ).
cnf(c_0_5658_5,axiom,
( ~ class_Rings_Oordered__semiring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5658]) ).
cnf(c_0_5659_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5659]) ).
cnf(c_0_5659_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5659]) ).
cnf(c_0_5659_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5659]) ).
cnf(c_0_5659_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5659]) ).
cnf(c_0_5660_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5660]) ).
cnf(c_0_5660_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5660]) ).
cnf(c_0_5660_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5660]) ).
cnf(c_0_5660_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5661_0,axiom,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(sk1_esk52_2(X2,X1)))),hAPP(X2,sk1_esk52_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5661]) ).
cnf(c_0_5661_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SEQ_Omonoseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(sk1_esk52_2(X2,X1)))),hAPP(X2,sk1_esk52_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5661]) ).
cnf(c_0_5661_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(sk1_esk52_2(X2,X1)))),hAPP(X2,sk1_esk52_2(X2,X1))))
| ~ class_Orderings_Oorder(X1)
| c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5661]) ).
cnf(c_0_5662_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sk1_esk66_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5662]) ).
cnf(c_0_5662_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sk1_esk66_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5662]) ).
cnf(c_0_5663_0,axiom,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_5663]) ).
cnf(c_0_5663_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_5663]) ).
cnf(c_0_5663_2,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_5663]) ).
cnf(c_0_5664_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5664]) ).
cnf(c_0_5664_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5664]) ).
cnf(c_0_5664_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(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_5664]) ).
cnf(c_0_5664_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5664]) ).
cnf(c_0_5665_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5665]) ).
cnf(c_0_5665_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5665]) ).
cnf(c_0_5665_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(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_5665]) ).
cnf(c_0_5665_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5665]) ).
cnf(c_0_5666_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_5666]) ).
cnf(c_0_5666_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5666]) ).
cnf(c_0_5667_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_5667]) ).
cnf(c_0_5667_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5668_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5668]) ).
cnf(c_0_5668_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5668]) ).
cnf(c_0_5668_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(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_5668]) ).
cnf(c_0_5668_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5669_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5669]) ).
cnf(c_0_5669_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5669]) ).
cnf(c_0_5669_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(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_5669]) ).
cnf(c_0_5669_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5670_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5672_0,axiom,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5673_0,axiom,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3
| ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5673_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5673_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5674_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_5674]) ).
cnf(c_0_5674_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(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_5674]) ).
cnf(c_0_5674_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5675_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_5675]) ).
cnf(c_0_5675_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(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_5675]) ).
cnf(c_0_5675_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5676_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5676_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5676_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5677_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(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_5677]) ).
cnf(c_0_5677_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_5677]) ).
cnf(c_0_5677_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5677]) ).
cnf(c_0_5678_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(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_5678]) ).
cnf(c_0_5678_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_5678]) ).
cnf(c_0_5678_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5679_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(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_5679]) ).
cnf(c_0_5679_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(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_5679]) ).
cnf(c_0_5679_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5679]) ).
cnf(c_0_5680_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(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_5680]) ).
cnf(c_0_5680_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(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_5680]) ).
cnf(c_0_5680_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5680]) ).
cnf(c_0_5681_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(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_5681]) ).
cnf(c_0_5681_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(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_5681]) ).
cnf(c_0_5681_2,axiom,
( ~ hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5682_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5683_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5684_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5685_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5686_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| hBOOL(hAPP(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_5686]) ).
cnf(c_0_5686_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5687_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5687]) ).
cnf(c_0_5687_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| hBOOL(hAPP(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_5687]) ).
cnf(c_0_5687_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5687]) ).
cnf(c_0_5688_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5688_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5688_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5689_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5689_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5689_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5690_0,axiom,
( X2 = X3
| X4 = X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_1,axiom,
( X4 = X5
| X2 = X3
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_2,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X4 = X5
| X2 = X3
| hAPP(hAPP(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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_3,axiom,
( hAPP(hAPP(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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X4 = X5
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5691_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_1,axiom,
( X2 = X4
| X3 = X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_2,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X4
| X3 = X5
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_3,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X4
| X3 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5692_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5692_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5692_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5692_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5692]) ).
cnf(c_0_5692_4,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5692]) ).
cnf(c_0_5693_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5693]) ).
cnf(c_0_5693_4,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5693]) ).
cnf(c_0_5694_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5694_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5694_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5694_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(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_5694]) ).
cnf(c_0_5694_4,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(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_5694]) ).
cnf(c_0_5695_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5696_0,axiom,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5697_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(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_5697]) ).
cnf(c_0_5697_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(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_5697]) ).
cnf(c_0_5697_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(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_5697]) ).
cnf(c_0_5697_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5698_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(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_5698]) ).
cnf(c_0_5699_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5700_0,axiom,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk51_2(X2,X1))),hAPP(X2,c_Nat_OSuc(sk1_esk51_2(X2,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SEQ_Omonoseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk51_2(X2,X1))),hAPP(X2,c_Nat_OSuc(sk1_esk51_2(X2,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk51_2(X2,X1))),hAPP(X2,c_Nat_OSuc(sk1_esk51_2(X2,X1)))))
| ~ class_Orderings_Oorder(X1)
| c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5701_0,axiom,
( c_SEQ_OBseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),sk1_esk20_4(X4,X2,X3,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5701_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),sk1_esk20_4(X4,X2,X3,X1)))
| c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5701_2,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),sk1_esk20_4(X4,X2,X3,X1)))
| c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5702_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5702_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5702_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5703_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5703_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5703_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5703_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(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_5703]) ).
cnf(c_0_5704_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5704_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5704_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5704_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(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_5704]) ).
cnf(c_0_5705_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5705]) ).
cnf(c_0_5705_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5705]) ).
cnf(c_0_5706_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(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_5706]) ).
cnf(c_0_5706_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5706]) ).
cnf(c_0_5707_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_5707]) ).
cnf(c_0_5707_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5707]) ).
cnf(c_0_5708_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk69_3(X3,X2,X1))),sk1_esk70_3(X3,X2,X1)) = X2
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk69_3(X3,X2,X1))),sk1_esk70_3(X3,X2,X1)) = X2
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_2,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk69_3(X3,X2,X1))),sk1_esk70_3(X3,X2,X1)) = X2
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5709_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_5709]) ).
cnf(c_0_5709_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5710_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(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_5710]) ).
cnf(c_0_5710_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5711_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5711_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5712_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5712_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5713_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(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_5713]) ).
cnf(c_0_5713_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5714_0,axiom,
( c_RComplete_Onatceiling(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5714]) ).
cnf(c_0_5714_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| c_RComplete_Onatceiling(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5714]) ).
cnf(c_0_5714_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| c_RComplete_Onatceiling(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_5714]) ).
cnf(c_0_5715_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5715]) ).
cnf(c_0_5715_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5715]) ).
cnf(c_0_5715_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5715]) ).
cnf(c_0_5715_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5715]) ).
cnf(c_0_5716_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk69_3(X3,X2,X1))),sk1_esk70_3(X3,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5716_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk69_3(X3,X2,X1))),sk1_esk70_3(X3,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5716_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),sk1_esk69_3(X3,X2,X1))),sk1_esk70_3(X3,X2,X1)) = X2
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5717_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5717_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5717_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5718_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_5718]) ).
cnf(c_0_5718_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2))
| ~ hBOOL(hAPP(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_5718]) ).
cnf(c_0_5718_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5718]) ).
cnf(c_0_5719_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5719]) ).
cnf(c_0_5719_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5719]) ).
cnf(c_0_5719_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_5719]) ).
cnf(c_0_5719_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_5719]) ).
cnf(c_0_5720_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5720]) ).
cnf(c_0_5720_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5720]) ).
cnf(c_0_5720_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5720]) ).
cnf(c_0_5720_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5720]) ).
cnf(c_0_5721_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__comm__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5721_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__comm__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5721_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_5721]) ).
cnf(c_0_5721_3,axiom,
( ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_5721]) ).
cnf(c_0_5722_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5722]) ).
cnf(c_0_5722_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5722]) ).
cnf(c_0_5722_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_5722]) ).
cnf(c_0_5722_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_5722]) ).
cnf(c_0_5723_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5723]) ).
cnf(c_0_5723_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5723]) ).
cnf(c_0_5723_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5723]) ).
cnf(c_0_5723_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5723]) ).
cnf(c_0_5724_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5724]) ).
cnf(c_0_5724_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5724]) ).
cnf(c_0_5724_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5724]) ).
cnf(c_0_5724_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5724]) ).
cnf(c_0_5725_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5725]) ).
cnf(c_0_5725_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5725]) ).
cnf(c_0_5725_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5725]) ).
cnf(c_0_5725_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5725]) ).
cnf(c_0_5726_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5726]) ).
cnf(c_0_5726_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5726]) ).
cnf(c_0_5726_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5726]) ).
cnf(c_0_5726_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5726]) ).
cnf(c_0_5727_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Oordered__comm__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5727]) ).
cnf(c_0_5727_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Oordered__comm__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5727]) ).
cnf(c_0_5727_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_5727]) ).
cnf(c_0_5727_3,axiom,
( ~ class_Rings_Oordered__comm__semiring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_5727]) ).
cnf(c_0_5728_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5728]) ).
cnf(c_0_5728_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5728]) ).
cnf(c_0_5728_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_5728]) ).
cnf(c_0_5728_3,axiom,
( ~ class_Rings_Oordered__semiring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_5728]) ).
cnf(c_0_5729_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5729]) ).
cnf(c_0_5729_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Rings_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5729]) ).
cnf(c_0_5729_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5729]) ).
cnf(c_0_5729_3,axiom,
( ~ class_Rings_Oordered__semiring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5729]) ).
cnf(c_0_5730_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5730]) ).
cnf(c_0_5730_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5730]) ).
cnf(c_0_5730_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5730]) ).
cnf(c_0_5730_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5730]) ).
cnf(c_0_5731_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5731]) ).
cnf(c_0_5731_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5731]) ).
cnf(c_0_5731_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5731]) ).
cnf(c_0_5731_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5731]) ).
cnf(c_0_5732_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5732]) ).
cnf(c_0_5732_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5732]) ).
cnf(c_0_5732_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5732]) ).
cnf(c_0_5733_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5733]) ).
cnf(c_0_5733_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5733]) ).
cnf(c_0_5734_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sk1_esk47_2(X2,X1))),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5734]) ).
cnf(c_0_5734_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sk1_esk47_2(X2,X1))),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5734]) ).
cnf(c_0_5735_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5735]) ).
cnf(c_0_5735_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5735]) ).
cnf(c_0_5736_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5736]) ).
cnf(c_0_5736_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5736]) ).
cnf(c_0_5736_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_5736]) ).
cnf(c_0_5736_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_5736]) ).
cnf(c_0_5737_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5737]) ).
cnf(c_0_5737_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5737]) ).
cnf(c_0_5737_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5737]) ).
cnf(c_0_5737_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(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_5737]) ).
cnf(c_0_5738_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5738]) ).
cnf(c_0_5738_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5738]) ).
cnf(c_0_5738_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_5738]) ).
cnf(c_0_5738_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_5738]) ).
cnf(c_0_5739_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5739]) ).
cnf(c_0_5739_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5739]) ).
cnf(c_0_5739_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5739]) ).
cnf(c_0_5739_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(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_5739]) ).
cnf(c_0_5740_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5740]) ).
cnf(c_0_5740_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5740]) ).
cnf(c_0_5740_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5740]) ).
cnf(c_0_5740_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5740]) ).
cnf(c_0_5741_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5741]) ).
cnf(c_0_5741_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5741]) ).
cnf(c_0_5741_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3))
| ~ hBOOL(hAPP(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_5741]) ).
cnf(c_0_5741_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5741]) ).
cnf(c_0_5741_4,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5741]) ).
cnf(c_0_5742_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5742]) ).
cnf(c_0_5742_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5742]) ).
cnf(c_0_5742_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2))
| ~ hBOOL(hAPP(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_5742]) ).
cnf(c_0_5742_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5742]) ).
cnf(c_0_5742_4,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5742]) ).
cnf(c_0_5743_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5743]) ).
cnf(c_0_5743_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5743]) ).
cnf(c_0_5743_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5743]) ).
cnf(c_0_5743_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5743]) ).
cnf(c_0_5744_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5744]) ).
cnf(c_0_5744_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5744]) ).
cnf(c_0_5744_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5744]) ).
cnf(c_0_5744_3,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5744]) ).
cnf(c_0_5745_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5745]) ).
cnf(c_0_5745_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5745]) ).
cnf(c_0_5745_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5745]) ).
cnf(c_0_5745_3,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5745]) ).
cnf(c_0_5746_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5746_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5746_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5746_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5746]) ).
cnf(c_0_5747_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5747_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5747_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5747_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5747]) ).
cnf(c_0_5748_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5748]) ).
cnf(c_0_5748_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5748]) ).
cnf(c_0_5748_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5748]) ).
cnf(c_0_5748_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5748]) ).
cnf(c_0_5749_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5749]) ).
cnf(c_0_5749_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5749]) ).
cnf(c_0_5749_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5749]) ).
cnf(c_0_5749_3,axiom,
( ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5749]) ).
cnf(c_0_5750_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5750_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
| ~ class_Rings_Oordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5750_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5750]) ).
cnf(c_0_5750_3,axiom,
( ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5750]) ).
cnf(c_0_5751_0,axiom,
( c_RComplete_Onatfloor(X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5751_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| c_RComplete_Onatfloor(X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5751_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| c_RComplete_Onatfloor(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5752_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5752_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))
| hBOOL(hAPP(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_5752]) ).
cnf(c_0_5753_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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5753]) ).
cnf(c_0_5753_1,axiom,
( ~ hBOOL(hAPP(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_5753]) ).
cnf(c_0_5753_2,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| ~ hBOOL(hAPP(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_5753]) ).
cnf(c_0_5754_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5754_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5754_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5754_3,axiom,
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5755_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5755_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5755_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5755_3,axiom,
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5756_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5756_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5756_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5756_3,axiom,
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5757_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5757_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5757_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5757_3,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5758_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5758_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5758_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5759_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5759_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5759_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5760_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5760_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5760_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5761_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5761]) ).
cnf(c_0_5761_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5761]) ).
cnf(c_0_5761_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5761]) ).
cnf(c_0_5762_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5762]) ).
cnf(c_0_5762_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5762]) ).
cnf(c_0_5762_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5762]) ).
cnf(c_0_5763_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5763_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5763_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(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_5763]) ).
cnf(c_0_5764_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5764]) ).
cnf(c_0_5764_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X1))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5764]) ).
cnf(c_0_5764_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X1))
| hBOOL(hAPP(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_5764]) ).
cnf(c_0_5765_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5765_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5766_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_5766]) ).
cnf(c_0_5766_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_5766]) ).
cnf(c_0_5767_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5767_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5767_2,axiom,
( X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5767_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5767_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5767_5,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5767_6,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5768_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ hBOOL(hAPP(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_5768]) ).
cnf(c_0_5768_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(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_5768]) ).
cnf(c_0_5768_2,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5768]) ).
cnf(c_0_5769_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ hBOOL(hAPP(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_5769]) ).
cnf(c_0_5769_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(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_5769]) ).
cnf(c_0_5769_2,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5770_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5770_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5770_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk74_3(X3,X2,X1))),sk1_esk75_3(X3,X2,X1)) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5771_0,axiom,
( epred1_3(X1,X2,X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5771_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5771_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sk1_esk72_3(X3,X2,X1))),sk1_esk73_3(X3,X2,X1)) = X3
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5773_0,axiom,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_5773]) ).
cnf(c_0_5773_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_5773]) ).
cnf(c_0_5773_2,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_5773]) ).
cnf(c_0_5774_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)
| ~ hBOOL(hAPP(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_5774]) ).
cnf(c_0_5774_1,axiom,
( ~ hBOOL(hAPP(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_5774]) ).
cnf(c_0_5774_2,axiom,
( ~ class_Groups_Omonoid__mult(X1)
| ~ hBOOL(hAPP(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_5774]) ).
cnf(c_0_5775_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5775_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| hBOOL(hAPP(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_5775]) ).
cnf(c_0_5776_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5777_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5778_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5779_0,axiom,
( hBOOL(hAPP(X1,X4))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_2,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,X4))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_3,axiom,
( X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X5)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5),X3))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X5)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5780_0,axiom,
( c_SEQ_Oincseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk15_2(X2,X1))),hAPP(X2,sk1_esk16_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SEQ_Oincseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk15_2(X2,X1))),hAPP(X2,sk1_esk16_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk15_2(X2,X1))),hAPP(X2,sk1_esk16_2(X2,X1))))
| ~ class_Orderings_Oorder(X1)
| c_SEQ_Oincseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5781_0,axiom,
( c_SEQ_Odecseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk12_2(X2,X1))),hAPP(X2,sk1_esk11_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SEQ_Odecseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk12_2(X2,X1))),hAPP(X2,sk1_esk11_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk12_2(X2,X1))),hAPP(X2,sk1_esk11_2(X2,X1))))
| ~ class_Orderings_Oorder(X1)
| c_SEQ_Odecseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5782_0,axiom,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk5_2(X2,X1))),hAPP(X2,sk1_esk6_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SEQ_Omonoseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk5_2(X2,X1))),hAPP(X2,sk1_esk6_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk5_2(X2,X1))),hAPP(X2,sk1_esk6_2(X2,X1))))
| ~ class_Orderings_Oorder(X1)
| c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5783_0,axiom,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk8_2(X2,X1))),hAPP(X2,sk1_esk7_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5783_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SEQ_Omonoseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk8_2(X2,X1))),hAPP(X2,sk1_esk7_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5783_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,sk1_esk8_2(X2,X1))),hAPP(X2,sk1_esk7_2(X2,X1))))
| ~ class_Orderings_Oorder(X1)
| c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5784_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5784_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(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_5784]) ).
cnf(c_0_5785_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5785_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(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_5785]) ).
cnf(c_0_5786_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
| ~ hBOOL(hAPP(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_5786]) ).
cnf(c_0_5786_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5787_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(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_5787]) ).
cnf(c_0_5787_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_5787]) ).
cnf(c_0_5787_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5787]) ).
cnf(c_0_5787_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5787]) ).
cnf(c_0_5788_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5788_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5788_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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_5788]) ).
cnf(c_0_5789_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5789_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5789_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(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_5789]) ).
cnf(c_0_5790_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5790_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5790_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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_5790]) ).
cnf(c_0_5791_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(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_5791]) ).
cnf(c_0_5792_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(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_5792]) ).
cnf(c_0_5793_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5793_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5793_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| hBOOL(hAPP(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_5793]) ).
cnf(c_0_5794_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5794_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5794_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(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_5794]) ).
cnf(c_0_5795_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5795_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5795_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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_5795]) ).
cnf(c_0_5796_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(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_5796]) ).
cnf(c_0_5797_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(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_5797]) ).
cnf(c_0_5798_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5798]) ).
cnf(c_0_5798_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5798]) ).
cnf(c_0_5798_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(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_5798]) ).
cnf(c_0_5799_0,axiom,
( hBOOL(hAPP(X1,X4))
| ~ epred1_3(X1,X2,X3)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5799_1,axiom,
( ~ epred1_3(X1,X2,X3)
| hBOOL(hAPP(X1,X4))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5799_2,axiom,
( X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ epred1_3(X1,X2,X3)
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5799_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X2))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ epred1_3(X1,X2,X3)
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5799_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X2))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ epred1_3(X1,X2,X3)
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5799_5,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X5),X2))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ epred1_3(X1,X2,X3)
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5800_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_5800]) ).
cnf(c_0_5800_1,axiom,
( ~ hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_5800]) ).
cnf(c_0_5800_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(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_5800]) ).
cnf(c_0_5800_3,axiom,
( ~ class_RealVector_Oreal__normed__vector(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(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_5800]) ).
cnf(c_0_5801_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5801]) ).
cnf(c_0_5801_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5801]) ).
cnf(c_0_5801_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5801]) ).
cnf(c_0_5802_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(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_5802]) ).
cnf(c_0_5802_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))),X2))
| ~ hBOOL(hAPP(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_5802]) ).
cnf(c_0_5802_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5802]) ).
cnf(c_0_5802_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(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_5802]) ).
cnf(c_0_5803_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(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_5803]) ).
cnf(c_0_5803_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5803]) ).
cnf(c_0_5804_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(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_5804]) ).
cnf(c_0_5804_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5805_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5805_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5805_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5806_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5806_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X4))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5806_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X4))
| hBOOL(hAPP(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_5806]) ).
cnf(c_0_5807_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5808_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5808_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5808_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5809_0,axiom,
( hBOOL(hAPP(X1,X4))
| ~ epred1_3(X1,X2,X3)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5809_1,axiom,
( ~ epred1_3(X1,X2,X3)
| hBOOL(hAPP(X1,X4))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5809_2,axiom,
( X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ epred1_3(X1,X2,X3)
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5809_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ epred1_3(X1,X2,X3)
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5809_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ epred1_3(X1,X2,X3)
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5809_5,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X5)
| ~ epred1_3(X1,X2,X3)
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5810_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5810_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5810_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5811_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5811]) ).
cnf(c_0_5811_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5811]) ).
cnf(c_0_5811_2,axiom,
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5811]) ).
cnf(c_0_5812_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5812_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5812_2,axiom,
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5813_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5813]) ).
cnf(c_0_5813_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5813]) ).
cnf(c_0_5813_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5813]) ).
cnf(c_0_5814_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5814]) ).
cnf(c_0_5814_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5814]) ).
cnf(c_0_5814_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5814]) ).
cnf(c_0_5815_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5815_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5815_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5816_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5816_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5816_2,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5817_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5817_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5817_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5818_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5818_1,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5818_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5820_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5820]) ).
cnf(c_0_5820_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5820]) ).
cnf(c_0_5820_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5820]) ).
cnf(c_0_5820_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5820]) ).
cnf(c_0_5821_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5821]) ).
cnf(c_0_5821_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5821]) ).
cnf(c_0_5821_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5821]) ).
cnf(c_0_5821_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5821]) ).
cnf(c_0_5822_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5822]) ).
cnf(c_0_5822_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5822]) ).
cnf(c_0_5822_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5822]) ).
cnf(c_0_5822_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5822]) ).
cnf(c_0_5823_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_Oordered__cancel__semiring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| hBOOL(hAPP(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_5823]) ).
cnf(c_0_5824_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_Oordered__cancel__semiring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| hBOOL(hAPP(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_5824]) ).
cnf(c_0_5825_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5825]) ).
cnf(c_0_5825_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5825]) ).
cnf(c_0_5825_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5825]) ).
cnf(c_0_5825_3,axiom,
( ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5825]) ).
cnf(c_0_5826_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5826]) ).
cnf(c_0_5826_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5826]) ).
cnf(c_0_5826_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5826]) ).
cnf(c_0_5826_3,axiom,
( ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5826]) ).
cnf(c_0_5827_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5827]) ).
cnf(c_0_5827_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5827]) ).
cnf(c_0_5827_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5827]) ).
cnf(c_0_5827_3,axiom,
( ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5827]) ).
cnf(c_0_5828_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5828_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5828_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5828_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5828]) ).
cnf(c_0_5829_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5829]) ).
cnf(c_0_5830_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5830_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))))
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5830_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))))
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5831_0,axiom,
( epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5831_1,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1)))
| epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5831_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1)))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5832_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5832_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5833_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5833_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| hBOOL(hAPP(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_5833]) ).
cnf(c_0_5834_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5834_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(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_5834]) ).
cnf(c_0_5835_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_2,axiom,
( X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_5,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X4),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5836_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5836]) ).
cnf(c_0_5836_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5836]) ).
cnf(c_0_5836_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5836_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5837_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5837]) ).
cnf(c_0_5837_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5837]) ).
cnf(c_0_5837_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5837_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5838_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5838]) ).
cnf(c_0_5838_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5838]) ).
cnf(c_0_5838_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5838_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5839_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5839]) ).
cnf(c_0_5839_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5839]) ).
cnf(c_0_5839_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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_5839]) ).
cnf(c_0_5839_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5841_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(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_5841]) ).
cnf(c_0_5841_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5842_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk70_3(X3,X2,X1)),X3))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5842]) ).
cnf(c_0_5842_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk70_3(X3,X2,X1)),X3))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5842]) ).
cnf(c_0_5842_2,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk70_3(X3,X2,X1)),X3))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5842]) ).
cnf(c_0_5843_0,axiom,
( ~ hBOOL(hAPP(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_5843]) ).
cnf(c_0_5843_1,axiom,
( ~ class_Rings_Olinordered__ring(X1)
| ~ hBOOL(hAPP(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_5843]) ).
cnf(c_0_5844_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5844]) ).
cnf(c_0_5844_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5844]) ).
cnf(c_0_5844_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5844]) ).
cnf(c_0_5844_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5844]) ).
cnf(c_0_5845_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5845]) ).
cnf(c_0_5845_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5845]) ).
cnf(c_0_5845_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5845]) ).
cnf(c_0_5845_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5846_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5846]) ).
cnf(c_0_5846_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5846]) ).
cnf(c_0_5846_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5846]) ).
cnf(c_0_5847_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5847_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5847_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5848_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5848_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5848_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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_5848]) ).
cnf(c_0_5849_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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_5849]) ).
cnf(c_0_5849_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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_5849]) ).
cnf(c_0_5849_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5849]) ).
cnf(c_0_5850_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(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_5850]) ).
cnf(c_0_5850_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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_5850]) ).
cnf(c_0_5850_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5850]) ).
cnf(c_0_5851_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5851]) ).
cnf(c_0_5851_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5851]) ).
cnf(c_0_5851_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5851]) ).
cnf(c_0_5852_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5852_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5852_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5853_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5853]) ).
cnf(c_0_5853_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5853]) ).
cnf(c_0_5853_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5853]) ).
cnf(c_0_5854_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5854]) ).
cnf(c_0_5854_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5854]) ).
cnf(c_0_5855_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5855]) ).
cnf(c_0_5855_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5855]) ).
cnf(c_0_5856_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5856]) ).
cnf(c_0_5856_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5856]) ).
cnf(c_0_5857_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5857_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5858_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5858_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5859_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5859_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5860_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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5860]) ).
cnf(c_0_5860_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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5860]) ).
cnf(c_0_5861_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5861_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5861_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5861_3,axiom,
( X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5861_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5861_5,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5862_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X5)),hAPP(X2,X6)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X6))
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5862]) ).
cnf(c_0_5862_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X5)),hAPP(X2,X6)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X6))
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5862]) ).
cnf(c_0_5862_2,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X5)),hAPP(X2,X6)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X6))
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5862]) ).
cnf(c_0_5862_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X5)),hAPP(X2,X6)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X6))
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5862]) ).
cnf(c_0_5862_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X5)),hAPP(X2,X6)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5862]) ).
cnf(c_0_5862_5,axiom,
( ~ c_SEQ_Omonoseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X6))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X5)),hAPP(X2,X6)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5862]) ).
cnf(c_0_5863_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk70_3(X3,X2,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5863]) ).
cnf(c_0_5863_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk70_3(X3,X2,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5863]) ).
cnf(c_0_5863_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk70_3(X3,X2,X1)),X3))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5863]) ).
cnf(c_0_5864_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5864]) ).
cnf(c_0_5864_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5864]) ).
cnf(c_0_5864_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5864]) ).
cnf(c_0_5865_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5865]) ).
cnf(c_0_5865_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5865]) ).
cnf(c_0_5866_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5866]) ).
cnf(c_0_5866_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5866]) ).
cnf(c_0_5867_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5867]) ).
cnf(c_0_5867_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(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_5867]) ).
cnf(c_0_5868_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5868]) ).
cnf(c_0_5868_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(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_5868]) ).
cnf(c_0_5869_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5869]) ).
cnf(c_0_5869_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(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_5869]) ).
cnf(c_0_5870_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5870_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(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_5870]) ).
cnf(c_0_5871_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5871_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5872_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5872_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5873_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5873]) ).
cnf(c_0_5873_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5873]) ).
cnf(c_0_5874_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5874_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5875_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5875_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5876_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5876_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5876_2,axiom,
( X2 != X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5877_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5877_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| X3 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5877_2,axiom,
( X3 != X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5878_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5878_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5878_2,axiom,
( X2 != X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5879_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5879]) ).
cnf(c_0_5879_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| X3 != X5 ),
inference(literals_permutation,[status(thm)],[c_0_5879]) ).
cnf(c_0_5879_2,axiom,
( X3 != X5
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5879]) ).
cnf(c_0_5880_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5880]) ).
cnf(c_0_5880_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1)))
| epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5880]) ).
cnf(c_0_5880_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1)))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5880]) ).
cnf(c_0_5881_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_5881]) ).
cnf(c_0_5881_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_5881]) ).
cnf(c_0_5882_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_5882]) ).
cnf(c_0_5882_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_5882]) ).
cnf(c_0_5883_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5883]) ).
cnf(c_0_5883_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5883]) ).
cnf(c_0_5884_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2)),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5884]) ).
cnf(c_0_5884_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2)),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5884]) ).
cnf(c_0_5884_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2)),X1)))
| X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5884]) ).
cnf(c_0_5891_0,axiom,
( hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5891]) ).
cnf(c_0_5891_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(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_5891]) ).
cnf(c_0_5892_0,axiom,
( hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5892_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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_5892]) ).
cnf(c_0_5893_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(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_5893]) ).
cnf(c_0_5893_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_5893]) ).
cnf(c_0_5893_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| hBOOL(hAPP(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_5893]) ).
cnf(c_0_5894_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(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_5894]) ).
cnf(c_0_5894_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_5894]) ).
cnf(c_0_5894_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| hBOOL(hAPP(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_5894]) ).
cnf(c_0_5895_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(X1,sk1_esk65_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5895]) ).
cnf(c_0_5895_1,axiom,
( hBOOL(hAPP(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_esk65_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5895]) ).
cnf(c_0_5895_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk65_3(X3,X2,X1)))
| hBOOL(hAPP(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_5895]) ).
cnf(c_0_5896_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(X1,sk1_esk64_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5896]) ).
cnf(c_0_5896_1,axiom,
( hBOOL(hAPP(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_esk64_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5896]) ).
cnf(c_0_5896_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk64_3(X3,X2,X1)))
| hBOOL(hAPP(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_5896]) ).
cnf(c_0_5897_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5897]) ).
cnf(c_0_5897_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5897]) ).
cnf(c_0_5897_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5897]) ).
cnf(c_0_5897_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5897]) ).
cnf(c_0_5898_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5898]) ).
cnf(c_0_5898_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5898]) ).
cnf(c_0_5898_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_5898]) ).
cnf(c_0_5898_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5898]) ).
cnf(c_0_5899_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5899]) ).
cnf(c_0_5899_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5899]) ).
cnf(c_0_5899_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5899]) ).
cnf(c_0_5899_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5900_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5900]) ).
cnf(c_0_5900_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(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_5900]) ).
cnf(c_0_5900_2,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5900]) ).
cnf(c_0_5900_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5901_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk56_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5901_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk56_2(X2,X1)))))
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5901_2,axiom,
( ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk56_2(X2,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5902_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk54_2(X2,X1)))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5902]) ).
cnf(c_0_5902_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk54_2(X2,X1)))))
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5902]) ).
cnf(c_0_5902_2,axiom,
( ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk54_2(X2,X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_5902]) ).
cnf(c_0_5903_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5903]) ).
cnf(c_0_5903_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5903]) ).
cnf(c_0_5903_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5903]) ).
cnf(c_0_5903_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(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_5903]) ).
cnf(c_0_5904_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(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,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5904]) ).
cnf(c_0_5904_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(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,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5904]) ).
cnf(c_0_5904_2,axiom,
( ~ hBOOL(hAPP(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,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5904]) ).
cnf(c_0_5905_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(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_5905]) ).
cnf(c_0_5905_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(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_5905]) ).
cnf(c_0_5905_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5905]) ).
cnf(c_0_5908_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5908]) ).
cnf(c_0_5908_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5908]) ).
cnf(c_0_5908_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5908]) ).
cnf(c_0_5909_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(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_5909]) ).
cnf(c_0_5909_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(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_5909]) ).
cnf(c_0_5909_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5909]) ).
cnf(c_0_5910_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,sk1_esk69_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5910]) ).
cnf(c_0_5910_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,sk1_esk69_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5910]) ).
cnf(c_0_5910_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk69_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5910]) ).
cnf(c_0_5911_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_esk65_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5911]) ).
cnf(c_0_5911_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_esk65_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5911]) ).
cnf(c_0_5911_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk65_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_5911]) ).
cnf(c_0_5912_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_esk64_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5912]) ).
cnf(c_0_5912_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_esk64_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5912]) ).
cnf(c_0_5912_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk64_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_5912]) ).
cnf(c_0_5913_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5913]) ).
cnf(c_0_5913_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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_5913]) ).
cnf(c_0_5914_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5914]) ).
cnf(c_0_5914_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5914]) ).
cnf(c_0_5914_2,axiom,
( ~ hBOOL(hAPP(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,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5914]) ).
cnf(c_0_5915_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_2,axiom,
( ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5916_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5916_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5918_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5918]) ).
cnf(c_0_5918_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
| X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5918]) ).
cnf(c_0_5918_2,axiom,
( X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5918]) ).
cnf(c_0_5919_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5919_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5919_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5920_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5920_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5920_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5921_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5921_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5921_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5922_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5922]) ).
cnf(c_0_5922_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5922]) ).
cnf(c_0_5922_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| hBOOL(hAPP(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_5922]) ).
cnf(c_0_5923_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5923_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5923_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| hBOOL(hAPP(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_5923]) ).
cnf(c_0_5924_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,sk1_esk71_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5924]) ).
cnf(c_0_5924_1,axiom,
( hBOOL(hAPP(X1,sk1_esk71_3(X3,X2,X1)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5924]) ).
cnf(c_0_5924_2,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,sk1_esk71_3(X3,X2,X1)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_5924]) ).
cnf(c_0_5925_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X3))
| ~ hBOOL(hAPP(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_5925]) ).
cnf(c_0_5925_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(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_5925]) ).
cnf(c_0_5925_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X3))
| hBOOL(hAPP(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_5925]) ).
cnf(c_0_5925_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X3))
| hBOOL(hAPP(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_5925]) ).
cnf(c_0_5926_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5926]) ).
cnf(c_0_5926_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(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_5926]) ).
cnf(c_0_5926_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5926]) ).
cnf(c_0_5926_3,axiom,
( ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5926]) ).
cnf(c_0_5927_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5927]) ).
cnf(c_0_5927_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5927]) ).
cnf(c_0_5927_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5927]) ).
cnf(c_0_5927_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(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_5927]) ).
cnf(c_0_5928_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5928]) ).
cnf(c_0_5928_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(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_5928]) ).
cnf(c_0_5928_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5928]) ).
cnf(c_0_5928_3,axiom,
( ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(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_5928]) ).
cnf(c_0_5929_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5929_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5929_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5929_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5929]) ).
cnf(c_0_5930_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5930]) ).
cnf(c_0_5930_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(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_5930]) ).
cnf(c_0_5930_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5930]) ).
cnf(c_0_5930_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5930]) ).
cnf(c_0_5931_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5931]) ).
cnf(c_0_5931_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(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_5931]) ).
cnf(c_0_5931_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5931]) ).
cnf(c_0_5931_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5931]) ).
cnf(c_0_5932_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5932]) ).
cnf(c_0_5932_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(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_5932]) ).
cnf(c_0_5932_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5932]) ).
cnf(c_0_5932_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5932]) ).
cnf(c_0_5933_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_5933]) ).
cnf(c_0_5933_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(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_5933]) ).
cnf(c_0_5933_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5933]) ).
cnf(c_0_5933_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5933]) ).
cnf(c_0_5934_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5934]) ).
cnf(c_0_5934_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5934]) ).
cnf(c_0_5934_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk75_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5934]) ).
cnf(c_0_5935_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(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_5935]) ).
cnf(c_0_5935_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(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_5935]) ).
cnf(c_0_5935_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| hBOOL(hAPP(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_5935]) ).
cnf(c_0_5936_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(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_5936]) ).
cnf(c_0_5936_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(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_5936]) ).
cnf(c_0_5936_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| hBOOL(hAPP(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_5936]) ).
cnf(c_0_5937_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X2))
| ~ hBOOL(hAPP(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_5937]) ).
cnf(c_0_5937_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X2))
| ~ hBOOL(hAPP(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_5937]) ).
cnf(c_0_5937_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| X1 = X2
| ~ hBOOL(hAPP(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_5937]) ).
cnf(c_0_5937_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X2))
| ~ hBOOL(hAPP(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_5937]) ).
cnf(c_0_5937_4,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X4),X1),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X2))
| ~ hBOOL(hAPP(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_5937]) ).
cnf(c_0_5937_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X2))
| ~ hBOOL(hAPP(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_5937]) ).
cnf(c_0_5938_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5938_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5938_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5938_3,axiom,
( ~ class_Fields_Ofield(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5939_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5939]) ).
cnf(c_0_5939_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5939]) ).
cnf(c_0_5939_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5939]) ).
cnf(c_0_5940_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5940_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5940_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5940_3,axiom,
( X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5940_4,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5941_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5941]) ).
cnf(c_0_5941_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_5941]) ).
cnf(c_0_5941_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk73_3(X3,X2,X1)),X2))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5941]) ).
cnf(c_0_5942_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),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_5942]) ).
cnf(c_0_5942_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Ominus__class_Ominus(X1,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5942]) ).
cnf(c_0_5943_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5943]) ).
cnf(c_0_5943_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4)
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5943]) ).
cnf(c_0_5943_2,axiom,
( ~ class_Fields_Ofield(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5943]) ).
cnf(c_0_5944_0,axiom,
( c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5944]) ).
cnf(c_0_5944_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5944]) ).
cnf(c_0_5944_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5944]) ).
cnf(c_0_5945_0,axiom,
( hAPP(hAPP(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_5945]) ).
cnf(c_0_5945_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(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_5945]) ).
cnf(c_0_5946_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,sk1_esk69_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5946]) ).
cnf(c_0_5946_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,sk1_esk69_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5946]) ).
cnf(c_0_5946_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk69_3(X3,X2,X1)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5946]) ).
cnf(c_0_5947_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ hBOOL(hAPP(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_5947]) ).
cnf(c_0_5947_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(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_5947]) ).
cnf(c_0_5947_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(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_5947]) ).
cnf(c_0_5947_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| hBOOL(hAPP(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_5947]) ).
cnf(c_0_5948_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5948]) ).
cnf(c_0_5948_1,axiom,
( ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5948]) ).
cnf(c_0_5949_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5949]) ).
cnf(c_0_5949_1,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5949]) ).
cnf(c_0_5950_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5950]) ).
cnf(c_0_5950_1,axiom,
( ~ class_Fields_Ofield__inverse__zero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5950]) ).
cnf(c_0_5951_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_5951]) ).
cnf(c_0_5951_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_5951]) ).
cnf(c_0_5952_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5952]) ).
cnf(c_0_5952_1,axiom,
( ~ class_Rings_Ocomm__semiring(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5952]) ).
cnf(c_0_5953_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5953]) ).
cnf(c_0_5953_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5953]) ).
cnf(c_0_5954_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5954]) ).
cnf(c_0_5954_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5954]) ).
cnf(c_0_5955_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5955]) ).
cnf(c_0_5955_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5955]) ).
cnf(c_0_5956_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5956]) ).
cnf(c_0_5956_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5956]) ).
cnf(c_0_5957_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_5957]) ).
cnf(c_0_5957_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_5957]) ).
cnf(c_0_5958_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,sk1_esk71_3(X3,X2,X1)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5958_1,axiom,
( hBOOL(hAPP(X1,sk1_esk71_3(X3,X2,X1)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5958_2,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,sk1_esk71_3(X3,X2,X1)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5959_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5959_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(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_5959]) ).
cnf(c_0_5960_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5960_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(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_5960]) ).
cnf(c_0_5962_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5962]) ).
cnf(c_0_5962_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(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_5962]) ).
cnf(c_0_5962_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5962]) ).
cnf(c_0_5962_3,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5962]) ).
cnf(c_0_5963_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5963]) ).
cnf(c_0_5963_1,axiom,
( ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5963]) ).
cnf(c_0_5963_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5963]) ).
cnf(c_0_5963_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__ring(X1)
| hBOOL(hAPP(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_5963]) ).
cnf(c_0_5964_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(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_5964]) ).
cnf(c_0_5964_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(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_5964]) ).
cnf(c_0_5964_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5964]) ).
cnf(c_0_5964_3,axiom,
( ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(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_5964]) ).
cnf(c_0_5965_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5965_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5965_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5965_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| hBOOL(hAPP(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_5965]) ).
cnf(c_0_5966_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5966]) ).
cnf(c_0_5966_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(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_5966]) ).
cnf(c_0_5968_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(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_5968]) ).
cnf(c_0_5968_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(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_5968]) ).
cnf(c_0_5969_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(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_5969]) ).
cnf(c_0_5969_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(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_5969]) ).
cnf(c_0_5970_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5970]) ).
cnf(c_0_5970_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5970]) ).
cnf(c_0_5970_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5970]) ).
cnf(c_0_5971_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5971]) ).
cnf(c_0_5971_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5971]) ).
cnf(c_0_5971_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5971]) ).
cnf(c_0_5972_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5972]) ).
cnf(c_0_5972_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5972]) ).
cnf(c_0_5972_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(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_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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(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_5973_1,axiom,
( ~ hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_5973_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(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_5973]) ).
cnf(c_0_5974_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5974_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5974_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5975_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5975_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5975_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5976_0,axiom,
( ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5976_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5976_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5977_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(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_5977]) ).
cnf(c_0_5977_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(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_5977]) ).
cnf(c_0_5977_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5977_3,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5978_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(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_5978]) ).
cnf(c_0_5978_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(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_5978]) ).
cnf(c_0_5978_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5978_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5979_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(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_5979]) ).
cnf(c_0_5979_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(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_5979]) ).
cnf(c_0_5979_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5979]) ).
cnf(c_0_5979_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5979]) ).
cnf(c_0_5980_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(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_5980]) ).
cnf(c_0_5980_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(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_5980]) ).
cnf(c_0_5980_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5980]) ).
cnf(c_0_5980_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5980]) ).
cnf(c_0_5981_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(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_5981]) ).
cnf(c_0_5981_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(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_5981]) ).
cnf(c_0_5981_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5981]) ).
cnf(c_0_5981_3,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5981]) ).
cnf(c_0_5982_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5982_1,axiom,
( ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5982_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5982_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5984_0,axiom,
( c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5984_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5984_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5985_0,axiom,
( c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5985]) ).
cnf(c_0_5985_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5985]) ).
cnf(c_0_5985_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5985]) ).
cnf(c_0_5986_0,axiom,
( c_Nat_OSuc(hAPP(hAPP(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)) = hAPP(hAPP(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_5986]) ).
cnf(c_0_5986_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5986]) ).
cnf(c_0_5987_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5987]) ).
cnf(c_0_5987_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5987]) ).
cnf(c_0_5987_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5987]) ).
cnf(c_0_5988_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5988]) ).
cnf(c_0_5988_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5988]) ).
cnf(c_0_5988_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5988]) ).
cnf(c_0_5989_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5989]) ).
cnf(c_0_5989_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(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_5989]) ).
cnf(c_0_5990_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5990]) ).
cnf(c_0_5990_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(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_5990]) ).
cnf(c_0_5991_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(X3))),hAPP(X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4)),hAPP(X2,c_Nat_OSuc(X4))))
| ~ class_Orderings_Oorder(X1)
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4)),hAPP(X2,c_Nat_OSuc(X4))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(X3))),hAPP(X2,X3)))
| ~ class_Orderings_Oorder(X1)
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_2,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4)),hAPP(X2,c_Nat_OSuc(X4))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(X3))),hAPP(X2,X3)))
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_3,axiom,
( ~ c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4)),hAPP(X2,c_Nat_OSuc(X4))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(X3))),hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5992_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(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_5992]) ).
cnf(c_0_5993_0,axiom,
( hBOOL(hAPP(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,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5993_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(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,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5993_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(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,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5994_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(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_5994]) ).
cnf(c_0_5994_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_5994]) ).
cnf(c_0_5994_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(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_5994]) ).
cnf(c_0_5995_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(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_5995]) ).
cnf(c_0_5995_1,axiom,
( ~ class_Rings_Oring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(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_5995]) ).
cnf(c_0_5996_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5996_1,axiom,
( ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5996_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5996_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5997_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5997_1,axiom,
( ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5997_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5997_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5998_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5998_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5998_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5998_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3))
| hBOOL(hAPP(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_5998]) ).
cnf(c_0_5999_0,axiom,
( c_SEQ_Osubseq(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,sk1_esk53_1(X1))),hAPP(X1,c_Nat_OSuc(sk1_esk53_1(X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_5999]) ).
cnf(c_0_5999_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,sk1_esk53_1(X1))),hAPP(X1,c_Nat_OSuc(sk1_esk53_1(X1)))))
| c_SEQ_Osubseq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5999]) ).
cnf(c_0_6000_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6000_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6000_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6001_0,axiom,
( hBOOL(hAPP(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,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(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,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(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,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6002_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6002_1,axiom,
( ~ hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6002_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(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_6002]) ).
cnf(c_0_6003_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6003_1,axiom,
( ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6003_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6003_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__ring__abs(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6005_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6005_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6005_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6006_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(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_6006]) ).
cnf(c_0_6006_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(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_6006]) ).
cnf(c_0_6006_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6007_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(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_6007]) ).
cnf(c_0_6007_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_6007]) ).
cnf(c_0_6007_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(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_6007]) ).
cnf(c_0_6008_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6008_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6008_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(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_6008]) ).
cnf(c_0_6009_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6009_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6009_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(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_6009]) ).
cnf(c_0_6010_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6010_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6014_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk68_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6014_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk68_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6014_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk68_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6015_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(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_6015]) ).
cnf(c_0_6015_1,axiom,
( ~ hBOOL(hAPP(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))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6015]) ).
cnf(c_0_6016_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_6016]) ).
cnf(c_0_6016_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6016]) ).
cnf(c_0_6017_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6017_1,axiom,
( ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6017_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6018_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_2,axiom,
( ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6019_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6019_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3)))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6019_2,axiom,
( ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1),X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6020_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6020_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6020_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6021_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6021_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6021_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6022_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6022]) ).
cnf(c_0_6022_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6022]) ).
cnf(c_0_6023_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6023]) ).
cnf(c_0_6023_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(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_6023]) ).
cnf(c_0_6026_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),c_Divides_Odiv__class_Odiv(X1,X2,X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6026_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),c_Divides_Odiv__class_Odiv(X1,X2,X3))
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6026_2,axiom,
( ~ class_Divides_Osemiring__div(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),c_Divides_Odiv__class_Odiv(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6027_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Divides_Odiv__class_Odiv(X1,X2,X4))
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6027]) ).
cnf(c_0_6027_1,axiom,
( X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Divides_Odiv__class_Odiv(X1,X2,X4))
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6027]) ).
cnf(c_0_6027_2,axiom,
( ~ class_Divides_Osemiring__div(X1)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Divides_Odiv__class_Odiv(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6027]) ).
cnf(c_0_6028_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6028]) ).
cnf(c_0_6028_1,axiom,
( ~ class_Rings_Odivision__ring(X1)
| c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6028]) ).
cnf(c_0_6029_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6029]) ).
cnf(c_0_6029_1,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6029]) ).
cnf(c_0_6030_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_6030]) ).
cnf(c_0_6030_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_6030]) ).
cnf(c_0_6031_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_6031]) ).
cnf(c_0_6031_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_6031]) ).
cnf(c_0_6032_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6032_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6032_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6032_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6033_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6033_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6033_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6033_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6034_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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6034]) ).
cnf(c_0_6034_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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6034]) ).
cnf(c_0_6034_2,axiom,
( ~ hBOOL(hAPP(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_6034]) ).
cnf(c_0_6035_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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6035]) ).
cnf(c_0_6035_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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6035]) ).
cnf(c_0_6035_2,axiom,
( ~ hBOOL(hAPP(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_6035]) ).
cnf(c_0_6036_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3)),X2))
| ~ hBOOL(hAPP(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_6036]) ).
cnf(c_0_6036_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3)),X2))
| X1 = X2
| ~ hBOOL(hAPP(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_6036]) ).
cnf(c_0_6036_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3)),X1))
| ~ hBOOL(hAPP(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_6036]) ).
cnf(c_0_6036_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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3)),X1))
| ~ hBOOL(hAPP(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_6036]) ).
cnf(c_0_6036_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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3)),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6036]) ).
cnf(c_0_6037_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6037_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6037_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6038_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6038_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6038_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk74_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6039_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6039]) ).
cnf(c_0_6039_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6039]) ).
cnf(c_0_6040_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6040_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6040_2,axiom,
( ~ hBOOL(hAPP(X1,sk1_esk72_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6041_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6041]) ).
cnf(c_0_6041_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6041]) ).
cnf(c_0_6042_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6042]) ).
cnf(c_0_6042_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6042]) ).
cnf(c_0_6043_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6043]) ).
cnf(c_0_6043_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6043]) ).
cnf(c_0_6044_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_6044]) ).
cnf(c_0_6044_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_6044]) ).
cnf(c_0_6045_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6045]) ).
cnf(c_0_6045_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6045]) ).
cnf(c_0_6047_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6047]) ).
cnf(c_0_6047_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X1))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6047]) ).
cnf(c_0_6048_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6048_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3),X2) = hAPP(hAPP(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_6048]) ).
cnf(c_0_6050_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sk1_esk21_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6050]) ).
cnf(c_0_6050_1,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sk1_esk21_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6050]) ).
cnf(c_0_6050_2,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sk1_esk21_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6050]) ).
cnf(c_0_6051_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_6051]) ).
cnf(c_0_6051_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_6051]) ).
cnf(c_0_6051_2,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6051]) ).
cnf(c_0_6052_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(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_6052]) ).
cnf(c_0_6052_1,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_6052]) ).
cnf(c_0_6052_2,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(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_6052]) ).
cnf(c_0_6053_0,axiom,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(X1,sk1_esk22_1(X1))),hAPP(X1,sk1_esk23_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_6053]) ).
cnf(c_0_6053_1,axiom,
( ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1)
| c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(X1,sk1_esk22_1(X1))),hAPP(X1,sk1_esk23_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_6053]) ).
cnf(c_0_6053_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(X1,sk1_esk22_1(X1))),hAPP(X1,sk1_esk23_1(X1))))
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1)
| c_SEQ_Oconvergent(tc_RealDef_Oreal,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6053]) ).
cnf(c_0_6054_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(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,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6054]) ).
cnf(c_0_6054_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6054]) ).
cnf(c_0_6054_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6054]) ).
cnf(c_0_6055_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6055]) ).
cnf(c_0_6055_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6055]) ).
cnf(c_0_6055_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6055]) ).
cnf(c_0_6055_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6055]) ).
cnf(c_0_6056_0,axiom,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_6056]) ).
cnf(c_0_6056_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_6056]) ).
cnf(c_0_6056_2,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_6056]) ).
cnf(c_0_6057_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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_6057]) ).
cnf(c_0_6057_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6057]) ).
cnf(c_0_6058_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(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_6058]) ).
cnf(c_0_6058_1,axiom,
( ~ hBOOL(hAPP(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)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6058]) ).
cnf(c_0_6059_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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6059]) ).
cnf(c_0_6059_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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6059]) ).
cnf(c_0_6060_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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6060]) ).
cnf(c_0_6060_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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6060]) ).
cnf(c_0_6061_0,axiom,
( X3 = sk1_esk34_2(X2,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6061_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X3 = sk1_esk34_2(X2,X1)
| ~ hBOOL(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6061_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X3 = sk1_esk34_2(X2,X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X1) != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6061_3,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X1) != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X3 = sk1_esk34_2(X2,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6061_4,axiom,
( ~ hBOOL(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X3 = sk1_esk34_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6062_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6062]) ).
cnf(c_0_6062_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2))))
| X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6062]) ).
cnf(c_0_6062_2,axiom,
( X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_6062]) ).
cnf(c_0_6063_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(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_6063]) ).
cnf(c_0_6063_1,axiom,
( hAPP(hAPP(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_6063]) ).
cnf(c_0_6064_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(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_6064]) ).
cnf(c_0_6064_1,axiom,
( hAPP(hAPP(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_6064]) ).
cnf(c_0_6065_0,axiom,
( X4 = X6
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(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_6065]) ).
cnf(c_0_6065_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| X4 = X6
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(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_6065]) ).
cnf(c_0_6065_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(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_6065]) ).
cnf(c_0_6065_3,axiom,
( X2 != X5
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(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_6065]) ).
cnf(c_0_6065_4,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 != X5
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(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_6065]) ).
cnf(c_0_6067_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_6067]) ).
cnf(c_0_6067_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| hBOOL(hAPP(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_6067]) ).
cnf(c_0_6068_0,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(literals_permutation,[status(thm)],[c_0_6068]) ).
cnf(c_0_6068_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(literals_permutation,[status(thm)],[c_0_6068]) ).
cnf(c_0_6068_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6068]) ).
cnf(c_0_6069_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(literals_permutation,[status(thm)],[c_0_6069]) ).
cnf(c_0_6069_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6069]) ).
cnf(c_0_6072_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6072]) ).
cnf(c_0_6072_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6072]) ).
cnf(c_0_6072_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_RComplete_Onatfloor(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6072]) ).
cnf(c_0_6075_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(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_6075]) ).
cnf(c_0_6075_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_6075]) ).
cnf(c_0_6075_2,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),X2))
| hBOOL(hAPP(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_6075]) ).
cnf(c_0_6076_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(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_6076]) ).
cnf(c_0_6076_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_6076]) ).
cnf(c_0_6076_2,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_6076]) ).
cnf(c_0_6077_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ hBOOL(hAPP(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_6077]) ).
cnf(c_0_6077_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_6077]) ).
cnf(c_0_6077_2,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(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_6077]) ).
cnf(c_0_6078_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6078_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6078_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6079_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6079_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6079_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6080_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6080]) ).
cnf(c_0_6080_1,axiom,
( ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6080]) ).
cnf(c_0_6080_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1),X3),X4))
| ~ class_Orderings_Oord(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6080]) ).
cnf(c_0_6081_0,axiom,
( c_SEQ_Osubseq(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,sk1_esk3_1(X1))),hAPP(X1,sk1_esk4_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_6081]) ).
cnf(c_0_6081_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,sk1_esk3_1(X1))),hAPP(X1,sk1_esk4_1(X1))))
| c_SEQ_Osubseq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6081]) ).
cnf(c_0_6082_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6082]) ).
cnf(c_0_6082_1,axiom,
( ~ class_Fields_Ofield__inverse__zero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6082]) ).
cnf(c_0_6083_0,axiom,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6083]) ).
cnf(c_0_6083_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,X4))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6083]) ).
cnf(c_0_6083_2,axiom,
( X2 != hAPP(hAPP(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_6083]) ).
cnf(c_0_6084_0,axiom,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6084_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,X4))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6084_2,axiom,
( X2 != hAPP(hAPP(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_6084]) ).
cnf(c_0_6085_0,axiom,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6085]) ).
cnf(c_0_6085_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6085]) ).
cnf(c_0_6085_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6085]) ).
cnf(c_0_6086_0,axiom,
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6086]) ).
cnf(c_0_6086_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1))
| c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6086]) ).
cnf(c_0_6087_0,axiom,
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6087]) ).
cnf(c_0_6087_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1))
| c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6087]) ).
cnf(c_0_6088_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_6088]) ).
cnf(c_0_6088_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_6088]) ).
cnf(c_0_6088_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_6088]) ).
cnf(c_0_6088_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_6088]) ).
cnf(c_0_6089_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),sk1_esk18_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6089]) ).
cnf(c_0_6089_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),sk1_esk18_2(X2,X1)))
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6089]) ).
cnf(c_0_6089_2,axiom,
( ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),sk1_esk18_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6089]) ).
cnf(c_0_6090_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),sk1_esk13_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6090]) ).
cnf(c_0_6090_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),sk1_esk13_2(X2,X1)))
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6090]) ).
cnf(c_0_6090_2,axiom,
( ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))),sk1_esk13_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6090]) ).
cnf(c_0_6091_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk65_3(X3,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6091]) ).
cnf(c_0_6091_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk65_3(X3,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6091]) ).
cnf(c_0_6091_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk65_3(X3,X2,X1)) = X2
| hBOOL(hAPP(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_6091]) ).
cnf(c_0_6092_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk64_3(X3,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6092]) ).
cnf(c_0_6092_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk64_3(X3,X2,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6092]) ).
cnf(c_0_6092_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk64_3(X3,X2,X1)) = X2
| hBOOL(hAPP(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_6092]) ).
cnf(c_0_6093_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6093]) ).
cnf(c_0_6093_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6093]) ).
cnf(c_0_6094_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6094]) ).
cnf(c_0_6094_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6094]) ).
cnf(c_0_6099_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk65_3(X3,X2,X1)) = X2
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6099]) ).
cnf(c_0_6099_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk65_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_6099]) ).
cnf(c_0_6099_2,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk65_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_6099]) ).
cnf(c_0_6100_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk64_3(X3,X2,X1)) = X2
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6100]) ).
cnf(c_0_6100_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk64_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_6100]) ).
cnf(c_0_6100_2,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),sk1_esk64_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_6100]) ).
cnf(c_0_6103_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_RComplete_Onatfloor(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6103_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_RComplete_Onatfloor(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6103_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6104_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6104]) ).
cnf(c_0_6104_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Oone__class_Oone(X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6104]) ).
cnf(c_0_6105_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Groups_Oone__class_Oone(X1))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6105]) ).
cnf(c_0_6105_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6105]) ).
cnf(c_0_6105_2,axiom,
( ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6105]) ).
cnf(c_0_6106_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),c_Groups_Oone__class_Oone(X1))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6106_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6106_2,axiom,
( ~ class_Divides_Osemiring__div(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),c_Groups_Oone__class_Oone(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6107_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6107_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6107_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sk1_esk73_3(X3,X2,X1)))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6108_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6108_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6109_0,axiom,
( c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6109]) ).
cnf(c_0_6109_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6109]) ).
cnf(c_0_6109_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(X1),c_Transcendental_Oln(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6109]) ).
cnf(c_0_6110_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_6110]) ).
cnf(c_0_6110_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_6110]) ).
cnf(c_0_6110_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_6110]) ).
cnf(c_0_6111_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6111_1,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6111_2,axiom,
( ~ hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6111_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6111_4,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_6111]) ).
cnf(c_0_6112_0,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6112]) ).
cnf(c_0_6112_1,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6112]) ).
cnf(c_0_6112_2,axiom,
( ~ hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6112]) ).
cnf(c_0_6112_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6112]) ).
cnf(c_0_6112_4,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(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_6112]) ).
cnf(c_0_6113_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)) = c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6113_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)) = c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6113_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(X1)),c_Transcendental_Oln(X2)) = c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6114_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6114]) ).
cnf(c_0_6114_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6114]) ).
cnf(c_0_6114_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),sk1_esk75_3(X3,X2,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6114]) ).
cnf(c_0_6115_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))
| ~ hBOOL(hAPP(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_6115]) ).
cnf(c_0_6115_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6115]) ).
cnf(c_0_6116_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6116]) ).
cnf(c_0_6116_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6116]) ).
cnf(c_0_6116_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6116]) ).
cnf(c_0_6117_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6117_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6117_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6118_0,axiom,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6118]) ).
cnf(c_0_6118_1,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| epred1_3(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6118]) ).
cnf(c_0_6120_0,axiom,
( ~ hBOOL(hAPP(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_6120]) ).
cnf(c_0_6120_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(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_6120]) ).
cnf(c_0_6121_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_6121]) ).
cnf(c_0_6121_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_6121]) ).
cnf(c_0_6122_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_6122]) ).
cnf(c_0_6122_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_6122]) ).
cnf(c_0_6123_0,axiom,
( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6123]) ).
cnf(c_0_6123_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6123]) ).
cnf(c_0_6124_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6124]) ).
cnf(c_0_6124_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(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_6124]) ).
cnf(c_0_6125_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6125]) ).
cnf(c_0_6125_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6125]) ).
cnf(c_0_6125_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6125]) ).
cnf(c_0_6126_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(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_6126]) ).
cnf(c_0_6126_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X1,X2)))
| ~ hBOOL(hAPP(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_6126]) ).
cnf(c_0_6126_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(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_6126]) ).
cnf(c_0_6127_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk35_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6127]) ).
cnf(c_0_6127_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk35_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6127]) ).
cnf(c_0_6127_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk35_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6127]) ).
cnf(c_0_6128_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk34_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6128]) ).
cnf(c_0_6128_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk34_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6128]) ).
cnf(c_0_6128_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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_6128]) ).
cnf(c_0_6129_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6129_1,axiom,
( ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6130_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_6130]) ).
cnf(c_0_6130_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_6130]) ).
cnf(c_0_6131_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_6131]) ).
cnf(c_0_6131_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_6131]) ).
cnf(c_0_6132_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_6132]) ).
cnf(c_0_6132_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_6132]) ).
cnf(c_0_6133_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_6133]) ).
cnf(c_0_6133_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_6133]) ).
cnf(c_0_6134_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6134_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6135_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6135]) ).
cnf(c_0_6135_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6135]) ).
cnf(c_0_6136_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6136]) ).
cnf(c_0_6136_1,axiom,
( ~ class_Groups_Oab__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6136]) ).
cnf(c_0_6137_0,axiom,
( hBOOL(hAPP(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_6137]) ).
cnf(c_0_6137_1,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(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_6137]) ).
cnf(c_0_6137_2,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6137]) ).
cnf(c_0_6137_3,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6137]) ).
cnf(c_0_6138_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(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_6138]) ).
cnf(c_0_6138_1,axiom,
( hBOOL(hAPP(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_6138]) ).
cnf(c_0_6138_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(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_6138]) ).
cnf(c_0_6138_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6138]) ).
cnf(c_0_6139_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6139]) ).
cnf(c_0_6139_1,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6139]) ).
cnf(c_0_6139_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6139]) ).
cnf(c_0_6140_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6140]) ).
cnf(c_0_6140_1,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6140]) ).
cnf(c_0_6140_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6140]) ).
cnf(c_0_6141_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_6141]) ).
cnf(c_0_6141_1,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(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_6141]) ).
cnf(c_0_6141_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(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_6141]) ).
cnf(c_0_6141_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| hAPP(hAPP(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_6141]) ).
cnf(c_0_6141_4,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| hAPP(hAPP(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_6141]) ).
cnf(c_0_6141_5,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6141]) ).
cnf(c_0_6142_0,axiom,
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6142]) ).
cnf(c_0_6142_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(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_6142]) ).
cnf(c_0_6143_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6143]) ).
cnf(c_0_6143_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(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_6143]) ).
cnf(c_0_6146_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6146_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6146_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6147_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6147]) ).
cnf(c_0_6147_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6147]) ).
cnf(c_0_6148_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6148]) ).
cnf(c_0_6148_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6148]) ).
cnf(c_0_6149_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6149_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6150_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6150_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6151_0,axiom,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6151]) ).
cnf(c_0_6151_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6151]) ).
cnf(c_0_6152_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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_6152]) ).
cnf(c_0_6152_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 = X3
| ~ hBOOL(hAPP(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_6152]) ).
cnf(c_0_6152_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_6152]) ).
cnf(c_0_6152_3,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6152]) ).
cnf(c_0_6153_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_6153]) ).
cnf(c_0_6153_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(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_6153]) ).
cnf(c_0_6154_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6154]) ).
cnf(c_0_6154_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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_6154]) ).
cnf(c_0_6155_0,axiom,
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6155]) ).
cnf(c_0_6155_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(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_6155]) ).
cnf(c_0_6156_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(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,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6156]) ).
cnf(c_0_6157_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6157]) ).
cnf(c_0_6157_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6157]) ).
cnf(c_0_6158_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_6158]) ).
cnf(c_0_6158_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_6158]) ).
cnf(c_0_6159_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_6159]) ).
cnf(c_0_6159_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_6159]) ).
cnf(c_0_6160_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_6160]) ).
cnf(c_0_6160_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_6160]) ).
cnf(c_0_6166_0,axiom,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)
| ~ hBOOL(hAPP(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_6166]) ).
cnf(c_0_6166_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6166]) ).
cnf(c_0_6166_2,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6166]) ).
cnf(c_0_6167_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6167]) ).
cnf(c_0_6167_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_6167]) ).
cnf(c_0_6168_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6168]) ).
cnf(c_0_6168_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X5))
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6168]) ).
cnf(c_0_6168_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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6168]) ).
cnf(c_0_6168_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6168]) ).
cnf(c_0_6169_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6169_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6169_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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6169_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6170_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6170]) ).
cnf(c_0_6170_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6170]) ).
cnf(c_0_6170_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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6170]) ).
cnf(c_0_6170_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6170]) ).
cnf(c_0_6171_0,axiom,
( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6171_1,axiom,
( ~ class_Groups_Oordered__ab__group__add(X1)
| hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6171_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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6171_3,axiom,
( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6172_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6172]) ).
cnf(c_0_6172_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6172]) ).
cnf(c_0_6173_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6173]) ).
cnf(c_0_6173_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6173]) ).
cnf(c_0_6173_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6173]) ).
cnf(c_0_6174_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6174]) ).
cnf(c_0_6174_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(literals_permutation,[status(thm)],[c_0_6174]) ).
cnf(c_0_6175_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6175]) ).
cnf(c_0_6175_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(literals_permutation,[status(thm)],[c_0_6175]) ).
cnf(c_0_6176_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ c_SEQ_Oincseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6176_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ c_SEQ_Oincseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6176_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ c_SEQ_Oincseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6176_3,axiom,
( ~ c_SEQ_Oincseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6177_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ c_SEQ_Odecseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6177_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ c_SEQ_Odecseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6177_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4)))
| ~ c_SEQ_Odecseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6177_3,axiom,
( ~ c_SEQ_Odecseq(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3)),hAPP(X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6178_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) = c_Groups_Ozero__class_Ozero(X1)
| ~ 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_6178]) ).
cnf(c_0_6178_1,axiom,
( ~ class_Rings_Olinordered__ring__strict(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) = c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6178]) ).
cnf(c_0_6178_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6178]) ).
cnf(c_0_6178_3,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6178]) ).
cnf(c_0_6179_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6179]) ).
cnf(c_0_6179_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6179]) ).
cnf(c_0_6179_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6179]) ).
cnf(c_0_6180_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6180_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6180_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6181_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6181]) ).
cnf(c_0_6181_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6181]) ).
cnf(c_0_6181_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6181]) ).
cnf(c_0_6182_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6182]) ).
cnf(c_0_6182_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6182]) ).
cnf(c_0_6182_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6182]) ).
cnf(c_0_6187_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6187]) ).
cnf(c_0_6187_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6187]) ).
cnf(c_0_6187_2,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6187]) ).
cnf(c_0_6188_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| ~ epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6188_1,axiom,
( ~ epred1_3(X1,X3,X2)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6188_2,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ epred1_3(X1,X3,X2)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6189_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6189_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6189_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6190_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6190]) ).
cnf(c_0_6190_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6190]) ).
cnf(c_0_6190_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6190]) ).
cnf(c_0_6191_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sk1_esk35_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6191]) ).
cnf(c_0_6191_1,axiom,
( ~ hBOOL(hAPP(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_esk35_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6191]) ).
cnf(c_0_6191_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(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_esk35_2(X2,X1)),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6191]) ).
cnf(c_0_6192_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sk1_esk34_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6192_1,axiom,
( ~ hBOOL(hAPP(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_esk34_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6192_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(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_esk34_2(X2,X1)),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6193_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6193_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6194_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6194]) ).
cnf(c_0_6194_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6194]) ).
cnf(c_0_6195_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6195]) ).
cnf(c_0_6195_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6195]) ).
cnf(c_0_6196_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6196_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6197_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6197_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6198_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6198_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6199_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6199]) ).
cnf(c_0_6199_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6199]) ).
cnf(c_0_6200_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6200]) ).
cnf(c_0_6200_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6200]) ).
cnf(c_0_6201_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6201_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6201_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6202_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6202]) ).
cnf(c_0_6202_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6202]) ).
cnf(c_0_6202_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6202]) ).
cnf(c_0_6203_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X2) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6203]) ).
cnf(c_0_6203_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| hAPP(hAPP(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_6203]) ).
cnf(c_0_6204_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6204]) ).
cnf(c_0_6204_1,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6204]) ).
cnf(c_0_6204_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6204]) ).
cnf(c_0_6204_3,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6204]) ).
cnf(c_0_6205_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6205]) ).
cnf(c_0_6205_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6205]) ).
cnf(c_0_6205_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6205]) ).
cnf(c_0_6213_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ c_SEQ_Osubseq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6213]) ).
cnf(c_0_6213_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,X3)))
| ~ c_SEQ_Osubseq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6213]) ).
cnf(c_0_6213_2,axiom,
( ~ c_SEQ_Osubseq(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6213]) ).
cnf(c_0_6214_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sk1_esk58_1(X1))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6214]) ).
cnf(c_0_6214_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sk1_esk58_1(X1))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6214]) ).
cnf(c_0_6215_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6215]) ).
cnf(c_0_6215_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6215]) ).
cnf(c_0_6216_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6216]) ).
cnf(c_0_6216_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6216]) ).
cnf(c_0_6216_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6216]) ).
cnf(c_0_6217_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_RComplete_Onatfloor(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6217]) ).
cnf(c_0_6217_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_RComplete_Onatfloor(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6217]) ).
cnf(c_0_6218_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6218]) ).
cnf(c_0_6218_1,axiom,
( ~ hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6218]) ).
cnf(c_0_6218_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_6218]) ).
cnf(c_0_6218_3,axiom,
( X2 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(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_6218]) ).
cnf(c_0_6219_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6219_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6219_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6219_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6220_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6220]) ).
cnf(c_0_6220_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6220]) ).
cnf(c_0_6220_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6220]) ).
cnf(c_0_6220_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6220]) ).
cnf(c_0_6221_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6221]) ).
cnf(c_0_6221_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6221]) ).
cnf(c_0_6221_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6221]) ).
cnf(c_0_6221_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6221]) ).
cnf(c_0_6222_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6222]) ).
cnf(c_0_6222_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6222]) ).
cnf(c_0_6222_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6222]) ).
cnf(c_0_6222_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6222]) ).
cnf(c_0_6223_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6223_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6223_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6223_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6224_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6224_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6224_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6224_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6225_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6225]) ).
cnf(c_0_6225_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6225]) ).
cnf(c_0_6225_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6225]) ).
cnf(c_0_6225_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6225]) ).
cnf(c_0_6226_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6226]) ).
cnf(c_0_6226_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6226]) ).
cnf(c_0_6226_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6226]) ).
cnf(c_0_6226_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6226]) ).
cnf(c_0_6228_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_6228]) ).
cnf(c_0_6228_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_6228]) ).
cnf(c_0_6228_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_6228]) ).
cnf(c_0_6228_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_6228]) ).
cnf(c_0_6229_0,axiom,
( X3 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(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_6229]) ).
cnf(c_0_6229_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| X3 = X4
| ~ hBOOL(hAPP(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_6229]) ).
cnf(c_0_6229_2,axiom,
( ~ hBOOL(hAPP(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_6229]) ).
cnf(c_0_6229_3,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)
| ~ hBOOL(hAPP(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_6229]) ).
cnf(c_0_6230_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6230]) ).
cnf(c_0_6230_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6230]) ).
cnf(c_0_6230_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6230]) ).
cnf(c_0_6231_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6231_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6231_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6232_0,axiom,
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X1)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6232]) ).
cnf(c_0_6232_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6232]) ).
cnf(c_0_6233_0,axiom,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6233]) ).
cnf(c_0_6233_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6233]) ).
cnf(c_0_6234_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6234]) ).
cnf(c_0_6234_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6234]) ).
cnf(c_0_6235_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk58_1(X1)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6235]) ).
cnf(c_0_6235_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sk1_esk58_1(X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_6235]) ).
cnf(c_0_6236_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),sk1_esk21_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6236_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),sk1_esk21_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6236_2,axiom,
( ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),sk1_esk21_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6236_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),sk1_esk21_2(X2,X1)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6237_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6237_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6237_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6238_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6238]) ).
cnf(c_0_6238_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6238]) ).
cnf(c_0_6239_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6239]) ).
cnf(c_0_6239_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6239]) ).
cnf(c_0_6241_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Transcendental_Oln(X1)) = c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6241]) ).
cnf(c_0_6241_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_Transcendental_Oln(X1)) = c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6241]) ).
cnf(c_0_6242_0,axiom,
( hAPP(hAPP(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_6242]) ).
cnf(c_0_6242_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(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_6242]) ).
cnf(c_0_6242_2,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(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_6242]) ).
cnf(c_0_6243_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ epred1_3(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6243]) ).
cnf(c_0_6243_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)))
| ~ epred1_3(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6243]) ).
cnf(c_0_6243_2,axiom,
( ~ epred1_3(X1,X3,X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6243]) ).
cnf(c_0_6245_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_6245]) ).
cnf(c_0_6245_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_6245]) ).
cnf(c_0_6245_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_6245]) ).
cnf(c_0_6246_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_6246]) ).
cnf(c_0_6246_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_6246]) ).
cnf(c_0_6246_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_6246]) ).
cnf(c_0_6247_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_6247]) ).
cnf(c_0_6247_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_6247]) ).
cnf(c_0_6247_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_6247]) ).
cnf(c_0_6248_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6248]) ).
cnf(c_0_6248_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6248]) ).
cnf(c_0_6248_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6248]) ).
cnf(c_0_6249_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk48_2(X2,X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6249]) ).
cnf(c_0_6249_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk48_2(X2,X1)),X2))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6249]) ).
cnf(c_0_6249_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk48_2(X2,X1)),X2))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6249]) ).
cnf(c_0_6250_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_6250]) ).
cnf(c_0_6250_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_6250]) ).
cnf(c_0_6251_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_6251]) ).
cnf(c_0_6251_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_6251]) ).
cnf(c_0_6252_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6252]) ).
cnf(c_0_6252_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6252]) ).
cnf(c_0_6253_0,axiom,
( hBOOL(hAPP(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)
| hBOOL(hAPP(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,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6254]) ).
cnf(c_0_6254_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_6254]) ).
cnf(c_0_6257_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_6257]) ).
cnf(c_0_6257_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_6257]) ).
cnf(c_0_6258_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6258]) ).
cnf(c_0_6258_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6258]) ).
cnf(c_0_6259_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6259]) ).
cnf(c_0_6259_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6259]) ).
cnf(c_0_6259_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6259]) ).
cnf(c_0_6260_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6260]) ).
cnf(c_0_6260_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6260]) ).
cnf(c_0_6260_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6260]) ).
cnf(c_0_6261_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6261]) ).
cnf(c_0_6261_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6261]) ).
cnf(c_0_6261_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6261]) ).
cnf(c_0_6262_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6262]) ).
cnf(c_0_6262_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6262]) ).
cnf(c_0_6262_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6262]) ).
cnf(c_0_6263_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(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_6263]) ).
cnf(c_0_6263_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6263]) ).
cnf(c_0_6263_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6263]) ).
cnf(c_0_6264_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(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_6264]) ).
cnf(c_0_6264_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6264]) ).
cnf(c_0_6264_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6264]) ).
cnf(c_0_6266_0,axiom,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6266]) ).
cnf(c_0_6266_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6266]) ).
cnf(c_0_6266_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6266]) ).
cnf(c_0_6267_0,axiom,
( c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6267]) ).
cnf(c_0_6267_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6267]) ).
cnf(c_0_6267_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6267]) ).
cnf(c_0_6268_0,axiom,
( c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6268]) ).
cnf(c_0_6268_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6268]) ).
cnf(c_0_6268_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6268]) ).
cnf(c_0_6271_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(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_6271]) ).
cnf(c_0_6271_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6271]) ).
cnf(c_0_6271_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6271]) ).
cnf(c_0_6272_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(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_6272]) ).
cnf(c_0_6272_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6272]) ).
cnf(c_0_6272_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6272]) ).
cnf(c_0_6273_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(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_6273]) ).
cnf(c_0_6273_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(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_6273]) ).
cnf(c_0_6273_2,axiom,
( ~ hBOOL(hAPP(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_6273]) ).
cnf(c_0_6274_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6274]) ).
cnf(c_0_6274_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6274]) ).
cnf(c_0_6274_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6274]) ).
cnf(c_0_6275_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6275]) ).
cnf(c_0_6275_1,axiom,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6275]) ).
cnf(c_0_6275_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6275]) ).
cnf(c_0_6276_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6276]) ).
cnf(c_0_6276_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6276]) ).
cnf(c_0_6276_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6276]) ).
cnf(c_0_6276_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6276]) ).
cnf(c_0_6277_0,axiom,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6277]) ).
cnf(c_0_6277_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6277]) ).
cnf(c_0_6278_0,axiom,
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6278]) ).
cnf(c_0_6278_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6278]) ).
cnf(c_0_6281_0,axiom,
( ~ hBOOL(hAPP(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_6281]) ).
cnf(c_0_6281_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(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_6281]) ).
cnf(c_0_6282_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6282]) ).
cnf(c_0_6282_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6282]) ).
cnf(c_0_6283_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| c_Transcendental_Oln(X1) != c_Transcendental_Oln(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6283_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| c_Transcendental_Oln(X1) != c_Transcendental_Oln(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6283_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| X1 = X2
| c_Transcendental_Oln(X1) != c_Transcendental_Oln(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6283_3,axiom,
( c_Transcendental_Oln(X1) != c_Transcendental_Oln(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6284_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6284]) ).
cnf(c_0_6284_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6284]) ).
cnf(c_0_6285_0,axiom,
( hBOOL(hAPP(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_6285]) ).
cnf(c_0_6285_1,axiom,
( X1 = X2
| hBOOL(hAPP(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_6285]) ).
cnf(c_0_6285_2,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6285]) ).
cnf(c_0_6285_3,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6285]) ).
cnf(c_0_6286_0,axiom,
( X3 = X2
| hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6286]) ).
cnf(c_0_6286_1,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6286]) ).
cnf(c_0_6286_2,axiom,
( hBOOL(hAPP(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_6286]) ).
cnf(c_0_6286_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(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_6286]) ).
cnf(c_0_6287_0,axiom,
( c_Transcendental_Oln(X1) = c_Transcendental_Oln(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6287]) ).
cnf(c_0_6287_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_Transcendental_Oln(X1) = c_Transcendental_Oln(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6287]) ).
cnf(c_0_6287_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_Transcendental_Oln(X1) = c_Transcendental_Oln(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6287]) ).
cnf(c_0_6287_3,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_Transcendental_Oln(X1) = c_Transcendental_Oln(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6287]) ).
cnf(c_0_6288_0,axiom,
( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6288]) ).
cnf(c_0_6288_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6288]) ).
cnf(c_0_6289_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6289]) ).
cnf(c_0_6289_1,axiom,
( ~ hBOOL(hAPP(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_6289]) ).
cnf(c_0_6290_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(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_6290]) ).
cnf(c_0_6290_1,axiom,
( ~ hBOOL(hAPP(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_6290]) ).
cnf(c_0_6290_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)
| ~ hBOOL(hAPP(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_6290]) ).
cnf(c_0_6293_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,sk1_esk66_1(X1))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6293]) ).
cnf(c_0_6293_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,sk1_esk66_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_6293]) ).
cnf(c_0_6294_0,axiom,
( c_Transcendental_Ocos(c_Transcendental_Oarccos(X1)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6294]) ).
cnf(c_0_6294_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_Transcendental_Ocos(c_Transcendental_Oarccos(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6294]) ).
cnf(c_0_6295_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6295]) ).
cnf(c_0_6295_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6295]) ).
cnf(c_0_6296_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X2) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6296]) ).
cnf(c_0_6296_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6296]) ).
cnf(c_0_6297_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6297]) ).
cnf(c_0_6297_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1)),X2))
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6297]) ).
cnf(c_0_6297_2,axiom,
( ~ hBOOL(hAPP(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_6297]) ).
cnf(c_0_6297_3,axiom,
( X3 != X4
| ~ hBOOL(hAPP(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_6297]) ).
cnf(c_0_6298_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk60_2(X2,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6298]) ).
cnf(c_0_6298_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk60_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6298]) ).
cnf(c_0_6299_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_6299]) ).
cnf(c_0_6299_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_6299]) ).
cnf(c_0_6299_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_6299]) ).
cnf(c_0_6300_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6300]) ).
cnf(c_0_6300_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6300]) ).
cnf(c_0_6301_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6301]) ).
cnf(c_0_6301_1,axiom,
( ~ hBOOL(hAPP(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_6301]) ).
cnf(c_0_6302_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6302]) ).
cnf(c_0_6302_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6302]) ).
cnf(c_0_6303_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6303]) ).
cnf(c_0_6303_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6303]) ).
cnf(c_0_6304_0,axiom,
( hBOOL(hAPP(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_6304]) ).
cnf(c_0_6304_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(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_6304]) ).
cnf(c_0_6305_0,axiom,
( hBOOL(hAPP(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_6305]) ).
cnf(c_0_6305_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(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_6305]) ).
cnf(c_0_6306_0,axiom,
( hAPP(hAPP(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_6306]) ).
cnf(c_0_6306_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6306]) ).
cnf(c_0_6307_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6307]) ).
cnf(c_0_6307_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6307]) ).
cnf(c_0_6309_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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6309]) ).
cnf(c_0_6309_1,axiom,
( ~ hBOOL(hAPP(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_6309]) ).
cnf(c_0_6310_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hBOOL(hAPP(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_6310]) ).
cnf(c_0_6310_1,axiom,
( hBOOL(hAPP(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_6310]) ).
cnf(c_0_6313_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6313]) ).
cnf(c_0_6313_1,axiom,
( X1 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(literals_permutation,[status(thm)],[c_0_6313]) ).
cnf(c_0_6314_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6314_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hAPP(hAPP(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_6314]) ).
cnf(c_0_6315_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6315_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6315_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6315_3,axiom,
( X2 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6316_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6316_1,axiom,
( ~ class_Orderings_Oorder(X1)
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6316_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Oorder(X1)
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6316_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6317_0,axiom,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6317_1,axiom,
( ~ class_Orderings_Oorder(X1)
| X3 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6317_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X3 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6317_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6318_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6318]) ).
cnf(c_0_6318_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6318]) ).
cnf(c_0_6318_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6318]) ).
cnf(c_0_6318_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6318]) ).
cnf(c_0_6319_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6319]) ).
cnf(c_0_6319_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6319]) ).
cnf(c_0_6319_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6319]) ).
cnf(c_0_6319_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6319]) ).
cnf(c_0_6320_0,axiom,
( c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sk1_esk50_2(X1,X2))) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6320]) ).
cnf(c_0_6320_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sk1_esk50_2(X1,X2))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6320]) ).
cnf(c_0_6321_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6321]) ).
cnf(c_0_6321_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6321]) ).
cnf(c_0_6321_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6321]) ).
cnf(c_0_6322_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6322_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6322_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6323_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6323_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6323_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6324_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6324_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6324_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6325_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6325_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6325_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6326_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6326]) ).
cnf(c_0_6326_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6326]) ).
cnf(c_0_6326_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6326]) ).
cnf(c_0_6327_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6327]) ).
cnf(c_0_6327_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6327]) ).
cnf(c_0_6327_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6327]) ).
cnf(c_0_6328_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6328]) ).
cnf(c_0_6328_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6328]) ).
cnf(c_0_6328_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6328]) ).
cnf(c_0_6329_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6329]) ).
cnf(c_0_6329_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6329]) ).
cnf(c_0_6329_2,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6329]) ).
cnf(c_0_6330_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6330]) ).
cnf(c_0_6330_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6330]) ).
cnf(c_0_6330_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6330]) ).
cnf(c_0_6331_0,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6331]) ).
cnf(c_0_6331_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6331]) ).
cnf(c_0_6331_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2)))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6331]) ).
cnf(c_0_6332_0,axiom,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk21_2(X2,X1)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6332]) ).
cnf(c_0_6332_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk21_2(X2,X1)),X2))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6332]) ).
cnf(c_0_6332_2,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk21_2(X2,X1)),X2))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6332]) ).
cnf(c_0_6333_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,c_Nat_OSuc(X2))))
| ~ c_SEQ_Osubseq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6333]) ).
cnf(c_0_6333_1,axiom,
( ~ c_SEQ_Osubseq(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,c_Nat_OSuc(X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_6333]) ).
cnf(c_0_6334_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6334_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6334_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6334_3,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6335_0,axiom,
( X2 = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6335_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6335_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6336_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(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,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6336]) ).
cnf(c_0_6341_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6341]) ).
cnf(c_0_6341_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6341]) ).
cnf(c_0_6341_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6341]) ).
cnf(c_0_6341_3,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6341]) ).
cnf(c_0_6342_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6342]) ).
cnf(c_0_6342_1,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6342]) ).
cnf(c_0_6342_2,axiom,
( ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6342]) ).
cnf(c_0_6343_0,axiom,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6343]) ).
cnf(c_0_6343_1,axiom,
( ~ hBOOL(hAPP(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_6343]) ).
cnf(c_0_6344_0,axiom,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6344]) ).
cnf(c_0_6344_1,axiom,
( ~ hBOOL(hAPP(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_6344]) ).
cnf(c_0_6345_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6345]) ).
cnf(c_0_6345_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6345]) ).
cnf(c_0_6346_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6346]) ).
cnf(c_0_6346_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6346]) ).
cnf(c_0_6347_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6347]) ).
cnf(c_0_6347_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6347]) ).
cnf(c_0_6348_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3)) = c_Groups_Osgn__class_Osgn(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_6348]) ).
cnf(c_0_6348_1,axiom,
( ~ class_RealVector_Oreal__normed__div__algebra(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3)) = c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6348]) ).
cnf(c_0_6349_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3)) = c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6349]) ).
cnf(c_0_6349_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3)) = c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6349]) ).
cnf(c_0_6350_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6350]) ).
cnf(c_0_6350_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6350]) ).
cnf(c_0_6351_0,axiom,
( c_SEQ_Oincseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk15_2(X2,X1)),sk1_esk16_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6351_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk15_2(X2,X1)),sk1_esk16_2(X2,X1)))
| c_SEQ_Oincseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6351_2,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk15_2(X2,X1)),sk1_esk16_2(X2,X1)))
| c_SEQ_Oincseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6352_0,axiom,
( c_SEQ_Odecseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk11_2(X2,X1)),sk1_esk12_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6352]) ).
cnf(c_0_6352_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk11_2(X2,X1)),sk1_esk12_2(X2,X1)))
| c_SEQ_Odecseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6352]) ).
cnf(c_0_6352_2,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk11_2(X2,X1)),sk1_esk12_2(X2,X1)))
| c_SEQ_Odecseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6352]) ).
cnf(c_0_6353_0,axiom,
( c_SEQ_Omonoseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk5_2(X2,X1)),sk1_esk6_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6353]) ).
cnf(c_0_6353_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk5_2(X2,X1)),sk1_esk6_2(X2,X1)))
| c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6353]) ).
cnf(c_0_6353_2,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk5_2(X2,X1)),sk1_esk6_2(X2,X1)))
| c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6353]) ).
cnf(c_0_6354_0,axiom,
( c_SEQ_Omonoseq(X1,X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk7_2(X2,X1)),sk1_esk8_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6354]) ).
cnf(c_0_6354_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk7_2(X2,X1)),sk1_esk8_2(X2,X1)))
| c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6354]) ).
cnf(c_0_6354_2,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk7_2(X2,X1)),sk1_esk8_2(X2,X1)))
| c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6354]) ).
cnf(c_0_6355_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(X1),X2),X3))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6355]) ).
cnf(c_0_6355_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6355]) ).
cnf(c_0_6355_2,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6355]) ).
cnf(c_0_6356_0,axiom,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)
| ~ hBOOL(hAPP(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_6356]) ).
cnf(c_0_6356_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 = hAPP(hAPP(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_6356]) ).
cnf(c_0_6356_2,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6356]) ).
cnf(c_0_6357_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6357]) ).
cnf(c_0_6357_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6357]) ).
cnf(c_0_6358_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6358]) ).
cnf(c_0_6358_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6358]) ).
cnf(c_0_6358_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6358]) ).
cnf(c_0_6358_3,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6358]) ).
cnf(c_0_6359_0,axiom,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6359]) ).
cnf(c_0_6359_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6359]) ).
cnf(c_0_6360_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_6360]) ).
cnf(c_0_6360_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_6360]) ).
cnf(c_0_6361_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6361]) ).
cnf(c_0_6361_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6361]) ).
cnf(c_0_6361_2,axiom,
( X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)
| ~ hBOOL(hAPP(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_6361]) ).
cnf(c_0_6362_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6362]) ).
cnf(c_0_6362_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6362]) ).
cnf(c_0_6362_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6362]) ).
cnf(c_0_6363_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_6363]) ).
cnf(c_0_6363_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_6363]) ).
cnf(c_0_6364_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6364]) ).
cnf(c_0_6364_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6364]) ).
cnf(c_0_6365_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sk1_esk60_2(X2,X1)),c_Nat_OSuc(X2)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6365]) ).
cnf(c_0_6365_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sk1_esk60_2(X2,X1)),c_Nat_OSuc(X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6365]) ).
cnf(c_0_6367_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6367]) ).
cnf(c_0_6367_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6367]) ).
cnf(c_0_6367_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6367]) ).
cnf(c_0_6367_3,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6367]) ).
cnf(c_0_6368_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6368]) ).
cnf(c_0_6368_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6368]) ).
cnf(c_0_6368_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6368]) ).
cnf(c_0_6369_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6369]) ).
cnf(c_0_6369_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6369]) ).
cnf(c_0_6369_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6369]) ).
cnf(c_0_6370_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6370]) ).
cnf(c_0_6370_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6370]) ).
cnf(c_0_6370_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6370]) ).
cnf(c_0_6371_0,axiom,
( c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6371]) ).
cnf(c_0_6371_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6371]) ).
cnf(c_0_6372_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6372]) ).
cnf(c_0_6372_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6372]) ).
cnf(c_0_6373_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6373]) ).
cnf(c_0_6373_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6373]) ).
cnf(c_0_6374_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6374]) ).
cnf(c_0_6374_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(X1)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6374]) ).
cnf(c_0_6375_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6375]) ).
cnf(c_0_6375_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6375]) ).
cnf(c_0_6376_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6376]) ).
cnf(c_0_6376_1,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6376]) ).
cnf(c_0_6376_2,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6376]) ).
cnf(c_0_6376_3,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1))
| X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6376]) ).
cnf(c_0_6377_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6377]) ).
cnf(c_0_6377_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(literals_permutation,[status(thm)],[c_0_6377]) ).
cnf(c_0_6378_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(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_6378]) ).
cnf(c_0_6378_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(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_6378]) ).
cnf(c_0_6378_2,axiom,
( ~ hBOOL(hAPP(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_6378]) ).
cnf(c_0_6379_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)
| ~ hBOOL(hAPP(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_6379]) ).
cnf(c_0_6379_1,axiom,
( ~ hBOOL(hAPP(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_6379]) ).
cnf(c_0_6379_2,axiom,
( X2 != X3
| ~ hBOOL(hAPP(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_6379]) ).
cnf(c_0_6380_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6380]) ).
cnf(c_0_6380_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6380]) ).
cnf(c_0_6381_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6381]) ).
cnf(c_0_6381_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6381]) ).
cnf(c_0_6382_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6382]) ).
cnf(c_0_6382_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6382]) ).
cnf(c_0_6383_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6383]) ).
cnf(c_0_6383_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6383]) ).
cnf(c_0_6384_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6384]) ).
cnf(c_0_6384_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6384]) ).
cnf(c_0_6385_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(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,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6385]) ).
cnf(c_0_6386_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6386]) ).
cnf(c_0_6386_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6386]) ).
cnf(c_0_6387_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6387]) ).
cnf(c_0_6387_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6387]) ).
cnf(c_0_6388_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_RComplete_Onatceiling(X2)))
| ~ hBOOL(hAPP(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,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_RComplete_Onatceiling(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6388]) ).
cnf(c_0_6389_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6389]) ).
cnf(c_0_6389_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6389]) ).
cnf(c_0_6390_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_6390]) ).
cnf(c_0_6390_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(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_6390]) ).
cnf(c_0_6390_2,axiom,
( ~ hBOOL(hAPP(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_6390]) ).
cnf(c_0_6391_0,axiom,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6391]) ).
cnf(c_0_6391_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6391]) ).
cnf(c_0_6392_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(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_6392]) ).
cnf(c_0_6392_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6392]) ).
cnf(c_0_6393_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6393]) ).
cnf(c_0_6393_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(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_6393]) ).
cnf(c_0_6394_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6394]) ).
cnf(c_0_6394_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| hAPP(hAPP(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_6394]) ).
cnf(c_0_6395_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X2 != c_Nat_OSuc(hAPP(hAPP(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_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6395]) ).
cnf(c_0_6396_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| c_Nat_OSuc(X1) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6396_1,axiom,
( c_Nat_OSuc(X1) = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6396_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| c_Nat_OSuc(X1) = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6397_0,axiom,
( epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6397]) ).
cnf(c_0_6397_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X2,X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6397]) ).
cnf(c_0_6397_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6397]) ).
cnf(c_0_6400_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6400]) ).
cnf(c_0_6400_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6400]) ).
cnf(c_0_6400_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6400]) ).
cnf(c_0_6400_3,axiom,
( X3 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6400]) ).
cnf(c_0_6401_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6401]) ).
cnf(c_0_6401_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6401]) ).
cnf(c_0_6401_2,axiom,
( X2 != X4
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6401]) ).
cnf(c_0_6401_3,axiom,
( ~ class_Orderings_Oord(X1)
| X2 != X4
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6401]) ).
cnf(c_0_6402_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6402_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6402_2,axiom,
( X3 != X4
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6402_3,axiom,
( ~ class_Orderings_Oorder(X1)
| X3 != X4
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6403_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6403]) ).
cnf(c_0_6403_1,axiom,
( X4 != X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6403]) ).
cnf(c_0_6403_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| X4 != X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6403]) ).
cnf(c_0_6403_3,axiom,
( ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X4))
| X4 != X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6403]) ).
cnf(c_0_6404_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X4 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6404]) ).
cnf(c_0_6404_1,axiom,
( X4 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6404]) ).
cnf(c_0_6404_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| X4 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6404]) ).
cnf(c_0_6404_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| X4 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6404]) ).
cnf(c_0_6405_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6405]) ).
cnf(c_0_6405_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6405]) ).
cnf(c_0_6405_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6405]) ).
cnf(c_0_6405_3,axiom,
( X3 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6405]) ).
cnf(c_0_6406_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6406]) ).
cnf(c_0_6406_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 != X4
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6406]) ).
cnf(c_0_6406_2,axiom,
( X2 != X4
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6406]) ).
cnf(c_0_6406_3,axiom,
( ~ class_Orderings_Oord(X1)
| X2 != X4
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6406]) ).
cnf(c_0_6407_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6407]) ).
cnf(c_0_6407_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 != X4
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6407]) ).
cnf(c_0_6407_2,axiom,
( X3 != X4
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6407]) ).
cnf(c_0_6407_3,axiom,
( ~ class_Orderings_Oorder(X1)
| X3 != X4
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6407]) ).
cnf(c_0_6408_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6408]) ).
cnf(c_0_6408_1,axiom,
( X4 != X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6408]) ).
cnf(c_0_6408_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| X4 != X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6408]) ).
cnf(c_0_6408_3,axiom,
( ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| X4 != X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6408]) ).
cnf(c_0_6409_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X4 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6409]) ).
cnf(c_0_6409_1,axiom,
( X4 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6409]) ).
cnf(c_0_6409_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| X4 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6409]) ).
cnf(c_0_6409_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| X4 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6409]) ).
cnf(c_0_6411_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_6411]) ).
cnf(c_0_6411_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_6411]) ).
cnf(c_0_6412_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6412]) ).
cnf(c_0_6412_1,axiom,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6412]) ).
cnf(c_0_6412_2,axiom,
( ~ class_Orderings_Oorder(X1)
| X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6412]) ).
cnf(c_0_6412_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6412]) ).
cnf(c_0_6413_0,axiom,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6413]) ).
cnf(c_0_6413_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6413]) ).
cnf(c_0_6413_2,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6413]) ).
cnf(c_0_6413_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6413]) ).
cnf(c_0_6414_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6414]) ).
cnf(c_0_6414_1,axiom,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6414]) ).
cnf(c_0_6414_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6414]) ).
cnf(c_0_6414_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6414]) ).
cnf(c_0_6415_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6415_1,axiom,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6415_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6415_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6416_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6416_1,axiom,
( X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6416_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6416_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6417_0,axiom,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6417_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6417_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6417_3,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6418_0,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6418_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6418_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6418_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6419_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6419_1,axiom,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6419_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6419_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6420_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6420_1,axiom,
( X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6420_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6420_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6421_0,axiom,
( X1 = c_Nat_OSuc(X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6421]) ).
cnf(c_0_6421_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 = c_Nat_OSuc(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6421]) ).
cnf(c_0_6421_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 = c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6421]) ).
cnf(c_0_6422_0,axiom,
( X1 = c_Nat_OSuc(X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6422]) ).
cnf(c_0_6422_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 = c_Nat_OSuc(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6422]) ).
cnf(c_0_6422_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 = c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6422]) ).
cnf(c_0_6423_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6423]) ).
cnf(c_0_6423_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6423]) ).
cnf(c_0_6424_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6424]) ).
cnf(c_0_6424_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6424]) ).
cnf(c_0_6425_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6425]) ).
cnf(c_0_6425_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6425]) ).
cnf(c_0_6426_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_6426]) ).
cnf(c_0_6426_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_6426]) ).
cnf(c_0_6427_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_6427]) ).
cnf(c_0_6427_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_6427]) ).
cnf(c_0_6428_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_6428]) ).
cnf(c_0_6428_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_6428]) ).
cnf(c_0_6429_0,axiom,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6429]) ).
cnf(c_0_6429_1,axiom,
( ~ hBOOL(hAPP(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_6429]) ).
cnf(c_0_6429_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6429]) ).
cnf(c_0_6430_0,axiom,
( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6430]) ).
cnf(c_0_6430_1,axiom,
( ~ hBOOL(hAPP(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_6430]) ).
cnf(c_0_6430_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6430]) ).
cnf(c_0_6431_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6431]) ).
cnf(c_0_6431_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6431]) ).
cnf(c_0_6431_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6431]) ).
cnf(c_0_6432_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6432]) ).
cnf(c_0_6432_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6432]) ).
cnf(c_0_6432_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6432]) ).
cnf(c_0_6433_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6433]) ).
cnf(c_0_6433_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6433]) ).
cnf(c_0_6433_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6433]) ).
cnf(c_0_6434_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6434]) ).
cnf(c_0_6434_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6434]) ).
cnf(c_0_6434_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6434]) ).
cnf(c_0_6435_0,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6435_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6435_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6436_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6436]) ).
cnf(c_0_6436_1,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6436]) ).
cnf(c_0_6436_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6436]) ).
cnf(c_0_6437_0,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6437]) ).
cnf(c_0_6437_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6437]) ).
cnf(c_0_6437_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6437]) ).
cnf(c_0_6438_0,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6438]) ).
cnf(c_0_6438_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6438]) ).
cnf(c_0_6438_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6438]) ).
cnf(c_0_6443_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| X1 != c_Nat_OSuc(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6443]) ).
cnf(c_0_6443_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| hBOOL(hAPP(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_6443]) ).
cnf(c_0_6443_2,axiom,
( X1 != c_Nat_OSuc(X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6443]) ).
cnf(c_0_6444_0,axiom,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6444]) ).
cnf(c_0_6444_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6444]) ).
cnf(c_0_6445_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6445]) ).
cnf(c_0_6445_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6445]) ).
cnf(c_0_6448_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6448]) ).
cnf(c_0_6448_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6448]) ).
cnf(c_0_6448_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6448]) ).
cnf(c_0_6450_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6450]) ).
cnf(c_0_6450_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1)))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6450]) ).
cnf(c_0_6450_2,axiom,
( X2 != X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Nat_OSuc(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6450]) ).
cnf(c_0_6451_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6451]) ).
cnf(c_0_6451_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6451]) ).
cnf(c_0_6452_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6452]) ).
cnf(c_0_6452_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6452]) ).
cnf(c_0_6453_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6453]) ).
cnf(c_0_6453_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6453]) ).
cnf(c_0_6454_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6454]) ).
cnf(c_0_6454_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6454]) ).
cnf(c_0_6455_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6455]) ).
cnf(c_0_6455_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(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,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6456]) ).
cnf(c_0_6456_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6456]) ).
cnf(c_0_6457_0,axiom,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6457]) ).
cnf(c_0_6457_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6457]) ).
cnf(c_0_6458_0,axiom,
( hBOOL(hAPP(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_6458]) ).
cnf(c_0_6458_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(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_6458]) ).
cnf(c_0_6458_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(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_6458]) ).
cnf(c_0_6459_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6459]) ).
cnf(c_0_6459_1,axiom,
( ~ hBOOL(hAPP(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_6459]) ).
cnf(c_0_6459_2,axiom,
( X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6459]) ).
cnf(c_0_6459_3,axiom,
( X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(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_6459]) ).
cnf(c_0_6460_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6460]) ).
cnf(c_0_6460_1,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6460]) ).
cnf(c_0_6460_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6460]) ).
cnf(c_0_6461_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6461]) ).
cnf(c_0_6461_1,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6461]) ).
cnf(c_0_6461_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6461]) ).
cnf(c_0_6462_0,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6462]) ).
cnf(c_0_6462_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6462]) ).
cnf(c_0_6462_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6462]) ).
cnf(c_0_6463_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6463]) ).
cnf(c_0_6463_1,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6463]) ).
cnf(c_0_6463_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6463]) ).
cnf(c_0_6464_0,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6464]) ).
cnf(c_0_6464_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6464]) ).
cnf(c_0_6464_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6464]) ).
cnf(c_0_6465_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6465]) ).
cnf(c_0_6465_1,axiom,
( X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6465]) ).
cnf(c_0_6465_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6465]) ).
cnf(c_0_6466_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6466]) ).
cnf(c_0_6466_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6466]) ).
cnf(c_0_6467_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6467]) ).
cnf(c_0_6467_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6467]) ).
cnf(c_0_6468_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6468]) ).
cnf(c_0_6468_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6468]) ).
cnf(c_0_6469_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6469]) ).
cnf(c_0_6469_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6469]) ).
cnf(c_0_6470_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6470]) ).
cnf(c_0_6470_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6470]) ).
cnf(c_0_6471_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6471]) ).
cnf(c_0_6471_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6471]) ).
cnf(c_0_6472_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6472]) ).
cnf(c_0_6472_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6472]) ).
cnf(c_0_6473_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6473]) ).
cnf(c_0_6473_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6473]) ).
cnf(c_0_6477_0,axiom,
( ~ hBOOL(hAPP(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_6477]) ).
cnf(c_0_6477_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(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_6477]) ).
cnf(c_0_6478_0,axiom,
( ~ hBOOL(hAPP(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_6478]) ).
cnf(c_0_6478_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(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_6478]) ).
cnf(c_0_6479_0,axiom,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6479]) ).
cnf(c_0_6479_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6479]) ).
cnf(c_0_6479_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6479]) ).
cnf(c_0_6480_0,axiom,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6480]) ).
cnf(c_0_6480_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6480]) ).
cnf(c_0_6480_2,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6480]) ).
cnf(c_0_6481_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sk1_esk17_2(X1,X2)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6481]) ).
cnf(c_0_6481_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sk1_esk17_2(X1,X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6481]) ).
cnf(c_0_6482_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sk1_esk10_2(X1,X2)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6482]) ).
cnf(c_0_6482_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sk1_esk10_2(X1,X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6482]) ).
cnf(c_0_6483_0,axiom,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6483]) ).
cnf(c_0_6483_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6483]) ).
cnf(c_0_6483_2,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| c_Groups_Oabs__class_Oabs(X1,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6483]) ).
cnf(c_0_6484_0,axiom,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6484]) ).
cnf(c_0_6484_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6484]) ).
cnf(c_0_6484_2,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| c_Groups_Oabs__class_Oabs(X1,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6484]) ).
cnf(c_0_6485_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6485]) ).
cnf(c_0_6485_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6485]) ).
cnf(c_0_6487_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Nat__Transfer_Otsub(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6487]) ).
cnf(c_0_6487_1,axiom,
( ~ hBOOL(hAPP(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_6487]) ).
cnf(c_0_6488_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Nat__Transfer_Otsub(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6488]) ).
cnf(c_0_6488_1,axiom,
( ~ hBOOL(hAPP(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_6488]) ).
cnf(c_0_6489_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_6489]) ).
cnf(c_0_6489_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_6489]) ).
cnf(c_0_6490_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_6490]) ).
cnf(c_0_6490_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_6490]) ).
cnf(c_0_6490_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_6490]) ).
cnf(c_0_6490_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_6490]) ).
cnf(c_0_6491_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_6491]) ).
cnf(c_0_6491_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_6491]) ).
cnf(c_0_6491_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_6491]) ).
cnf(c_0_6491_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_6491]) ).
cnf(c_0_6492_0,axiom,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)
| c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6492]) ).
cnf(c_0_6492_1,axiom,
( c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)) != X1
| c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6492]) ).
cnf(c_0_6493_0,axiom,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(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_6493]) ).
cnf(c_0_6493_1,axiom,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6493]) ).
cnf(c_0_6494_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| X1 != 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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6494]) ).
cnf(c_0_6495_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6495]) ).
cnf(c_0_6495_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(literals_permutation,[status(thm)],[c_0_6495]) ).
cnf(c_0_6496_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_6496]) ).
cnf(c_0_6496_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_6496]) ).
cnf(c_0_6496_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_6496]) ).
cnf(c_0_6497_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6497]) ).
cnf(c_0_6497_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6497]) ).
cnf(c_0_6498_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6498]) ).
cnf(c_0_6498_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6498]) ).
cnf(c_0_6499_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6499]) ).
cnf(c_0_6499_1,axiom,
( ~ hBOOL(hAPP(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_6499]) ).
cnf(c_0_6500_0,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6500]) ).
cnf(c_0_6500_1,axiom,
( ~ hBOOL(hAPP(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_6500]) ).
cnf(c_0_6501_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6501]) ).
cnf(c_0_6501_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6501]) ).
cnf(c_0_6501_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6501]) ).
cnf(c_0_6501_3,axiom,
( X2 != X3
| ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6501]) ).
cnf(c_0_6502_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6502]) ).
cnf(c_0_6502_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6502]) ).
cnf(c_0_6502_2,axiom,
( X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6502]) ).
cnf(c_0_6502_3,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6502]) ).
cnf(c_0_6503_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6503]) ).
cnf(c_0_6503_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6503]) ).
cnf(c_0_6503_2,axiom,
( X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6503]) ).
cnf(c_0_6503_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6503]) ).
cnf(c_0_6504_0,axiom,
( X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6504_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X2 = X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6504_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6504_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6505_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6505]) ).
cnf(c_0_6505_1,axiom,
( X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6505]) ).
cnf(c_0_6505_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6505]) ).
cnf(c_0_6505_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6505]) ).
cnf(c_0_6506_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6506]) ).
cnf(c_0_6506_1,axiom,
( X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6506]) ).
cnf(c_0_6506_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6506]) ).
cnf(c_0_6506_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6506]) ).
cnf(c_0_6507_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6507]) ).
cnf(c_0_6507_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6507]) ).
cnf(c_0_6507_2,axiom,
( X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6507]) ).
cnf(c_0_6507_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6507]) ).
cnf(c_0_6508_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6508]) ).
cnf(c_0_6508_1,axiom,
( X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6508]) ).
cnf(c_0_6508_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6508]) ).
cnf(c_0_6508_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X3 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6508]) ).
cnf(c_0_6509_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(sk1_esk48_2(X2,X1)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6509]) ).
cnf(c_0_6509_1,axiom,
( c_Nat_OSuc(sk1_esk48_2(X2,X1)) = X1
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6509]) ).
cnf(c_0_6509_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| c_Nat_OSuc(sk1_esk48_2(X2,X1)) = X1
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6509]) ).
cnf(c_0_6510_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X2),X4)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6510_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X2),X4)
| X1 = X2
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6510_2,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6511_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6511]) ).
cnf(c_0_6511_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6511]) ).
cnf(c_0_6511_2,axiom,
( ~ class_Groups_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6511]) ).
cnf(c_0_6512_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6512]) ).
cnf(c_0_6512_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6512]) ).
cnf(c_0_6512_2,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6512]) ).
cnf(c_0_6513_0,axiom,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6513]) ).
cnf(c_0_6513_1,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6513]) ).
cnf(c_0_6513_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6513]) ).
cnf(c_0_6514_0,axiom,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6514]) ).
cnf(c_0_6514_1,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6514]) ).
cnf(c_0_6514_2,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6514]) ).
cnf(c_0_6516_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6516]) ).
cnf(c_0_6516_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6516]) ).
cnf(c_0_6516_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6516]) ).
cnf(c_0_6517_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6517_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6517_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6518_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6518]) ).
cnf(c_0_6518_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6518]) ).
cnf(c_0_6518_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6518]) ).
cnf(c_0_6519_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6519]) ).
cnf(c_0_6519_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6519]) ).
cnf(c_0_6519_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6519]) ).
cnf(c_0_6520_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6520]) ).
cnf(c_0_6520_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6520]) ).
cnf(c_0_6520_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6520]) ).
cnf(c_0_6521_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6521]) ).
cnf(c_0_6521_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6521]) ).
cnf(c_0_6521_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6521]) ).
cnf(c_0_6522_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6522]) ).
cnf(c_0_6522_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6522]) ).
cnf(c_0_6522_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6522]) ).
cnf(c_0_6523_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2)))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6523]) ).
cnf(c_0_6523_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6523]) ).
cnf(c_0_6523_2,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6523]) ).
cnf(c_0_6524_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_6524]) ).
cnf(c_0_6524_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_6524]) ).
cnf(c_0_6524_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_6524]) ).
cnf(c_0_6525_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_6525]) ).
cnf(c_0_6525_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_6525]) ).
cnf(c_0_6525_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_6525]) ).
cnf(c_0_6526_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk18_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6526]) ).
cnf(c_0_6526_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk18_2(X2,X1)))
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6526]) ).
cnf(c_0_6526_2,axiom,
( ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk18_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6526]) ).
cnf(c_0_6527_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk13_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6527]) ).
cnf(c_0_6527_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk13_2(X2,X1)))
| ~ c_SEQ_OBseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6527]) ).
cnf(c_0_6527_2,axiom,
( ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk13_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6527]) ).
cnf(c_0_6528_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6528]) ).
cnf(c_0_6528_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6528]) ).
cnf(c_0_6528_2,axiom,
( X1 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6528]) ).
cnf(c_0_6529_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6529]) ).
cnf(c_0_6529_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oabs__class_Oabs(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6529]) ).
cnf(c_0_6530_0,axiom,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6530]) ).
cnf(c_0_6530_1,axiom,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6530]) ).
cnf(c_0_6531_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6531]) ).
cnf(c_0_6531_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6531]) ).
cnf(c_0_6532_0,axiom,
( hBOOL(hAPP(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_6532]) ).
cnf(c_0_6532_1,axiom,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6532]) ).
cnf(c_0_6533_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_6533]) ).
cnf(c_0_6533_1,axiom,
( ~ hBOOL(hAPP(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_6533]) ).
cnf(c_0_6538_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X2 = X1
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6538]) ).
cnf(c_0_6538_1,axiom,
( X2 = X1
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6538]) ).
cnf(c_0_6538_2,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X1))
| X2 = X1
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6538]) ).
cnf(c_0_6539_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6539]) ).
cnf(c_0_6539_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6539]) ).
cnf(c_0_6539_2,axiom,
( X2 = X1
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6539]) ).
cnf(c_0_6540_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6540]) ).
cnf(c_0_6540_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6540]) ).
cnf(c_0_6540_2,axiom,
( X2 = X1
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6540]) ).
cnf(c_0_6541_0,axiom,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6541]) ).
cnf(c_0_6541_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6541]) ).
cnf(c_0_6542_0,axiom,
( X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_Transcendental_Oln(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6542]) ).
cnf(c_0_6542_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Oln(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6542]) ).
cnf(c_0_6542_2,axiom,
( c_Transcendental_Oln(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6542]) ).
cnf(c_0_6543_0,axiom,
( hBOOL(hAPP(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_6543]) ).
cnf(c_0_6543_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(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_6543]) ).
cnf(c_0_6543_2,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(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_6543]) ).
cnf(c_0_6545_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6545]) ).
cnf(c_0_6545_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6545]) ).
cnf(c_0_6546_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6546]) ).
cnf(c_0_6546_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6546]) ).
cnf(c_0_6547_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6547]) ).
cnf(c_0_6547_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6547]) ).
cnf(c_0_6548_0,axiom,
( c_Transcendental_Oln(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6548]) ).
cnf(c_0_6548_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_Transcendental_Oln(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6548]) ).
cnf(c_0_6548_2,axiom,
( X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| c_Transcendental_Oln(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6548]) ).
cnf(c_0_6549_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_6549]) ).
cnf(c_0_6549_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_6549]) ).
cnf(c_0_6549_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_6549]) ).
cnf(c_0_6550_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_6550]) ).
cnf(c_0_6550_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_6550]) ).
cnf(c_0_6550_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_6550]) ).
cnf(c_0_6551_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_6551]) ).
cnf(c_0_6551_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_6551]) ).
cnf(c_0_6551_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_6551]) ).
cnf(c_0_6552_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_6552]) ).
cnf(c_0_6552_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_6552]) ).
cnf(c_0_6552_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_6552]) ).
cnf(c_0_6553_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_6553]) ).
cnf(c_0_6553_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_6553]) ).
cnf(c_0_6553_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_6553]) ).
cnf(c_0_6554_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6554]) ).
cnf(c_0_6554_1,axiom,
( X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6554]) ).
cnf(c_0_6555_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6555]) ).
cnf(c_0_6555_1,axiom,
( X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6555]) ).
cnf(c_0_6556_0,axiom,
( c_Nat_OSuc(sk1_esk49_1(X1)) = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6556]) ).
cnf(c_0_6556_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| c_Nat_OSuc(sk1_esk49_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6556]) ).
cnf(c_0_6559_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = X4
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6559]) ).
cnf(c_0_6559_1,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = X4
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6559]) ).
cnf(c_0_6559_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = X4
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6559]) ).
cnf(c_0_6559_3,axiom,
( X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = X4
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6559]) ).
cnf(c_0_6560_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6560]) ).
cnf(c_0_6560_1,axiom,
( X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6560]) ).
cnf(c_0_6560_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6560]) ).
cnf(c_0_6560_3,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != X4
| ~ class_Rings_Odivision__ring(X1)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6560]) ).
cnf(c_0_6561_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6561]) ).
cnf(c_0_6561_1,axiom,
( X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6561]) ).
cnf(c_0_6561_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6561]) ).
cnf(c_0_6561_3,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != X4
| ~ class_Rings_Odivision__ring(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6561]) ).
cnf(c_0_6562_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = X4
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6562]) ).
cnf(c_0_6562_1,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = X4
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6562]) ).
cnf(c_0_6562_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = X4
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6562]) ).
cnf(c_0_6562_3,axiom,
( X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = X4
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6562]) ).
cnf(c_0_6563_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) = X4
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6563]) ).
cnf(c_0_6563_1,axiom,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) = X4
| X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6563]) ).
cnf(c_0_6563_2,axiom,
( X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) = X4
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6563]) ).
cnf(c_0_6563_3,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_6563]) ).
cnf(c_0_6564_0,axiom,
( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4)
| X4 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4) != X3
| ~ class_Rings_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6564]) ).
cnf(c_0_6564_1,axiom,
( X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4) != X3
| ~ class_Rings_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6564]) ).
cnf(c_0_6564_2,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4) != X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4)
| ~ class_Rings_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6564]) ).
cnf(c_0_6564_3,axiom,
( ~ class_Rings_Odivision__ring(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4) != X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6564]) ).
cnf(c_0_6565_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk38_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6565]) ).
cnf(c_0_6565_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk38_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6565]) ).
cnf(c_0_6566_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk37_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6566]) ).
cnf(c_0_6566_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk37_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6566]) ).
cnf(c_0_6567_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk31_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6567]) ).
cnf(c_0_6567_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk31_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6567]) ).
cnf(c_0_6568_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk30_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6568]) ).
cnf(c_0_6568_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk30_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6568]) ).
cnf(c_0_6569_0,axiom,
( hBOOL(hAPP(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_6569]) ).
cnf(c_0_6569_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| hBOOL(hAPP(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_6569]) ).
cnf(c_0_6570_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6570]) ).
cnf(c_0_6570_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6570]) ).
cnf(c_0_6571_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6571]) ).
cnf(c_0_6571_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6571]) ).
cnf(c_0_6574_0,axiom,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk22_1(X1)),sk1_esk23_1(X1)))
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6574]) ).
cnf(c_0_6574_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk22_1(X1)),sk1_esk23_1(X1)))
| c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6574]) ).
cnf(c_0_6574_2,axiom,
( ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sk1_esk22_1(X1)),sk1_esk23_1(X1)))
| c_SEQ_Oconvergent(tc_RealDef_Oreal,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6574]) ).
cnf(c_0_6576_0,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6576]) ).
cnf(c_0_6576_1,axiom,
( ~ hBOOL(hAPP(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_6576]) ).
cnf(c_0_6579_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6579]) ).
cnf(c_0_6579_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6579]) ).
cnf(c_0_6579_2,axiom,
( c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6579]) ).
cnf(c_0_6580_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oabs__class_Oabs(X1,X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6580]) ).
cnf(c_0_6580_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Oabs__class_Oabs(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6580]) ).
cnf(c_0_6581_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6581]) ).
cnf(c_0_6581_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6581]) ).
cnf(c_0_6581_2,axiom,
( X2 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6581]) ).
cnf(c_0_6582_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6582]) ).
cnf(c_0_6582_1,axiom,
( X2 != X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6582]) ).
cnf(c_0_6582_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6582]) ).
cnf(c_0_6583_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| X2 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6583]) ).
cnf(c_0_6583_1,axiom,
( X2 != X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6583]) ).
cnf(c_0_6583_2,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6583]) ).
cnf(c_0_6584_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6584]) ).
cnf(c_0_6584_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6584]) ).
cnf(c_0_6584_2,axiom,
( X2 != X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6584]) ).
cnf(c_0_6585_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6585]) ).
cnf(c_0_6585_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6585]) ).
cnf(c_0_6585_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6585]) ).
cnf(c_0_6586_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6586]) ).
cnf(c_0_6586_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6586]) ).
cnf(c_0_6586_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6586]) ).
cnf(c_0_6587_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6587]) ).
cnf(c_0_6587_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X2),X1))
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6587]) ).
cnf(c_0_6587_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X3,X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6587]) ).
cnf(c_0_6588_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6588]) ).
cnf(c_0_6588_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6588]) ).
cnf(c_0_6589_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6589]) ).
cnf(c_0_6589_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6589]) ).
cnf(c_0_6590_0,axiom,
( c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6590]) ).
cnf(c_0_6590_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6590]) ).
cnf(c_0_6591_0,axiom,
( c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(literals_permutation,[status(thm)],[c_0_6591]) ).
cnf(c_0_6591_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6591]) ).
cnf(c_0_6592_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(X2,X1)))
| ~ c_SEQ_Osubseq(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6592]) ).
cnf(c_0_6592_1,axiom,
( ~ c_SEQ_Osubseq(X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6592]) ).
cnf(c_0_6594_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_6594]) ).
cnf(c_0_6594_1,axiom,
( ~ hBOOL(hAPP(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_6594]) ).
cnf(c_0_6598_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_6598]) ).
cnf(c_0_6598_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_6598]) ).
cnf(c_0_6599_0,axiom,
( hBOOL(hAPP(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_6599]) ).
cnf(c_0_6599_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(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_6599]) ).
cnf(c_0_6600_0,axiom,
( hBOOL(hAPP(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_6600]) ).
cnf(c_0_6600_1,axiom,
( ~ class_Rings_Olinordered__semidom(X1)
| hBOOL(hAPP(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_6600]) ).
cnf(c_0_6601_0,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6601]) ).
cnf(c_0_6601_1,axiom,
( ~ hBOOL(hAPP(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_6601]) ).
cnf(c_0_6602_0,axiom,
( c_SEQ_Oconvergent(X1,c_COMBK(X1,tc_Nat_Onat,X2))
| ~ class_RealVector_Ometric__space(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6602]) ).
cnf(c_0_6602_1,axiom,
( ~ class_RealVector_Ometric__space(X1)
| c_SEQ_Oconvergent(X1,c_COMBK(X1,tc_Nat_Onat,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6602]) ).
cnf(c_0_6603_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6603]) ).
cnf(c_0_6603_1,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6603]) ).
cnf(c_0_6604_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_6604]) ).
cnf(c_0_6604_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_6604]) ).
cnf(c_0_6604_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_6604]) ).
cnf(c_0_6604_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_6604]) ).
cnf(c_0_6604_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_6604]) ).
cnf(c_0_6604_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_6604]) ).
cnf(c_0_6605_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6605]) ).
cnf(c_0_6605_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6605]) ).
cnf(c_0_6606_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6606]) ).
cnf(c_0_6606_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6606]) ).
cnf(c_0_6607_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6607]) ).
cnf(c_0_6607_1,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6607]) ).
cnf(c_0_6608_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6608]) ).
cnf(c_0_6608_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6608]) ).
cnf(c_0_6609_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6609]) ).
cnf(c_0_6609_1,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6609]) ).
cnf(c_0_6610_0,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6610]) ).
cnf(c_0_6610_1,axiom,
( X1 != X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6610]) ).
cnf(c_0_6611_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_6611]) ).
cnf(c_0_6611_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_6611]) ).
cnf(c_0_6611_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_6611]) ).
cnf(c_0_6611_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_6611]) ).
cnf(c_0_6611_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_6611]) ).
cnf(c_0_6611_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_6611]) ).
cnf(c_0_6615_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_6615]) ).
cnf(c_0_6615_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_6615]) ).
cnf(c_0_6619_0,axiom,
( c_SEQ_Osubseq(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk3_1(X1)),sk1_esk4_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6619]) ).
cnf(c_0_6619_1,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk3_1(X1)),sk1_esk4_1(X1)))
| c_SEQ_Osubseq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6619]) ).
cnf(c_0_6620_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6620]) ).
cnf(c_0_6620_1,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6620]) ).
cnf(c_0_6620_2,axiom,
( X2 != X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6620]) ).
cnf(c_0_6621_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6621]) ).
cnf(c_0_6621_1,axiom,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_6621]) ).
cnf(c_0_6621_2,axiom,
( X3 != X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6621]) ).
cnf(c_0_6623_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_6623]) ).
cnf(c_0_6623_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_6623]) ).
cnf(c_0_6624_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6624]) ).
cnf(c_0_6624_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6624]) ).
cnf(c_0_6626_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk36_1(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)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk36_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6626]) ).
cnf(c_0_6627_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk29_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6627]) ).
cnf(c_0_6627_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk29_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6627]) ).
cnf(c_0_6630_0,axiom,
( hBOOL(hAPP(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_6630]) ).
cnf(c_0_6630_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(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_6630]) ).
cnf(c_0_6631_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_6631]) ).
cnf(c_0_6631_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_6631]) ).
cnf(c_0_6631_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_6631]) ).
cnf(c_0_6631_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_6631]) ).
cnf(c_0_6632_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_6632]) ).
cnf(c_0_6632_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_6632]) ).
cnf(c_0_6632_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_6632]) ).
cnf(c_0_6632_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_6632]) ).
cnf(c_0_6633_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_6633]) ).
cnf(c_0_6633_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_6633]) ).
cnf(c_0_6633_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_6633]) ).
cnf(c_0_6633_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_6633]) ).
cnf(c_0_6634_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = X2
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6634]) ).
cnf(c_0_6634_1,axiom,
( X3 = X2
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6634]) ).
cnf(c_0_6634_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X3 = X2
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6634]) ).
cnf(c_0_6634_3,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1)
| X3 = X2
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6634]) ).
cnf(c_0_6635_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_6635]) ).
cnf(c_0_6635_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_6635]) ).
cnf(c_0_6635_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_6635]) ).
cnf(c_0_6636_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_6636]) ).
cnf(c_0_6636_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_6636]) ).
cnf(c_0_6636_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_6636]) ).
cnf(c_0_6637_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_6637]) ).
cnf(c_0_6637_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_6637]) ).
cnf(c_0_6637_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_6637]) ).
cnf(c_0_6638_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6638]) ).
cnf(c_0_6638_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6638]) ).
cnf(c_0_6638_2,axiom,
( hAPP(hAPP(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_6638]) ).
cnf(c_0_6639_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6639]) ).
cnf(c_0_6639_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6639]) ).
cnf(c_0_6639_2,axiom,
( hAPP(hAPP(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_6639]) ).
cnf(c_0_6640_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))
| hAPP(hAPP(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_6640]) ).
cnf(c_0_6640_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))
| hAPP(hAPP(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_6640]) ).
cnf(c_0_6640_2,axiom,
( hAPP(hAPP(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_6640]) ).
cnf(c_0_6641_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))
| hAPP(hAPP(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_6641]) ).
cnf(c_0_6641_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))
| hAPP(hAPP(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_6641]) ).
cnf(c_0_6641_2,axiom,
( hAPP(hAPP(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_6641]) ).
cnf(c_0_6645_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_6645]) ).
cnf(c_0_6645_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_6645]) ).
cnf(c_0_6645_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_6645]) ).
cnf(c_0_6646_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_6646]) ).
cnf(c_0_6646_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_6646]) ).
cnf(c_0_6646_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_6646]) ).
cnf(c_0_6647_0,axiom,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6647]) ).
cnf(c_0_6647_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6647]) ).
cnf(c_0_6648_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_6648]) ).
cnf(c_0_6648_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_6648]) ).
cnf(c_0_6649_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_6649]) ).
cnf(c_0_6649_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_6649]) ).
cnf(c_0_6650_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_6650]) ).
cnf(c_0_6650_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_6650]) ).
cnf(c_0_6651_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_6651]) ).
cnf(c_0_6651_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_6651]) ).
cnf(c_0_6651_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_6651]) ).
cnf(c_0_6651_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_6651]) ).
cnf(c_0_6651_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_6651]) ).
cnf(c_0_6651_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_6651]) ).
cnf(c_0_6651_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_6651]) ).
cnf(c_0_6652_0,axiom,
( hBOOL(hAPP(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_6652]) ).
cnf(c_0_6652_1,axiom,
( X1 != c_Nat_OSuc(X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6652]) ).
cnf(c_0_6653_0,axiom,
( hBOOL(hAPP(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_6653]) ).
cnf(c_0_6653_1,axiom,
( X1 != c_Nat_OSuc(X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6653]) ).
cnf(c_0_6654_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6654]) ).
cnf(c_0_6654_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6654]) ).
cnf(c_0_6654_2,axiom,
( hAPP(hAPP(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_6654]) ).
cnf(c_0_6655_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_6655]) ).
cnf(c_0_6655_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_6655]) ).
cnf(c_0_6655_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_6655]) ).
cnf(c_0_6656_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(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)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(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_6656]) ).
cnf(c_0_6656_2,axiom,
( hAPP(hAPP(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_6656]) ).
cnf(c_0_6657_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(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_6657]) ).
cnf(c_0_6657_1,axiom,
( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6657]) ).
cnf(c_0_6657_2,axiom,
( hAPP(hAPP(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_6657]) ).
cnf(c_0_6658_0,axiom,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6658]) ).
cnf(c_0_6658_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(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_6658]) ).
cnf(c_0_6658_2,axiom,
( hAPP(hAPP(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_6658]) ).
cnf(c_0_6659_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(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_6659]) ).
cnf(c_0_6659_1,axiom,
( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6659]) ).
cnf(c_0_6659_2,axiom,
( hAPP(hAPP(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_6659]) ).
cnf(c_0_6660_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_6660]) ).
cnf(c_0_6660_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_6660]) ).
cnf(c_0_6661_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_6661]) ).
cnf(c_0_6661_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_6661]) ).
cnf(c_0_6662_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_6662]) ).
cnf(c_0_6662_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_6662]) ).
cnf(c_0_6663_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6663]) ).
cnf(c_0_6663_1,axiom,
( X2 != X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6663]) ).
cnf(c_0_6664_0,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6664]) ).
cnf(c_0_6664_1,axiom,
( X1 != X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6664]) ).
cnf(c_0_6668_0,axiom,
( hBOOL(hAPP(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_6668]) ).
cnf(c_0_6668_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6668]) ).
cnf(c_0_6669_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6669]) ).
cnf(c_0_6669_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6669]) ).
cnf(c_0_6669_2,axiom,
( X2 != X3
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6669]) ).
cnf(c_0_6670_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6670]) ).
cnf(c_0_6670_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6670]) ).
cnf(c_0_6670_2,axiom,
( X2 != X3
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6670]) ).
cnf(c_0_6671_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6671]) ).
cnf(c_0_6671_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6671]) ).
cnf(c_0_6671_2,axiom,
( X2 != X3
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6671]) ).
cnf(c_0_6672_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 != X3
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6672]) ).
cnf(c_0_6672_1,axiom,
( X2 != X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6672]) ).
cnf(c_0_6672_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| X2 != X3
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6672]) ).
cnf(c_0_6673_0,axiom,
( c_Nat__Transfer_Otsub(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6673]) ).
cnf(c_0_6673_1,axiom,
( hBOOL(hAPP(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_6673]) ).
cnf(c_0_6674_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_6674]) ).
cnf(c_0_6674_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_6674]) ).
cnf(c_0_6675_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_6675]) ).
cnf(c_0_6675_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_6675]) ).
cnf(c_0_6681_0,axiom,
( hBOOL(hAPP(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_6681]) ).
cnf(c_0_6681_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6681]) ).
cnf(c_0_6682_0,axiom,
( hBOOL(hAPP(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_6682]) ).
cnf(c_0_6682_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6682]) ).
cnf(c_0_6683_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2)))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6683]) ).
cnf(c_0_6683_1,axiom,
( X1 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6683]) ).
cnf(c_0_6684_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6684]) ).
cnf(c_0_6684_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6684]) ).
cnf(c_0_6684_2,axiom,
( hAPP(hAPP(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_6684]) ).
cnf(c_0_6685_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6685]) ).
cnf(c_0_6685_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(literals_permutation,[status(thm)],[c_0_6685]) ).
cnf(c_0_6685_2,axiom,
( hAPP(hAPP(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_6685]) ).
cnf(c_0_6688_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6688]) ).
cnf(c_0_6688_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6688]) ).
cnf(c_0_6689_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_6689]) ).
cnf(c_0_6689_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_6689]) ).
cnf(c_0_6689_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_6689]) ).
cnf(c_0_6690_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_6690]) ).
cnf(c_0_6690_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_6690]) ).
cnf(c_0_6690_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_6690]) ).
cnf(c_0_6690_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_6690]) ).
cnf(c_0_6694_0,axiom,
( hBOOL(hAPP(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_6694]) ).
cnf(c_0_6694_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(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_6694]) ).
cnf(c_0_6695_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_6695]) ).
cnf(c_0_6695_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_6695]) ).
cnf(c_0_6695_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_6695]) ).
cnf(c_0_6695_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_6695]) ).
cnf(c_0_6701_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_6701]) ).
cnf(c_0_6701_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_6701]) ).
cnf(c_0_6701_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_6701]) ).
cnf(c_0_6702_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_6702]) ).
cnf(c_0_6702_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_6702]) ).
cnf(c_0_6702_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_6702]) ).
cnf(c_0_6704_0,axiom,
( X1 = X2
| hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6704]) ).
cnf(c_0_6704_1,axiom,
( hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| X1 = X2
| hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6704]) ).
cnf(c_0_6704_2,axiom,
( hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2)
| hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6704]) ).
cnf(c_0_6705_0,axiom,
( X1 = X2
| hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6705]) ).
cnf(c_0_6705_1,axiom,
( hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| X1 = X2
| hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6705]) ).
cnf(c_0_6705_2,axiom,
( hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2)
| hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6705]) ).
cnf(c_0_6706_0,axiom,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6706]) ).
cnf(c_0_6706_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6706]) ).
cnf(c_0_6707_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_6707]) ).
cnf(c_0_6707_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_6707]) ).
cnf(c_0_6708_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_6708]) ).
cnf(c_0_6708_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_6708]) ).
cnf(c_0_6709_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_6709]) ).
cnf(c_0_6709_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_6709]) ).
cnf(c_0_6710_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_6710]) ).
cnf(c_0_6710_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_6710]) ).
cnf(c_0_6711_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6711]) ).
cnf(c_0_6711_1,axiom,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6711]) ).
cnf(c_0_6712_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6712]) ).
cnf(c_0_6712_1,axiom,
( hAPP(hAPP(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_6712]) ).
cnf(c_0_6713_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6713]) ).
cnf(c_0_6713_1,axiom,
( X1 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6713]) ).
cnf(c_0_6714_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6714]) ).
cnf(c_0_6714_1,axiom,
( X1 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6714]) ).
cnf(c_0_6715_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6715]) ).
cnf(c_0_6715_1,axiom,
( X1 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6715]) ).
cnf(c_0_6716_0,axiom,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6716]) ).
cnf(c_0_6716_1,axiom,
( X1 != X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6716]) ).
cnf(c_0_6717_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_6717]) ).
cnf(c_0_6717_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_6717]) ).
cnf(c_0_6717_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_6717]) ).
cnf(c_0_6718_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_6718]) ).
cnf(c_0_6718_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_6718]) ).
cnf(c_0_6719_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6719]) ).
cnf(c_0_6719_1,axiom,
( hAPP(hAPP(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_6719]) ).
cnf(c_0_6724_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6724]) ).
cnf(c_0_6724_1,axiom,
( ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6724]) ).
cnf(c_0_6725_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6725]) ).
cnf(c_0_6725_1,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6725]) ).
cnf(c_0_6726_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_6726]) ).
cnf(c_0_6726_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_6726]) ).
cnf(c_0_6727_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_6727]) ).
cnf(c_0_6727_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_6727]) ).
cnf(c_0_6728_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_6728]) ).
cnf(c_0_6728_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_6728]) ).
cnf(c_0_6729_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_6729]) ).
cnf(c_0_6729_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_6729]) ).
cnf(c_0_6730_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_6730]) ).
cnf(c_0_6730_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_6730]) ).
cnf(c_0_6731_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_6731]) ).
cnf(c_0_6731_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_6731]) ).
cnf(c_0_6732_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_6732]) ).
cnf(c_0_6732_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_6732]) ).
cnf(c_0_6733_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_6733]) ).
cnf(c_0_6733_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_6733]) ).
cnf(c_0_6734_0,axiom,
( hAPP(hAPP(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_6734]) ).
cnf(c_0_6734_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6734]) ).
cnf(c_0_6735_0,axiom,
( hAPP(hAPP(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_6735]) ).
cnf(c_0_6735_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6735]) ).
cnf(c_0_6736_0,axiom,
( hAPP(hAPP(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_6736]) ).
cnf(c_0_6736_1,axiom,
( ~ class_Groups_Omonoid__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6736]) ).
cnf(c_0_6737_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6737]) ).
cnf(c_0_6737_1,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6737]) ).
cnf(c_0_6737_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6737]) ).
cnf(c_0_6737_3,axiom,
( X3 != X2
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6737]) ).
cnf(c_0_6738_0,axiom,
( hAPP(hAPP(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_6738]) ).
cnf(c_0_6738_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(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_6738]) ).
cnf(c_0_6738_2,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_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_6738]) ).
cnf(c_0_6739_0,axiom,
( hAPP(hAPP(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_6739]) ).
cnf(c_0_6739_1,axiom,
( X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(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_6739]) ).
cnf(c_0_6739_2,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(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_6739]) ).
cnf(c_0_6740_0,axiom,
( hAPP(hAPP(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_6740]) ).
cnf(c_0_6740_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(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_6740]) ).
cnf(c_0_6740_2,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_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_6740]) ).
cnf(c_0_6741_0,axiom,
( hAPP(hAPP(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_6741]) ).
cnf(c_0_6741_1,axiom,
( X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(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_6741]) ).
cnf(c_0_6741_2,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(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_6741]) ).
cnf(c_0_6742_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),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_6742]) ).
cnf(c_0_6742_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),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_6742_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6742]) ).
cnf(c_0_6743_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_6743]) ).
cnf(c_0_6743_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_6743]) ).
cnf(c_0_6744_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_6744]) ).
cnf(c_0_6744_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_6744]) ).
cnf(c_0_6745_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_6745]) ).
cnf(c_0_6745_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_6745]) ).
cnf(c_0_6745_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_6745]) ).
cnf(c_0_6746_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_6746]) ).
cnf(c_0_6746_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_6746]) ).
cnf(c_0_6746_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_6746]) ).
cnf(c_0_6747_0,axiom,
( hAPP(hAPP(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_6747]) ).
cnf(c_0_6747_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(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_6747]) ).
cnf(c_0_6747_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6747]) ).
cnf(c_0_6748_0,axiom,
( hAPP(hAPP(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_6748]) ).
cnf(c_0_6748_1,axiom,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(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_6748]) ).
cnf(c_0_6748_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6748]) ).
cnf(c_0_6749_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6749]) ).
cnf(c_0_6749_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6749]) ).
cnf(c_0_6749_2,axiom,
( ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6749]) ).
cnf(c_0_6750_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6750]) ).
cnf(c_0_6750_1,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6750]) ).
cnf(c_0_6751_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_6751]) ).
cnf(c_0_6751_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_6751]) ).
cnf(c_0_6752_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_6752]) ).
cnf(c_0_6752_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_6752]) ).
cnf(c_0_6753_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_6753]) ).
cnf(c_0_6753_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_6753]) ).
cnf(c_0_6754_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_6754]) ).
cnf(c_0_6754_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_6754]) ).
cnf(c_0_6755_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_6755]) ).
cnf(c_0_6755_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_6755]) ).
cnf(c_0_6755_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_6755]) ).
cnf(c_0_6756_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_6756]) ).
cnf(c_0_6756_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_6756]) ).
cnf(c_0_6756_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_6756]) ).
cnf(c_0_6757_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_6757]) ).
cnf(c_0_6757_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_6757]) ).
cnf(c_0_6757_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_6757]) ).
cnf(c_0_6758_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6758]) ).
cnf(c_0_6758_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6758]) ).
cnf(c_0_6758_2,axiom,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6758]) ).
cnf(c_0_6759_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_6759]) ).
cnf(c_0_6759_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6759]) ).
cnf(c_0_6759_2,axiom,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6759]) ).
cnf(c_0_6760_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6760]) ).
cnf(c_0_6760_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6760]) ).
cnf(c_0_6761_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_6761]) ).
cnf(c_0_6761_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_6761]) ).
cnf(c_0_6762_0,axiom,
( hAPP(hAPP(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_6762]) ).
cnf(c_0_6762_1,axiom,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = X2
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6762]) ).
cnf(c_0_6762_2,axiom,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6762]) ).
cnf(c_0_6763_0,axiom,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6763]) ).
cnf(c_0_6763_1,axiom,
( ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6763]) ).
cnf(c_0_6764_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_6764]) ).
cnf(c_0_6764_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_6764]) ).
cnf(c_0_6765_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_6765]) ).
cnf(c_0_6765_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_6765]) ).
cnf(c_0_6766_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_6766]) ).
cnf(c_0_6766_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_6766]) ).
cnf(c_0_6767_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_6767]) ).
cnf(c_0_6767_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_6767]) ).
cnf(c_0_6768_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_6768]) ).
cnf(c_0_6768_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_6768]) ).
cnf(c_0_6769_0,axiom,
( hAPP(hAPP(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_6769]) ).
cnf(c_0_6769_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6769]) ).
cnf(c_0_6770_0,axiom,
( hAPP(hAPP(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_6770]) ).
cnf(c_0_6770_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6770]) ).
cnf(c_0_6771_0,axiom,
( hAPP(hAPP(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_6771]) ).
cnf(c_0_6771_1,axiom,
( ~ class_Groups_Omonoid__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6771]) ).
cnf(c_0_6772_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_6772]) ).
cnf(c_0_6772_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_6772]) ).
cnf(c_0_6774_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_6774]) ).
cnf(c_0_6774_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_6774]) ).
cnf(c_0_6776_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_6776]) ).
cnf(c_0_6776_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_6776]) ).
cnf(c_0_6777_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_6777]) ).
cnf(c_0_6777_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_6777]) ).
cnf(c_0_6779_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6779]) ).
cnf(c_0_6779_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6779]) ).
cnf(c_0_6780_0,axiom,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Osgn__class_Osgn(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6780]) ).
cnf(c_0_6780_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Osgn__class_Osgn(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6780]) ).
cnf(c_0_6781_0,axiom,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6781]) ).
cnf(c_0_6781_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6781]) ).
cnf(c_0_6783_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_6783]) ).
cnf(c_0_6783_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_6783]) ).
cnf(c_0_6783_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_6783]) ).
cnf(c_0_6784_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_6784]) ).
cnf(c_0_6784_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_6784]) ).
cnf(c_0_6784_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_6784]) ).
cnf(c_0_6785_0,axiom,
( hAPP(hAPP(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_6785]) ).
cnf(c_0_6785_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6785]) ).
cnf(c_0_6785_2,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6785]) ).
cnf(c_0_6786_0,axiom,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6786]) ).
cnf(c_0_6786_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6786]) ).
cnf(c_0_6787_0,axiom,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6787]) ).
cnf(c_0_6787_1,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(literals_permutation,[status(thm)],[c_0_6787]) ).
cnf(c_0_6788_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_6788]) ).
cnf(c_0_6788_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_6788]) ).
cnf(c_0_6791_0,axiom,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(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_6791]) ).
cnf(c_0_6791_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6791]) ).
cnf(c_0_6791_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6791]) ).
cnf(c_0_6795_0,axiom,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6795]) ).
cnf(c_0_6795_1,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6795]) ).
cnf(c_0_6795_2,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6795]) ).
cnf(c_0_6797_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_6797]) ).
cnf(c_0_6797_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_6797]) ).
cnf(c_0_6798_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_6798]) ).
cnf(c_0_6798_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_6798]) ).
cnf(c_0_6799_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_6799]) ).
cnf(c_0_6799_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_6799]) ).
cnf(c_0_6800_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_6800]) ).
cnf(c_0_6800_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_6800]) ).
cnf(c_0_6801_0,axiom,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,X1)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6801]) ).
cnf(c_0_6801_1,axiom,
( ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,X1)
| c_SEQ_Oconvergent(tc_RealDef_Oreal,X1)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6801]) ).
cnf(c_0_6801_2,axiom,
( ~ c_SEQ_OBseq(tc_RealDef_Oreal,X1)
| ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,X1)
| c_SEQ_Oconvergent(tc_RealDef_Oreal,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6801]) ).
cnf(c_0_6808_0,axiom,
( hAPP(hAPP(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_6808]) ).
cnf(c_0_6808_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6808]) ).
cnf(c_0_6816_0,axiom,
( X1 = X3
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6816]) ).
cnf(c_0_6816_1,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4)
| X1 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6816]) ).
cnf(c_0_6817_0,axiom,
( X2 = X4
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6817]) ).
cnf(c_0_6817_1,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4)
| X2 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_6817]) ).
cnf(c_0_6818_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_6818]) ).
cnf(c_0_6818_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_6818]) ).
cnf(c_0_6818_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_6818]) ).
cnf(c_0_6819_0,axiom,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_SEQ_Odecseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6819]) ).
cnf(c_0_6819_1,axiom,
( ~ c_SEQ_Odecseq(X1,X2)
| c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6819]) ).
cnf(c_0_6819_2,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_SEQ_Odecseq(X1,X2)
| c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6819]) ).
cnf(c_0_6820_0,axiom,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_SEQ_Oincseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6820]) ).
cnf(c_0_6820_1,axiom,
( ~ c_SEQ_Oincseq(X1,X2)
| c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6820]) ).
cnf(c_0_6820_2,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_SEQ_Oincseq(X1,X2)
| c_SEQ_Omonoseq(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6820]) ).
cnf(c_0_6821_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_6821]) ).
cnf(c_0_6821_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_6821]) ).
cnf(c_0_6821_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_6821]) ).
cnf(c_0_6822_0,axiom,
( X1 = X2
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_RealDef_Oreal(tc_Nat_Onat,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6822]) ).
cnf(c_0_6822_1,axiom,
( c_RealDef_Oreal(tc_Nat_Onat,X1) != c_RealDef_Oreal(tc_Nat_Onat,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6822]) ).
cnf(c_0_6823_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6823]) ).
cnf(c_0_6823_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6823]) ).
cnf(c_0_6823_2,axiom,
( c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6823]) ).
cnf(c_0_6824_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6824]) ).
cnf(c_0_6824_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6824]) ).
cnf(c_0_6824_2,axiom,
( c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6824]) ).
cnf(c_0_6825_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6825]) ).
cnf(c_0_6825_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6825]) ).
cnf(c_0_6825_2,axiom,
( c_Groups_Oabs__class_Oabs(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6825]) ).
cnf(c_0_6829_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_6829]) ).
cnf(c_0_6829_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_6829]) ).
cnf(c_0_6829_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_6829]) ).
cnf(c_0_6830_0,axiom,
( class_Orderings_Oord(tc_fun(X1,X2))
| ~ class_Orderings_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6830]) ).
cnf(c_0_6830_1,axiom,
( ~ class_Orderings_Oord(X2)
| class_Orderings_Oord(tc_fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6830]) ).
cnf(c_0_6831_0,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6831]) ).
cnf(c_0_6831_1,axiom,
( ~ class_Orderings_Oorder(X2)
| class_Orderings_Oorder(tc_fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6831]) ).
cnf(c_0_6832_0,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6832]) ).
cnf(c_0_6832_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| class_Orderings_Opreorder(tc_fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6832]) ).
cnf(c_0_6833_0,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Complex_Ocomplex_OComplex(X3,X4)
| X2 != X4
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6833]) ).
cnf(c_0_6833_1,axiom,
( X2 != X4
| c_Complex_Ocomplex_OComplex(X1,X2) = c_Complex_Ocomplex_OComplex(X3,X4)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6833]) ).
cnf(c_0_6833_2,axiom,
( X1 != X3
| X2 != X4
| c_Complex_Ocomplex_OComplex(X1,X2) = c_Complex_Ocomplex_OComplex(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6833]) ).
cnf(c_0_6834_0,axiom,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6834]) ).
cnf(c_0_6834_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6834]) ).
cnf(c_0_6834_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6834]) ).
cnf(c_0_6835_0,axiom,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6835]) ).
cnf(c_0_6835_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6835]) ).
cnf(c_0_6835_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6835]) ).
cnf(c_0_6836_0,axiom,
( c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6836]) ).
cnf(c_0_6836_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6836]) ).
cnf(c_0_6836_2,axiom,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6836]) ).
cnf(c_0_6838_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_6838]) ).
cnf(c_0_6838_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_6838]) ).
cnf(c_0_6838_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_6838]) ).
cnf(c_0_6839_0,axiom,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6839]) ).
cnf(c_0_6839_1,axiom,
( c_Transcendental_Osin(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6839]) ).
cnf(c_0_6840_0,axiom,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6840]) ).
cnf(c_0_6840_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_Groups_Osgn__class_Osgn(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6840]) ).
cnf(c_0_6841_0,axiom,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6841]) ).
cnf(c_0_6841_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6841]) ).
cnf(c_0_6842_0,axiom,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Osgn__if(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6842]) ).
cnf(c_0_6842_1,axiom,
( ~ class_Groups_Osgn__if(X1)
| c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6842]) ).
cnf(c_0_6843_0,axiom,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6843]) ).
cnf(c_0_6843_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Oabs__class_Oabs(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6843]) ).
cnf(c_0_6844_0,axiom,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6844]) ).
cnf(c_0_6844_1,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6844]) ).
cnf(c_0_6847_0,axiom,
( X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6847]) ).
cnf(c_0_6847_1,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6847]) ).
cnf(c_0_6848_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6848]) ).
cnf(c_0_6848_1,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6848]) ).
cnf(c_0_6849_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6849]) ).
cnf(c_0_6849_1,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6849]) ).
cnf(c_0_6850_0,axiom,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6850]) ).
cnf(c_0_6850_1,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6850]) ).
cnf(c_0_6851_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_6851]) ).
cnf(c_0_6851_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_6851]) ).
cnf(c_0_6852_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_6852]) ).
cnf(c_0_6852_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_6852]) ).
cnf(c_0_6853_0,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6853]) ).
cnf(c_0_6853_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6853]) ).
cnf(c_0_6853_2,axiom,
( X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6853]) ).
cnf(c_0_6854_0,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| 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_6854]) ).
cnf(c_0_6854_1,axiom,
( X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6854]) ).
cnf(c_0_6854_2,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6854]) ).
cnf(c_0_6855_0,axiom,
( c_RealDef_Oreal(tc_Nat_Onat,X1) = c_RealDef_Oreal(tc_Nat_Onat,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6855]) ).
cnf(c_0_6855_1,axiom,
( X1 != X2
| c_RealDef_Oreal(tc_Nat_Onat,X1) = c_RealDef_Oreal(tc_Nat_Onat,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6855]) ).
cnf(c_0_6856_0,axiom,
( hAPP(c_Complex_ORe,X1) = hAPP(c_Complex_ORe,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6856]) ).
cnf(c_0_6856_1,axiom,
( X1 != X2
| hAPP(c_Complex_ORe,X1) = hAPP(c_Complex_ORe,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6856]) ).
cnf(c_0_6857_0,axiom,
( hAPP(c_Complex_OIm,X1) = hAPP(c_Complex_OIm,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6857]) ).
cnf(c_0_6857_1,axiom,
( X1 != X2
| hAPP(c_Complex_OIm,X1) = hAPP(c_Complex_OIm,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6857]) ).
cnf(c_0_6860_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6860]) ).
cnf(c_0_6860_1,axiom,
( c_RealDef_Oreal(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6860]) ).
cnf(c_0_6862_0,axiom,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Oii ),
inference(literals_permutation,[status(thm)],[c_0_6862]) ).
cnf(c_0_6862_1,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Oii
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6862]) ).
cnf(c_0_6863_0,axiom,
( X2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Oii ),
inference(literals_permutation,[status(thm)],[c_0_6863]) ).
cnf(c_0_6863_1,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Oii
| X2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6863]) ).
cnf(c_0_6864_0,axiom,
( c_Complex_Ocomplex_OComplex(X1,X2) = c_Complex_Oii
| X2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6864]) ).
cnf(c_0_6864_1,axiom,
( X2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) = c_Complex_Oii
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6864]) ).
cnf(c_0_6864_2,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) = c_Complex_Oii ),
inference(literals_permutation,[status(thm)],[c_0_6864]) ).
cnf(c_0_6871_0,axiom,
( c_RealDef_Oreal(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(literals_permutation,[status(thm)],[c_0_6871]) ).
cnf(c_0_6871_1,axiom,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6871]) ).
cnf(c_0_6872_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_6872]) ).
cnf(c_0_6872_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_6872]) ).
cnf(c_0_6872_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_6872]) ).
cnf(c_0_6873_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_6873]) ).
cnf(c_0_6873_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_6873]) ).
cnf(c_0_6873_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_6873]) ).
cnf(c_0_6874_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_6874]) ).
cnf(c_0_6874_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_6874]) ).
cnf(c_0_6874_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_6874]) ).
cnf(c_0_6875_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_6875]) ).
cnf(c_0_6875_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_6875]) ).
cnf(c_0_6875_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_6875]) ).
cnf(c_0_6877_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_6877]) ).
cnf(c_0_6877_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_6877]) ).
cnf(c_0_6878_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_6878]) ).
cnf(c_0_6878_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_6878]) ).
cnf(c_0_6886_0,axiom,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6886]) ).
cnf(c_0_6886_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Groups_Oone(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6886]) ).
cnf(c_0_6887_0,axiom,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6887]) ).
cnf(c_0_6887_1,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Oring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6887]) ).
cnf(c_0_6888_0,axiom,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6888]) ).
cnf(c_0_6888_1,axiom,
( ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6888]) ).
cnf(c_0_6889_0,axiom,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6889]) ).
cnf(c_0_6889_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Power_Opower(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6889]) ).
cnf(c_0_6890_0,axiom,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6890]) ).
cnf(c_0_6890_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6890]) ).
cnf(c_0_6891_0,axiom,
( class_Groups_Osgn__if(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6891]) ).
cnf(c_0_6891_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Osgn__if(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6891]) ).
cnf(c_0_6892_0,axiom,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6892]) ).
cnf(c_0_6892_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Orderings_Oord(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6892]) ).
cnf(c_0_6893_0,axiom,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6893]) ).
cnf(c_0_6893_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6893]) ).
cnf(c_0_6894_0,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6894]) ).
cnf(c_0_6894_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6894]) ).
cnf(c_0_6895_0,axiom,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6895]) ).
cnf(c_0_6895_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6895]) ).
cnf(c_0_6896_0,axiom,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6896]) ).
cnf(c_0_6896_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6896]) ).
cnf(c_0_6897_0,axiom,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6897]) ).
cnf(c_0_6897_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6897]) ).
cnf(c_0_6898_0,axiom,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6898]) ).
cnf(c_0_6898_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6898]) ).
cnf(c_0_6899_0,axiom,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6899]) ).
cnf(c_0_6899_1,axiom,
( ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6899]) ).
cnf(c_0_6900_0,axiom,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6900]) ).
cnf(c_0_6900_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6900]) ).
cnf(c_0_6901_0,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6901]) ).
cnf(c_0_6901_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6901]) ).
cnf(c_0_6902_0,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6902]) ).
cnf(c_0_6902_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6902]) ).
cnf(c_0_6903_0,axiom,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6903]) ).
cnf(c_0_6903_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6903]) ).
cnf(c_0_6904_0,axiom,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6904]) ).
cnf(c_0_6904_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6904]) ).
cnf(c_0_6905_0,axiom,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6905]) ).
cnf(c_0_6905_1,axiom,
( ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6905]) ).
cnf(c_0_6906_0,axiom,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6906]) ).
cnf(c_0_6906_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6906]) ).
cnf(c_0_6907_0,axiom,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6907]) ).
cnf(c_0_6907_1,axiom,
( ~ class_Fields_Ofield(X1)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6907]) ).
cnf(c_0_6908_0,axiom,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6908]) ).
cnf(c_0_6908_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6908]) ).
cnf(c_0_6909_0,axiom,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6909]) ).
cnf(c_0_6909_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6909]) ).
cnf(c_0_6910_0,axiom,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6910]) ).
cnf(c_0_6910_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6910]) ).
cnf(c_0_6911_0,axiom,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6911]) ).
cnf(c_0_6911_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6911]) ).
cnf(c_0_6912_0,axiom,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6912]) ).
cnf(c_0_6912_1,axiom,
( ~ class_Rings_Oidom(X1)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6912]) ).
cnf(c_0_6913_0,axiom,
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6913]) ).
cnf(c_0_6913_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6913]) ).
cnf(c_0_6914_0,axiom,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6914]) ).
cnf(c_0_6914_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6914]) ).
cnf(c_0_6915_0,axiom,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6915]) ).
cnf(c_0_6915_1,axiom,
( ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6915]) ).
cnf(c_0_6916_0,axiom,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6916]) ).
cnf(c_0_6916_1,axiom,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6916]) ).
cnf(c_0_6917_0,axiom,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6917]) ).
cnf(c_0_6917_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6917]) ).
cnf(c_0_6918_0,axiom,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6918]) ).
cnf(c_0_6918_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6918]) ).
cnf(c_0_6919_0,axiom,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6919]) ).
cnf(c_0_6919_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6919]) ).
cnf(c_0_6920_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_6920]) ).
cnf(c_0_6920_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_6920]) ).
cnf(c_0_6921_0,axiom,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6921]) ).
cnf(c_0_6921_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6921]) ).
cnf(c_0_6922_0,axiom,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6922]) ).
cnf(c_0_6922_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6922]) ).
cnf(c_0_6923_0,axiom,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6923]) ).
cnf(c_0_6923_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6923]) ).
cnf(c_0_6924_0,axiom,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6924]) ).
cnf(c_0_6924_1,axiom,
( ~ class_Rings_Oidom(X1)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6924]) ).
cnf(c_0_6925_0,axiom,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6925]) ).
cnf(c_0_6925_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6925]) ).
cnf(c_0_6926_0,axiom,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6926]) ).
cnf(c_0_6926_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6926]) ).
cnf(c_0_6927_0,axiom,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6927]) ).
cnf(c_0_6927_1,axiom,
( ~ class_Rings_Oidom(X1)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6927]) ).
cnf(c_0_6928_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_6928]) ).
cnf(c_0_6928_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_6928]) ).
cnf(c_0_6929_0,axiom,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6929]) ).
cnf(c_0_6929_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6929]) ).
cnf(c_0_6930_0,axiom,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6930]) ).
cnf(c_0_6930_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6930]) ).
cnf(c_0_6931_0,axiom,
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6931]) ).
cnf(c_0_6931_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6931]) ).
cnf(c_0_6932_0,axiom,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6932]) ).
cnf(c_0_6932_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6932]) ).
cnf(c_0_6933_0,axiom,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6933]) ).
cnf(c_0_6933_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6933]) ).
cnf(c_0_6934_0,axiom,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6934]) ).
cnf(c_0_6934_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6934]) ).
cnf(c_0_6935_0,axiom,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6935]) ).
cnf(c_0_6935_1,axiom,
( ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6935]) ).
cnf(c_0_6936_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_6936]) ).
cnf(c_0_6936_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_6936]) ).
cnf(c_0_6937_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_6937]) ).
cnf(c_0_6937_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_6937]) ).
cnf(c_0_6938_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_6938]) ).
cnf(c_0_6938_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_6938]) ).
cnf(c_0_6939_0,axiom,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6939]) ).
cnf(c_0_6939_1,axiom,
( ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6939]) ).
cnf(c_0_6940_0,axiom,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6940]) ).
cnf(c_0_6940_1,axiom,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6940]) ).
cnf(c_0_6941_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_6941]) ).
cnf(c_0_6941_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_6941]) ).
cnf(c_0_6942_0,axiom,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6942]) ).
cnf(c_0_6942_1,axiom,
( ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6942]) ).
cnf(c_0_6943_0,axiom,
( c_Transcendental_Osin(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6943]) ).
cnf(c_0_6943_1,axiom,
( c_Transcendental_Ocos(X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_6943]) ).
cnf(c_0_6944_0,axiom,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6944]) ).
cnf(c_0_6944_1,axiom,
( c_Nat_OSuc(X1) != c_Nat_OSuc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6944]) ).
cnf(c_0_6945_0,axiom,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6945]) ).
cnf(c_0_6945_1,axiom,
( c_Nat_OSuc(X1) != c_Nat_OSuc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6945]) ).
cnf(c_0_6948_0,axiom,
( c_Nat_OSuc(X1) = c_Nat_OSuc(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6948]) ).
cnf(c_0_6948_1,axiom,
( X1 != X2
| c_Nat_OSuc(X1) = c_Nat_OSuc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6948]) ).
cnf(c_0_5652_0,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1)),
inference(literals_permutation,[status(thm)],[c_0_5652]) ).
cnf(c_0_5906_0,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(literals_permutation,[status(thm)],[c_0_5906]) ).
cnf(c_0_5907_0,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(literals_permutation,[status(thm)],[c_0_5907]) ).
cnf(c_0_6162_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6162]) ).
cnf(c_0_6308_0,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(literals_permutation,[status(thm)],[c_0_6308]) ).
cnf(c_0_6537_0,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),X1)),
inference(literals_permutation,[status(thm)],[c_0_6537]) ).
cnf(c_0_6595_0,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(literals_permutation,[status(thm)],[c_0_6595]) ).
cnf(c_0_6596_0,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(literals_permutation,[status(thm)],[c_0_6596]) ).
cnf(c_0_6597_0,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(literals_permutation,[status(thm)],[c_0_6597]) ).
cnf(c_0_6616_0,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_6616]) ).
cnf(c_0_6617_0,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_6617]) ).
cnf(c_0_6949_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6949]) ).
cnf(c_0_6950_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6950]) ).
cnf(c_0_6951_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6951]) ).
cnf(c_0_6952_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6952]) ).
cnf(c_0_6953_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6953]) ).
cnf(c_0_6954_0,axiom,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6954]) ).
cnf(c_0_6965_0,axiom,
c_Nat_OSuc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_6965]) ).
cnf(c_0_6966_0,axiom,
c_Nat_OSuc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_6966]) ).
cnf(c_0_6967_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_6967]) ).
cnf(c_0_6968_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_6968]) ).
cnf(c_0_6969_0,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
inference(literals_permutation,[status(thm)],[c_0_6969]) ).
cnf(c_0_6970_0,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
inference(literals_permutation,[status(thm)],[c_0_6970]) ).
cnf(c_0_5499_0,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,sk1_esk9_0)))),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5500_0,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5516_0,axiom,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X3),hAPP(X1,X2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2))),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(X1,X3),hAPP(X1,X2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2))),X3)),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5528_0,axiom,
c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5529_0,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5530_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1),hAPP(c_Complex_ORe,X2)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1),hAPP(c_Complex_OIm,X2)))))),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5539_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(literals_permutation,[status(thm)],[c_0_5539]) ).
cnf(c_0_5562_0,axiom,
c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_OIm,X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_ORe,X2)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5564_0,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5565_0,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5566_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5571_0,axiom,
hBOOL(hAPP(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,hAPP(hAPP(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_5571]) ).
cnf(c_0_5582_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))))),
inference(literals_permutation,[status(thm)],[c_0_5582]) ).
cnf(c_0_5584_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_5584]) ).
cnf(c_0_5600_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)),X4),
inference(literals_permutation,[status(thm)],[c_0_5600]) ).
cnf(c_0_5622_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)))),
inference(literals_permutation,[status(thm)],[c_0_5622]) ).
cnf(c_0_5671_0,axiom,
c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(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),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X1,X2)),c_Complex_Ocomplex_OComplex(X3,X4)),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5772_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5819_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_OIm,X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_ORe,X2))) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5840_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_5840]) ).
cnf(c_0_5885_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),sk1_esk33_0))),
inference(literals_permutation,[status(thm)],[c_0_5885]) ).
cnf(c_0_5886_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),sk1_esk32_0))),
inference(literals_permutation,[status(thm)],[c_0_5886]) ).
cnf(c_0_5887_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),sk1_esk28_0))),
inference(literals_permutation,[status(thm)],[c_0_5887]) ).
cnf(c_0_5888_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),sk1_esk27_0))),
inference(literals_permutation,[status(thm)],[c_0_5888]) ).
cnf(c_0_5889_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),sk1_esk26_0))),
inference(literals_permutation,[status(thm)],[c_0_5889]) ).
cnf(c_0_5890_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),sk1_esk25_0))),
inference(literals_permutation,[status(thm)],[c_0_5890]) ).
cnf(c_0_5917_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X2)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2))) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))),X2)),
inference(literals_permutation,[status(thm)],[c_0_5917]) ).
cnf(c_0_5961_0,axiom,
hBOOL(hAPP(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_5961]) ).
cnf(c_0_5967_0,axiom,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2))) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_5967]) ).
cnf(c_0_5983_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)))),
inference(literals_permutation,[status(thm)],[c_0_5983]) ).
cnf(c_0_6004_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(literals_permutation,[status(thm)],[c_0_6004]) ).
cnf(c_0_6011_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6012_0,axiom,
hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_6012]) ).
cnf(c_0_6013_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_6013]) ).
cnf(c_0_6024_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X2)),c_Transcendental_Ocos(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X2)),c_Transcendental_Osin(X1))) = c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6024]) ).
cnf(c_0_6025_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Ocos(X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Osin(X2))) = c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6025]) ).
cnf(c_0_6046_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Ocos(X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Osin(X2))) = c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_6046]) ).
cnf(c_0_6049_0,axiom,
c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6066_0,axiom,
hBOOL(hAPP(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_6066]) ).
cnf(c_0_6070_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),X1)),
inference(literals_permutation,[status(thm)],[c_0_6070]) ).
cnf(c_0_6071_0,axiom,
hBOOL(hAPP(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_6071]) ).
cnf(c_0_6073_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_6073]) ).
cnf(c_0_6074_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_6074]) ).
cnf(c_0_6095_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_6095]) ).
cnf(c_0_6096_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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_6096]) ).
cnf(c_0_6097_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_6097]) ).
cnf(c_0_6098_0,axiom,
hBOOL(hAPP(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2))),
inference(literals_permutation,[status(thm)],[c_0_6098]) ).
cnf(c_0_6101_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))),
inference(literals_permutation,[status(thm)],[c_0_6101]) ).
cnf(c_0_6102_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
inference(literals_permutation,[status(thm)],[c_0_6102]) ).
cnf(c_0_6119_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Ocos(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Osin(X1))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6119]) ).
cnf(c_0_6144_0,axiom,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Ocos(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Osin(X2))) = c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6144]) ).
cnf(c_0_6145_0,axiom,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X2)),c_Transcendental_Osin(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X2)),c_Transcendental_Ocos(X1))) = c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6145]) ).
cnf(c_0_6161_0,axiom,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Ocos(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Osin(X2))) = c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_6161]) ).
cnf(c_0_6163_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(literals_permutation,[status(thm)],[c_0_6163]) ).
cnf(c_0_6164_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(literals_permutation,[status(thm)],[c_0_6164]) ).
cnf(c_0_6165_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
inference(literals_permutation,[status(thm)],[c_0_6165]) ).
cnf(c_0_6183_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)))),
inference(literals_permutation,[status(thm)],[c_0_6183]) ).
cnf(c_0_6184_0,axiom,
c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3)),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X1,X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_6184]) ).
cnf(c_0_6185_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_6185]) ).
cnf(c_0_6186_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_6186]) ).
cnf(c_0_6206_0,axiom,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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),X1)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X2),X1),
inference(literals_permutation,[status(thm)],[c_0_6206]) ).
cnf(c_0_6207_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_6207]) ).
cnf(c_0_6208_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_6208]) ).
cnf(c_0_6209_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_6209]) ).
cnf(c_0_6210_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_6210]) ).
cnf(c_0_6211_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_6211]) ).
cnf(c_0_6212_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_6212]) ).
cnf(c_0_6227_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X1))),v_r)),
inference(literals_permutation,[status(thm)],[c_0_6227]) ).
cnf(c_0_6240_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_6240]) ).
cnf(c_0_6244_0,axiom,
c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X3),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2),c_Complex_Ocomplex_OComplex(X3,X4)),
inference(literals_permutation,[status(thm)],[c_0_6244]) ).
cnf(c_0_6255_0,axiom,
c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X1,X2)),c_Complex_Ocomplex_OComplex(X3,X4)),
inference(literals_permutation,[status(thm)],[c_0_6255]) ).
cnf(c_0_6256_0,axiom,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X1,X2)),c_Complex_Orcis(X3,X4)),
inference(literals_permutation,[status(thm)],[c_0_6256]) ).
cnf(c_0_6265_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_6265]) ).
cnf(c_0_6269_0,axiom,
c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X2)),X1)),
inference(literals_permutation,[status(thm)],[c_0_6269]) ).
cnf(c_0_6270_0,axiom,
c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X2)),X1)),
inference(literals_permutation,[status(thm)],[c_0_6270]) ).
cnf(c_0_6279_0,axiom,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_6279]) ).
cnf(c_0_6280_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),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_6280]) ).
cnf(c_0_6291_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_6291]) ).
cnf(c_0_6292_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
inference(literals_permutation,[status(thm)],[c_0_6292]) ).
cnf(c_0_6311_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_6311]) ).
cnf(c_0_6312_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_6312]) ).
cnf(c_0_6337_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_6337]) ).
cnf(c_0_6338_0,axiom,
hBOOL(hAPP(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_6338]) ).
cnf(c_0_6339_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(literals_permutation,[status(thm)],[c_0_6339]) ).
cnf(c_0_6340_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))),
inference(literals_permutation,[status(thm)],[c_0_6340]) ).
cnf(c_0_6366_0,axiom,
c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_6366]) ).
cnf(c_0_6398_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(literals_permutation,[status(thm)],[c_0_6398]) ).
cnf(c_0_6399_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(literals_permutation,[status(thm)],[c_0_6399]) ).
cnf(c_0_6410_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_6410]) ).
cnf(c_0_6439_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_6439]) ).
cnf(c_0_6440_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_6440]) ).
cnf(c_0_6441_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),hAPP(c_Complex_OIm,X2)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_6441]) ).
cnf(c_0_6442_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_Complex_ORe,X2)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_6442]) ).
cnf(c_0_6446_0,axiom,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1),hAPP(c_Complex_OIm,X2)) = hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6446]) ).
cnf(c_0_6447_0,axiom,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1),hAPP(c_Complex_ORe,X2)) = hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6447]) ).
cnf(c_0_6449_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(literals_permutation,[status(thm)],[c_0_6449]) ).
cnf(c_0_6474_0,axiom,
hAPP(hAPP(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_6474]) ).
cnf(c_0_6475_0,axiom,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_6475]) ).
cnf(c_0_6476_0,axiom,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_6476]) ).
cnf(c_0_6486_0,axiom,
hAPP(hAPP(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_6486]) ).
cnf(c_0_6515_0,axiom,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X2)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6515]) ).
cnf(c_0_6534_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X2)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_6534]) ).
cnf(c_0_6535_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)))),
inference(literals_permutation,[status(thm)],[c_0_6535]) ).
cnf(c_0_6536_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X2)) = c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_6536]) ).
cnf(c_0_6544_0,axiom,
c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_6544]) ).
cnf(c_0_6557_0,axiom,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) = hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X1)),
inference(literals_permutation,[status(thm)],[c_0_6557]) ).
cnf(c_0_6558_0,axiom,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) = hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X1)),
inference(literals_permutation,[status(thm)],[c_0_6558]) ).
cnf(c_0_6572_0,axiom,
c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Nat_OSuc(X2)),
inference(literals_permutation,[status(thm)],[c_0_6572]) ).
cnf(c_0_6573_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1)))),
inference(literals_permutation,[status(thm)],[c_0_6573]) ).
cnf(c_0_6575_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6575]) ).
cnf(c_0_6577_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_6577]) ).
cnf(c_0_6578_0,axiom,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_6578]) ).
cnf(c_0_6593_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X1))),
inference(literals_permutation,[status(thm)],[c_0_6593]) ).
cnf(c_0_6612_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X3,
inference(literals_permutation,[status(thm)],[c_0_6612]) ).
cnf(c_0_6613_0,axiom,
c_Complex_Ocomplex_Ocomplex__case(X1,X2,c_Complex_Ocomplex_OComplex(X3,X4)) = hAPP(hAPP(X2,X3),X4),
inference(literals_permutation,[status(thm)],[c_0_6613]) ).
cnf(c_0_6614_0,axiom,
c_Complex_Ocomplex_Ocomplex__rec(X1,X2,c_Complex_Ocomplex_OComplex(X3,X4)) = hAPP(hAPP(X2,X3),X4),
inference(literals_permutation,[status(thm)],[c_0_6614]) ).
cnf(c_0_6618_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_6618]) ).
cnf(c_0_6622_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)),
inference(literals_permutation,[status(thm)],[c_0_6622]) ).
cnf(c_0_6625_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Nat_OSuc(X2)),
inference(literals_permutation,[status(thm)],[c_0_6625]) ).
cnf(c_0_6628_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(literals_permutation,[status(thm)],[c_0_6628]) ).
cnf(c_0_6629_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(literals_permutation,[status(thm)],[c_0_6629]) ).
cnf(c_0_6642_0,axiom,
hBOOL(hAPP(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_6642]) ).
cnf(c_0_6643_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(X1))),
inference(literals_permutation,[status(thm)],[c_0_6643]) ).
cnf(c_0_6644_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))),
inference(literals_permutation,[status(thm)],[c_0_6644]) ).
cnf(c_0_6665_0,axiom,
hBOOL(hAPP(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_6665]) ).
cnf(c_0_6666_0,axiom,
hBOOL(hAPP(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_6666]) ).
cnf(c_0_6667_0,axiom,
hBOOL(hAPP(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_6667]) ).
cnf(c_0_6676_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1),
inference(literals_permutation,[status(thm)],[c_0_6676]) ).
cnf(c_0_6677_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_6677]) ).
cnf(c_0_6678_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_6678]) ).
cnf(c_0_6679_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_6679]) ).
cnf(c_0_6680_0,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
inference(literals_permutation,[status(thm)],[c_0_6680]) ).
cnf(c_0_6686_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Ocos(X2)) = hAPP(c_Complex_ORe,c_Complex_Orcis(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6686]) ).
cnf(c_0_6687_0,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Osin(X2)) = hAPP(c_Complex_OIm,c_Complex_Orcis(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_6687]) ).
cnf(c_0_6691_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Nat_OSuc(X1))),
inference(literals_permutation,[status(thm)],[c_0_6691]) ).
cnf(c_0_6692_0,axiom,
hBOOL(hAPP(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_6692]) ).
cnf(c_0_6693_0,axiom,
hBOOL(hAPP(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_6693]) ).
cnf(c_0_6696_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk28_0)),
inference(literals_permutation,[status(thm)],[c_0_6696]) ).
cnf(c_0_6697_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk27_0)),
inference(literals_permutation,[status(thm)],[c_0_6697]) ).
cnf(c_0_6698_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk26_0)),
inference(literals_permutation,[status(thm)],[c_0_6698]) ).
cnf(c_0_6699_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk25_0)),
inference(literals_permutation,[status(thm)],[c_0_6699]) ).
cnf(c_0_6700_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(literals_permutation,[status(thm)],[c_0_6700]) ).
cnf(c_0_6703_0,axiom,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),X1),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1),
inference(literals_permutation,[status(thm)],[c_0_6703]) ).
cnf(c_0_6720_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_6720]) ).
cnf(c_0_6721_0,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_6721]) ).
cnf(c_0_6722_0,axiom,
hBOOL(hAPP(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,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_6723]) ).
cnf(c_0_6773_0,axiom,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X1,
inference(literals_permutation,[status(thm)],[c_0_6773]) ).
cnf(c_0_6775_0,axiom,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X1),c_Transcendental_Osin(X1))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6775]) ).
cnf(c_0_6778_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_6778]) ).
cnf(c_0_6782_0,axiom,
c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X1),hAPP(c_Complex_OIm,X1)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6782]) ).
cnf(c_0_6789_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_6789]) ).
cnf(c_0_6790_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_6790]) ).
cnf(c_0_6792_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_6792]) ).
cnf(c_0_6793_0,axiom,
hAPP(hAPP(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_6793]) ).
cnf(c_0_6794_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_6794]) ).
cnf(c_0_6796_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_6796]) ).
cnf(c_0_6802_0,axiom,
hAPP(hAPP(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_6802]) ).
cnf(c_0_6803_0,axiom,
hAPP(hAPP(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_6803]) ).
cnf(c_0_6804_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_6804]) ).
cnf(c_0_6805_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_6805]) ).
cnf(c_0_6806_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_6806]) ).
cnf(c_0_6807_0,axiom,
hAPP(hAPP(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_6807]) ).
cnf(c_0_6809_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_6809]) ).
cnf(c_0_6810_0,axiom,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(literals_permutation,[status(thm)],[c_0_6810]) ).
cnf(c_0_6811_0,axiom,
hAPP(hAPP(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_6811]) ).
cnf(c_0_6812_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_6812]) ).
cnf(c_0_6813_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_6813]) ).
cnf(c_0_6814_0,axiom,
hAPP(hAPP(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_6814]) ).
cnf(c_0_6815_0,axiom,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)) = c_RealDef_Oreal(tc_Nat_Onat,X1),
inference(literals_permutation,[status(thm)],[c_0_6815]) ).
cnf(c_0_6826_0,axiom,
c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6826]) ).
cnf(c_0_6827_0,axiom,
hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X1,X2)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6827]) ).
cnf(c_0_6828_0,axiom,
hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X1,X2)) = X2,
inference(literals_permutation,[status(thm)],[c_0_6828]) ).
cnf(c_0_6837_0,axiom,
c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6837]) ).
cnf(c_0_6845_0,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)) = c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),
inference(literals_permutation,[status(thm)],[c_0_6845]) ).
cnf(c_0_6846_0,axiom,
c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X1),c_Transcendental_Osin(X1)) = c_Complex_Ocis(X1),
inference(literals_permutation,[status(thm)],[c_0_6846]) ).
cnf(c_0_6858_0,axiom,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6858]) ).
cnf(c_0_6859_0,axiom,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6859]) ).
cnf(c_0_6861_0,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6861]) ).
cnf(c_0_6865_0,axiom,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(literals_permutation,[status(thm)],[c_0_6865]) ).
cnf(c_0_6866_0,axiom,
c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6866]) ).
cnf(c_0_6867_0,axiom,
c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6867]) ).
cnf(c_0_6868_0,axiom,
hAPP(c_Complex_ORe,c_Complex_Ocis(X1)) = c_Transcendental_Ocos(X1),
inference(literals_permutation,[status(thm)],[c_0_6868]) ).
cnf(c_0_6869_0,axiom,
hAPP(c_Complex_OIm,c_Complex_Ocis(X1)) = c_Transcendental_Osin(X1),
inference(literals_permutation,[status(thm)],[c_0_6869]) ).
cnf(c_0_6870_0,axiom,
c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = c_Complex_Ocis(X1),
inference(literals_permutation,[status(thm)],[c_0_6870]) ).
cnf(c_0_6876_0,axiom,
c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Complex_Oii,
inference(literals_permutation,[status(thm)],[c_0_6876]) ).
cnf(c_0_6879_0,axiom,
c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6879]) ).
cnf(c_0_6880_0,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6880]) ).
cnf(c_0_6881_0,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6881]) ).
cnf(c_0_6882_0,axiom,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6882]) ).
cnf(c_0_6883_0,axiom,
hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6883]) ).
cnf(c_0_6884_0,axiom,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6884]) ).
cnf(c_0_6885_0,axiom,
hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6885]) ).
cnf(c_0_6946_0,axiom,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6946]) ).
cnf(c_0_6947_0,axiom,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6947]) ).
cnf(c_0_6955_0,axiom,
c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6955]) ).
cnf(c_0_6956_0,axiom,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6956]) ).
cnf(c_0_6957_0,axiom,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_6957]) ).
cnf(c_0_6958_0,axiom,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6958]) ).
cnf(c_0_6959_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_6959]) ).
cnf(c_0_6960_0,axiom,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6960]) ).
cnf(c_0_6961_0,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6961]) ).
cnf(c_0_6962_0,axiom,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6962]) ).
cnf(c_0_6963_0,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_6963]) ).
cnf(c_0_6964_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_6964]) ).
cnf(c_0_6971_0,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6971]) ).
cnf(c_0_6972_0,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6972]) ).
cnf(c_0_6973_0,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6973]) ).
cnf(c_0_6974_0,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6974]) ).
cnf(c_0_6975_0,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6975]) ).
cnf(c_0_6976_0,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6976]) ).
cnf(c_0_6977_0,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6977]) ).
cnf(c_0_6978_0,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6978]) ).
cnf(c_0_6979_0,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6979]) ).
cnf(c_0_6980_0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6980]) ).
cnf(c_0_6981_0,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6981]) ).
cnf(c_0_6982_0,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6982]) ).
cnf(c_0_6983_0,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6983]) ).
cnf(c_0_6984_0,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6984]) ).
cnf(c_0_6985_0,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6985]) ).
cnf(c_0_6986_0,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6986]) ).
cnf(c_0_6987_0,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6987]) ).
cnf(c_0_6988_0,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6988]) ).
cnf(c_0_6989_0,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6989]) ).
cnf(c_0_6990_0,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6990]) ).
cnf(c_0_6991_0,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6991]) ).
cnf(c_0_6992_0,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6992]) ).
cnf(c_0_6993_0,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6993]) ).
cnf(c_0_6994_0,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6994]) ).
cnf(c_0_6995_0,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6995]) ).
cnf(c_0_6996_0,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6996]) ).
cnf(c_0_6997_0,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6997]) ).
cnf(c_0_6998_0,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6998]) ).
cnf(c_0_6999_0,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6999]) ).
cnf(c_0_7000_0,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7000]) ).
cnf(c_0_7001_0,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7001]) ).
cnf(c_0_7002_0,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7002]) ).
cnf(c_0_7003_0,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7003]) ).
cnf(c_0_7004_0,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7004]) ).
cnf(c_0_7005_0,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7005]) ).
cnf(c_0_7006_0,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7006]) ).
cnf(c_0_7007_0,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7007]) ).
cnf(c_0_7008_0,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7008]) ).
cnf(c_0_7009_0,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7009]) ).
cnf(c_0_7010_0,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7010]) ).
cnf(c_0_7011_0,axiom,
class_Power_Opower(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7011]) ).
cnf(c_0_7012_0,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7012]) ).
cnf(c_0_7013_0,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7013]) ).
cnf(c_0_7014_0,axiom,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7014]) ).
cnf(c_0_7015_0,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7015]) ).
cnf(c_0_7016_0,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7016]) ).
cnf(c_0_7017_0,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7017]) ).
cnf(c_0_7018_0,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7018]) ).
cnf(c_0_7019_0,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7019]) ).
cnf(c_0_7020_0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7020]) ).
cnf(c_0_7021_0,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7021]) ).
cnf(c_0_7022_0,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7022]) ).
cnf(c_0_7023_0,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7023]) ).
cnf(c_0_7024_0,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7024]) ).
cnf(c_0_7025_0,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7025]) ).
cnf(c_0_7026_0,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7026]) ).
cnf(c_0_7027_0,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7027]) ).
cnf(c_0_7028_0,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7028]) ).
cnf(c_0_7029_0,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7029]) ).
cnf(c_0_7030_0,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7030]) ).
cnf(c_0_7031_0,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7031]) ).
cnf(c_0_7032_0,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7032]) ).
cnf(c_0_7033_0,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7033]) ).
cnf(c_0_7034_0,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7034]) ).
cnf(c_0_7035_0,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7035]) ).
cnf(c_0_7036_0,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7036]) ).
cnf(c_0_7037_0,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7037]) ).
cnf(c_0_7038_0,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7038]) ).
cnf(c_0_7039_0,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7039]) ).
cnf(c_0_7040_0,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7040]) ).
cnf(c_0_7041_0,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7041]) ).
cnf(c_0_7042_0,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7042]) ).
cnf(c_0_7043_0,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7043]) ).
cnf(c_0_7044_0,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7044]) ).
cnf(c_0_7045_0,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7045]) ).
cnf(c_0_7046_0,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7046]) ).
cnf(c_0_7047_0,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7047]) ).
cnf(c_0_7048_0,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7048]) ).
cnf(c_0_7049_0,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7049]) ).
cnf(c_0_7050_0,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7050]) ).
cnf(c_0_7051_0,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7051]) ).
cnf(c_0_7052_0,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7052]) ).
cnf(c_0_7053_0,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7053]) ).
cnf(c_0_7054_0,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7054]) ).
cnf(c_0_7055_0,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7055]) ).
cnf(c_0_7056_0,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7056]) ).
cnf(c_0_7057_0,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7057]) ).
cnf(c_0_7058_0,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7058]) ).
cnf(c_0_7059_0,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7059]) ).
cnf(c_0_7060_0,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7060]) ).
cnf(c_0_7061_0,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7061]) ).
cnf(c_0_7062_0,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7062]) ).
cnf(c_0_7063_0,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7063]) ).
cnf(c_0_7064_0,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7064]) ).
cnf(c_0_7065_0,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7065]) ).
cnf(c_0_7066_0,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7066]) ).
cnf(c_0_7067_0,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7067]) ).
cnf(c_0_7068_0,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7068]) ).
cnf(c_0_7069_0,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7069]) ).
cnf(c_0_7070_0,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7070]) ).
cnf(c_0_7071_0,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7071]) ).
cnf(c_0_7072_0,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7072]) ).
cnf(c_0_7073_0,axiom,
class_Orderings_Oord(tc_HOL_Obool),
inference(literals_permutation,[status(thm)],[c_0_7073]) ).
cnf(c_0_7074_0,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
inference(literals_permutation,[status(thm)],[c_0_7074]) ).
cnf(c_0_7075_0,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(literals_permutation,[status(thm)],[c_0_7075]) ).
cnf(c_0_7076_0,axiom,
class_Groups_Oone(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7076]) ).
cnf(c_0_7077_0,axiom,
class_Groups_Ozero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7077]) ).
cnf(c_0_7078_0,axiom,
class_Power_Opower(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7078]) ).
cnf(c_0_7079_0,axiom,
class_Orderings_Oord(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7079]) ).
cnf(c_0_7080_0,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7080]) ).
cnf(c_0_7081_0,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7081]) ).
cnf(c_0_7082_0,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7082]) ).
cnf(c_0_7083_0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7083]) ).
cnf(c_0_7084_0,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7084]) ).
cnf(c_0_7085_0,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7085]) ).
cnf(c_0_7086_0,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7086]) ).
cnf(c_0_7087_0,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7087]) ).
cnf(c_0_7088_0,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7088]) ).
cnf(c_0_7089_0,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7089]) ).
cnf(c_0_7090_0,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7090]) ).
cnf(c_0_7091_0,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7091]) ).
cnf(c_0_7092_0,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7092]) ).
cnf(c_0_7093_0,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7093]) ).
cnf(c_0_7094_0,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7094]) ).
cnf(c_0_7095_0,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7095]) ).
cnf(c_0_7096_0,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7096]) ).
cnf(c_0_7097_0,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7097]) ).
cnf(c_0_7098_0,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7098]) ).
cnf(c_0_7099_0,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7099]) ).
cnf(c_0_7100_0,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7100]) ).
cnf(c_0_7101_0,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7101]) ).
cnf(c_0_7102_0,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7102]) ).
cnf(c_0_7103_0,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7103]) ).
cnf(c_0_7104_0,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7104]) ).
cnf(c_0_7105_0,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7105]) ).
cnf(c_0_7106_0,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7106]) ).
cnf(c_0_7107_0,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7107]) ).
cnf(c_0_7108_0,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7108]) ).
cnf(c_0_7109_0,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7109]) ).
cnf(c_0_7110_0,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7110]) ).
cnf(c_0_7111_0,axiom,
class_Groups_Oone(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7111]) ).
cnf(c_0_7112_0,axiom,
class_Rings_Oring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7112]) ).
cnf(c_0_7113_0,axiom,
class_Groups_Ozero(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7113]) ).
cnf(c_0_7114_0,axiom,
class_Power_Opower(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7114]) ).
cnf(c_0_7115_0,axiom,
class_Rings_Oring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7115]) ).
cnf(c_0_7116_0,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7116]) ).
cnf(c_0_7117_0,axiom,
class_Orderings_Oord(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7117]) ).
cnf(c_0_7118_0,axiom,
class_Rings_Osemiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7118]) ).
cnf(c_0_7119_0,axiom,
class_Orderings_Oorder(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7119]) ).
cnf(c_0_7120_0,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7120]) ).
cnf(c_0_7121_0,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7121]) ).
cnf(c_0_7122_0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7122]) ).
cnf(c_0_7123_0,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7123]) ).
cnf(c_0_7124_0,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7124]) ).
cnf(c_0_7125_0,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7125]) ).
cnf(c_0_7126_0,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7126]) ).
cnf(c_0_7127_0,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7127]) ).
cnf(c_0_7128_0,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7128]) ).
cnf(c_0_7129_0,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7129]) ).
cnf(c_0_7130_0,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7130]) ).
cnf(c_0_7131_0,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7131]) ).
cnf(c_0_7132_0,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7132]) ).
cnf(c_0_7133_0,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7133]) ).
cnf(c_0_7134_0,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7134]) ).
cnf(c_0_7135_0,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7135]) ).
cnf(c_0_7136_0,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7136]) ).
cnf(c_0_7137_0,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7137]) ).
cnf(c_0_7138_0,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7138]) ).
cnf(c_0_7139_0,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7139]) ).
cnf(c_0_7140_0,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7140]) ).
cnf(c_0_7141_0,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7141]) ).
cnf(c_0_7142_0,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7142]) ).
cnf(c_0_7143_0,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7143]) ).
cnf(c_0_7144_0,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7144]) ).
cnf(c_0_7145_0,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7145]) ).
cnf(c_0_7146_0,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7146]) ).
cnf(c_0_7147_0,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7147]) ).
cnf(c_0_7148_0,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7148]) ).
cnf(c_0_7149_0,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7149]) ).
cnf(c_0_7150_0,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7150]) ).
cnf(c_0_7151_0,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7151]) ).
cnf(c_0_7152_0,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7152]) ).
cnf(c_0_7153_0,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7153]) ).
cnf(c_0_7154_0,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7154]) ).
cnf(c_0_7155_0,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7155]) ).
cnf(c_0_7156_0,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7156]) ).
cnf(c_0_7157_0,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7157]) ).
cnf(c_0_7158_0,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7158]) ).
cnf(c_0_7159_0,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7159]) ).
cnf(c_0_7160_0,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7160]) ).
cnf(c_0_7161_0,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7161]) ).
cnf(c_0_7162_0,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7162]) ).
cnf(c_0_7163_0,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7163]) ).
cnf(c_0_7164_0,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7164]) ).
cnf(c_0_7165_0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7165]) ).
cnf(c_0_7166_0,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7166]) ).
cnf(c_0_7167_0,axiom,
class_Rings_Oidom(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_7167]) ).
cnf(c_0_7168_0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7168]) ).
cnf(c_0_7169_0,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(literals_permutation,[status(thm)],[c_0_7169]) ).
cnf(c_0_7170_0,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7170]) ).
cnf(c_0_7171_0,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7171]) ).
cnf(c_0_7172_0,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7172]) ).
cnf(c_0_7173_0,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(literals_permutation,[status(thm)],[c_0_7173]) ).
cnf(c_0_7174_0,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7174]) ).
cnf(c_0_7175_0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7175]) ).
cnf(c_0_7176_0,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7176]) ).
cnf(c_0_7177_0,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_7177]) ).
cnf(c_0_7178_0,axiom,
c_SEQ_Osubseq(sk1_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_7178]) ).
cnf(c_0_7179_0,axiom,
c_SEQ_Osubseq(v_ga____),
inference(literals_permutation,[status(thm)],[c_0_7179]) ).
cnf(c_0_7180_0,axiom,
c_SEQ_Osubseq(v_f____),
inference(literals_permutation,[status(thm)],[c_0_7180]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,conjecture,
? [X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
& ! [X2] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X2)))))),X1)) ),
file('<stdin>',conj_0) ).
fof(c_0_1_002,negated_conjecture,
~ ? [X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
& ! [X2] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X2)))))),X1)) ),
inference(assume_negation,[status(cth)],[c_0_0]) ).
fof(c_0_2_003,negated_conjecture,
! [X3] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk1_1(X3))))))),X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).
cnf(c_0_3_004,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk1_1(X1))))))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_005,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk1_1(X1))))))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_3991,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk2_esk1_1(X0))))))),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_066c2a.p',c_0_4) ).
cnf(c_5103,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk2_esk1_1(X0))))))),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(copy,[status(esa)],[c_3991]) ).
cnf(c_5107,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk2_esk1_1(X0))))))),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(copy,[status(esa)],[c_5103]) ).
cnf(c_5108,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk2_esk1_1(X0))))))),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(copy,[status(esa)],[c_5107]) ).
cnf(c_5109,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk2_esk1_1(X0))))))),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(copy,[status(esa)],[c_5108]) ).
cnf(c_16947,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk2_esk1_1(X0))))))),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(copy,[status(esa)],[c_5109]) ).
cnf(c_397,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X0)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('/export/starexec/sandbox2/tmp/iprover_modulo_066c2a.p',c_0_5772_0) ).
cnf(c_9765,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X0)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(copy,[status(esa)],[c_397]) ).
cnf(c_16953,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(resolution,[status(thm)],[c_16947,c_9765]) ).
cnf(c_16954,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(rewriting,[status(thm)],[c_16953]) ).
cnf(c_1961,plain,
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X3),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X3),X2)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_066c2a.p',c_0_6222_0) ).
cnf(c_12887,plain,
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X3),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X3),X2)) ),
inference(copy,[status(esa)],[c_1961]) ).
cnf(c_16975,plain,
( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(resolution,[status(thm)],[c_16954,c_12887]) ).
cnf(c_16978,plain,
( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(rewriting,[status(thm)],[c_16975]) ).
cnf(c_163,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/iprover_modulo_066c2a.p',c_0_7017_0) ).
cnf(c_9428,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(copy,[status(esa)],[c_163]) ).
cnf(c_17292,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16978,c_9428]) ).
cnf(c_17293,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(rewriting,[status(thm)],[c_17292]) ).
cnf(c_1175,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_066c2a.p',c_0_6547_1) ).
cnf(c_11315,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
inference(copy,[status(esa)],[c_1175]) ).
cnf(c_17300,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(resolution,[status(thm)],[c_17293,c_11315]) ).
cnf(c_17301,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(rewriting,[status(thm)],[c_17300]) ).
cnf(c_1865,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X2)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_066c2a.p',c_0_6261_0) ).
cnf(c_12695,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X2)) ),
inference(copy,[status(esa)],[c_1865]) ).
cnf(c_16965,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk2_esk1_1(X0))))))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(resolution,[status(thm)],[c_16947,c_12695]) ).
cnf(c_16966,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk2_esk1_1(X0))))))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(rewriting,[status(thm)],[c_16965]) ).
cnf(c_17187,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(resolution,[status(thm)],[c_16966,c_9765]) ).
cnf(c_17188,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(rewriting,[status(thm)],[c_17187]) ).
cnf(c_17391,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_17301,c_17188]) ).
cnf(c_17392,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)),
inference(rewriting,[status(thm)],[c_17391]) ).
cnf(c_275,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk26_0)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_066c2a.p',c_0_6698_0) ).
cnf(c_9592,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sk1_esk26_0)),
inference(copy,[status(esa)],[c_275]) ).
cnf(c_17394,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_17392,c_9592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW207+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 5 07:23:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.53/0.70 % Orienting using strategy Equiv(ClausalAll)
% 0.53/0.70 % FOF problem with conjecture
% 0.53/0.70 % 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_25e430.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_066c2a.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_e60cde | grep -v "SZS"
% 0.53/0.72
% 0.53/0.72 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.53/0.72
% 0.53/0.72 %
% 0.53/0.72 % ------ iProver source info
% 0.53/0.72
% 0.53/0.72 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.53/0.72 % git: non_committed_changes: true
% 0.53/0.72 % git: last_make_outside_of_git: true
% 0.53/0.72
% 0.53/0.72 %
% 0.53/0.72 % ------ Input Options
% 0.53/0.72
% 0.53/0.72 % --out_options all
% 0.53/0.72 % --tptp_safe_out true
% 0.53/0.72 % --problem_path ""
% 0.53/0.72 % --include_path ""
% 0.53/0.72 % --clausifier .//eprover
% 0.53/0.72 % --clausifier_options --tstp-format
% 0.53/0.72 % --stdin false
% 0.53/0.72 % --dbg_backtrace false
% 0.53/0.72 % --dbg_dump_prop_clauses false
% 0.53/0.72 % --dbg_dump_prop_clauses_file -
% 0.53/0.72 % --dbg_out_stat false
% 0.53/0.72
% 0.53/0.72 % ------ General Options
% 0.53/0.72
% 0.53/0.72 % --fof false
% 0.53/0.72 % --time_out_real 150.
% 0.53/0.72 % --time_out_prep_mult 0.2
% 0.53/0.72 % --time_out_virtual -1.
% 0.53/0.72 % --schedule none
% 0.53/0.72 % --ground_splitting input
% 0.53/0.72 % --splitting_nvd 16
% 0.53/0.72 % --non_eq_to_eq false
% 0.53/0.72 % --prep_gs_sim true
% 0.53/0.72 % --prep_unflatten false
% 0.53/0.72 % --prep_res_sim true
% 0.53/0.72 % --prep_upred true
% 0.53/0.72 % --res_sim_input true
% 0.53/0.72 % --clause_weak_htbl true
% 0.53/0.72 % --gc_record_bc_elim false
% 0.53/0.72 % --symbol_type_check false
% 0.53/0.72 % --clausify_out false
% 0.53/0.72 % --large_theory_mode false
% 0.53/0.72 % --prep_sem_filter none
% 0.53/0.72 % --prep_sem_filter_out false
% 0.53/0.72 % --preprocessed_out false
% 0.53/0.72 % --sub_typing false
% 0.53/0.72 % --brand_transform false
% 0.53/0.72 % --pure_diseq_elim true
% 0.53/0.72 % --min_unsat_core false
% 0.53/0.72 % --pred_elim true
% 0.53/0.72 % --add_important_lit false
% 0.53/0.72 % --soft_assumptions false
% 0.53/0.72 % --reset_solvers false
% 0.53/0.72 % --bc_imp_inh []
% 0.53/0.72 % --conj_cone_tolerance 1.5
% 0.53/0.72 % --prolific_symb_bound 500
% 0.53/0.72 % --lt_threshold 2000
% 0.53/0.72
% 0.53/0.72 % ------ SAT Options
% 0.53/0.72
% 0.53/0.72 % --sat_mode false
% 0.53/0.72 % --sat_fm_restart_options ""
% 0.53/0.72 % --sat_gr_def false
% 0.53/0.72 % --sat_epr_types true
% 0.53/0.72 % --sat_non_cyclic_types false
% 0.53/0.72 % --sat_finite_models false
% 0.53/0.72 % --sat_fm_lemmas false
% 0.53/0.72 % --sat_fm_prep false
% 0.53/0.72 % --sat_fm_uc_incr true
% 0.53/0.72 % --sat_out_model small
% 0.53/0.72 % --sat_out_clauses false
% 0.53/0.72
% 0.53/0.72 % ------ QBF Options
% 0.53/0.72
% 0.53/0.72 % --qbf_mode false
% 0.53/0.72 % --qbf_elim_univ true
% 0.53/0.72 % --qbf_sk_in true
% 0.53/0.72 % --qbf_pred_elim true
% 0.53/0.72 % --qbf_split 32
% 0.53/0.72
% 0.53/0.72 % ------ BMC1 Options
% 0.53/0.73
% 0.53/0.73 % --bmc1_incremental false
% 0.53/0.73 % --bmc1_axioms reachable_all
% 0.53/0.73 % --bmc1_min_bound 0
% 0.53/0.73 % --bmc1_max_bound -1
% 0.53/0.73 % --bmc1_max_bound_default -1
% 0.53/0.73 % --bmc1_symbol_reachability true
% 0.53/0.73 % --bmc1_property_lemmas false
% 0.53/0.73 % --bmc1_k_induction false
% 0.53/0.73 % --bmc1_non_equiv_states false
% 0.53/0.73 % --bmc1_deadlock false
% 0.53/0.73 % --bmc1_ucm false
% 0.53/0.73 % --bmc1_add_unsat_core none
% 0.53/0.73 % --bmc1_unsat_core_children false
% 0.53/0.73 % --bmc1_unsat_core_extrapolate_axioms false
% 0.53/0.73 % --bmc1_out_stat full
% 0.53/0.73 % --bmc1_ground_init false
% 0.53/0.73 % --bmc1_pre_inst_next_state false
% 0.53/0.73 % --bmc1_pre_inst_state false
% 0.53/0.73 % --bmc1_pre_inst_reach_state false
% 0.53/0.73 % --bmc1_out_unsat_core false
% 0.53/0.73 % --bmc1_aig_witness_out false
% 0.53/0.73 % --bmc1_verbose false
% 0.53/0.73 % --bmc1_dump_clauses_tptp false
% 0.53/0.75 % --bmc1_dump_unsat_core_tptp false
% 0.53/0.75 % --bmc1_dump_file -
% 0.53/0.75 % --bmc1_ucm_expand_uc_limit 128
% 0.53/0.75 % --bmc1_ucm_n_expand_iterations 6
% 0.53/0.75 % --bmc1_ucm_extend_mode 1
% 0.53/0.75 % --bmc1_ucm_init_mode 2
% 0.53/0.75 % --bmc1_ucm_cone_mode none
% 0.53/0.75 % --bmc1_ucm_reduced_relation_type 0
% 0.53/0.75 % --bmc1_ucm_relax_model 4
% 0.53/0.75 % --bmc1_ucm_full_tr_after_sat true
% 0.53/0.75 % --bmc1_ucm_expand_neg_assumptions false
% 0.53/0.75 % --bmc1_ucm_layered_model none
% 0.53/0.75 % --bmc1_ucm_max_lemma_size 10
% 0.53/0.75
% 0.53/0.75 % ------ AIG Options
% 0.53/0.75
% 0.53/0.75 % --aig_mode false
% 0.53/0.75
% 0.53/0.75 % ------ Instantiation Options
% 0.53/0.75
% 0.53/0.75 % --instantiation_flag true
% 0.53/0.75 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.53/0.75 % --inst_solver_per_active 750
% 0.53/0.75 % --inst_solver_calls_frac 0.5
% 0.53/0.75 % --inst_passive_queue_type priority_queues
% 0.53/0.75 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.53/0.75 % --inst_passive_queues_freq [25;2]
% 0.53/0.75 % --inst_dismatching true
% 0.53/0.75 % --inst_eager_unprocessed_to_passive true
% 0.53/0.75 % --inst_prop_sim_given true
% 0.53/0.75 % --inst_prop_sim_new false
% 0.53/0.75 % --inst_orphan_elimination true
% 0.53/0.75 % --inst_learning_loop_flag true
% 0.53/0.75 % --inst_learning_start 3000
% 0.53/0.75 % --inst_learning_factor 2
% 0.53/0.75 % --inst_start_prop_sim_after_learn 3
% 0.53/0.75 % --inst_sel_renew solver
% 0.53/0.75 % --inst_lit_activity_flag true
% 0.53/0.75 % --inst_out_proof true
% 0.53/0.75
% 0.53/0.75 % ------ Resolution Options
% 0.53/0.75
% 0.53/0.75 % --resolution_flag true
% 0.53/0.75 % --res_lit_sel kbo_max
% 0.53/0.75 % --res_to_prop_solver none
% 0.53/0.75 % --res_prop_simpl_new false
% 0.53/0.75 % --res_prop_simpl_given false
% 0.53/0.75 % --res_passive_queue_type priority_queues
% 0.53/0.75 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.53/0.75 % --res_passive_queues_freq [15;5]
% 0.53/0.75 % --res_forward_subs full
% 0.53/0.75 % --res_backward_subs full
% 0.53/0.75 % --res_forward_subs_resolution true
% 0.53/0.75 % --res_backward_subs_resolution true
% 0.53/0.75 % --res_orphan_elimination false
% 0.53/0.75 % --res_time_limit 1000.
% 0.53/0.75 % --res_out_proof true
% 0.53/0.75 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_25e430.s
% 0.53/0.75 % --modulo true
% 0.53/0.75
% 0.53/0.75 % ------ Combination Options
% 0.53/0.75
% 0.53/0.75 % --comb_res_mult 1000
% 0.53/0.75 % --comb_inst_mult 300
% 0.53/0.75 % ------
% 0.53/0.75
% 0.53/0.75 % ------ Parsing...%
% 0.53/0.75
% 0.53/0.75
% 0.53/0.75 % ------ Statistics
% 0.53/0.75
% 0.53/0.75 % ------ General
% 0.53/0.75
% 0.53/0.75 % num_of_input_clauses: 714
% 0.53/0.75 % num_of_input_neg_conjectures: 0
% 0.53/0.75 % num_of_splits: 0
% 0.53/0.75 % num_of_split_atoms: 0
% 0.53/0.75 % num_of_sem_filtered_clauses: 0
% 0.53/0.75 % num_of_subtypes: 0
% 0.53/0.75 % monotx_restored_types: 0
% 0.53/0.75 % sat_num_of_epr_types: 0
% 0.53/0.75 % sat_num_of_non_cyclic_types: 0
% 0.53/0.75 % sat_guarded_non_collapsed_types: 0
% 0.53/0.75 % is_epr: 0
% 0.53/0.75 % is_horn: 0
% 0.53/0.75 % has_eq: 0
% 0.53/0.75 % num_pure_diseq_elim: 0
% 0.53/0.75 % simp_replaced_by: 0
% 0.53/0.75 % res_preprocessed: 0
% 0.53/0.75 % prep_upred: 0
% 0.53/0.75 % prep_unflattend: 0
% 0.53/0.75 % pred_elim_cands: 0
% 0.53/0.75 % pred_elim: 0
% 0.53/0.75 % pred_elim_cl: 0
% 0.53/0.75 % pred_elim_cycles: 0
% 0.53/0.75 % forced_gc_time: 0
% 0.53/0.75 % gc_basic_clause_elim: 0
% 0.53/0.75 % parsing_time: 0.
% 0.53/0.75 % sem_filter_time: 0.
% 0.53/0.75 % pred_elim_time: 0.
% 0.53/0.75 % out_proof_time: 0.
% 0.53/0.75 % monotx_time: 0.
% 0.53/0.75 % subtype_inf_time: 0.
% 0.53/0.75 % unif_index_cands_time: 0.
% 0.53/0.75 % Fatal error: exception Failure("Parse error in: /export/starexec/sandbox2/tmp/iprover_modulo_066c2a.p line: 717 near token: '!='")
% 0.53/0.75 unif_index_add_time: 0.
% 0.53/0.75 % total_time: 0.045
% 0.53/0.75 % num_of_symbols: 162
% 0.53/0.75 % num_of_terms: 2357
% 0.53/0.75
% 0.53/0.75 % ------ Propositional Solver
% 0.53/0.75
% 0.53/0.75 % prop_solver_calls: 0
% 0.53/0.75 % prop_fast_solver_calls: 0
% 0.53/0.75 % prop_num_of_clauses: 0
% 0.53/0.75 % prop_preprocess_simplified: 0
% 0.53/0.75 % prop_fo_subsumed: 0
% 0.53/0.75 % prop_solver_time: 0.
% 0.53/0.75 % prop_fast_solver_time: 0.
% 0.53/0.75 % prop_unsat_core_time: 0.
% 0.53/0.75
% 0.53/0.75 % ------ QBF
% 0.53/0.75
% 0.53/0.75 % qbf_q_res: 0
% 0.53/0.75 % qbf_num_tautologies: 0
% 0.53/0.75 % qbf_prep_cycles: 0
% 0.53/0.75
% 0.53/0.75 % ------ BMC1
% 0.53/0.75
% 0.53/0.75 % bmc1_current_bound: -1
% 0.53/0.75 % bmc1_last_solved_bound: -1
% 0.53/0.75 % bmc1_unsat_core_size: -1
% 0.53/0.75 % bmc1_unsat_core_parents_size: -1
% 0.53/0.75 % bmc1_merge_next_fun: 0
% 0.53/0.75 % bmc1_unsat_core_clauses_time: 0.
% 0.53/0.75
% 0.53/0.75 % ------ Instantiation
% 0.53/0.75
% 0.53/0.75 % inst_num_of_clauses: undef
% 0.53/0.75 % inst_num_in_passive: undef
% 0.53/0.75 % inst_num_in_active: 0
% 0.53/0.75 % inst_num_in_unprocessed: 0
% 0.53/0.75 % inst_num_of_loops: 0
% 0.53/0.75 % inst_num_of_learning_restarts: 0
% 0.53/0.75 % inst_num_moves_active_passive: 0
% 0.53/0.75 % inst_lit_activity: 0
% 0.53/0.75 % inst_lit_activity_moves: 0
% 0.53/0.75 % inst_num_tautologies: 0
% 0.53/0.75 % inst_num_prop_implied: 0
% 0.53/0.75 % inst_num_existing_simplified: 0
% 0.53/0.75 % inst_num_eq_res_simplified: 0
% 0.53/0.75 % inst_num_child_elim: 0
% 0.53/0.75 % inst_num_of_dismatching_blockings: 0
% 0.53/0.75 % inst_num_of_non_proper_insts: 0
% 0.53/0.75 % inst_num_of_duplicates: 0
% 0.53/0.75 % inst_inst_num_from_inst_to_res: 0
% 0.53/0.75 % inst_dismatching_checking_time: 0.
% 0.53/0.75
% 0.53/0.75 % ------ Resolution
% 0.53/0.75
% 0.53/0.75 % res_num_of_clauses: undef
% 0.53/0.75 % res_num_in_passive: undef
% 0.53/0.75 % res_num_in_active: 0
% 0.53/0.75 % res_num_of_loops: 0
% 0.53/0.75 % res_forward_subset_subsumed: 0
% 0.53/0.75 % res_backward_subset_subsumed: 0
% 0.53/0.75 % res_forward_subsumed: 0
% 0.53/0.75 % res_backward_subsumed: 0
% 0.53/0.75 % res_forward_subsumption_resolution: 0
% 0.53/0.75 % res_backward_subsumption_resolution: 0
% 0.53/0.75 % res_clause_to_clause_subsumption: 0
% 0.53/0.75 % res_orphan_elimination: 0
% 0.53/0.75 % res_tautology_del: 0
% 0.53/0.75 % res_num_eq_res_simplified: 0
% 0.53/0.75 % res_num_sel_changes: 0
% 0.53/0.75 % res_moves_from_active_to_pass: 0
% 0.53/0.75
% 0.53/0.75 % Status Unknown
% 0.62/1.06 % Orienting using strategy ClausalAll
% 0.62/1.06 % FOF problem with conjecture
% 0.62/1.06 % 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_25e430.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_066c2a.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_e3296f | grep -v "SZS"
% 0.95/1.07
% 0.95/1.07 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.95/1.07
% 0.95/1.07 %
% 0.95/1.07 % ------ iProver source info
% 0.95/1.07
% 0.95/1.07 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.95/1.07 % git: non_committed_changes: true
% 0.95/1.07 % git: last_make_outside_of_git: true
% 0.95/1.07
% 0.95/1.07 %
% 0.95/1.07 % ------ Input Options
% 0.95/1.07
% 0.95/1.07 % --out_options all
% 0.95/1.07 % --tptp_safe_out true
% 0.95/1.07 % --problem_path ""
% 0.95/1.07 % --include_path ""
% 0.95/1.07 % --clausifier .//eprover
% 0.95/1.07 % --clausifier_options --tstp-format
% 0.95/1.07 % --stdin false
% 0.95/1.07 % --dbg_backtrace false
% 0.95/1.07 % --dbg_dump_prop_clauses false
% 0.95/1.07 % --dbg_dump_prop_clauses_file -
% 0.95/1.07 % --dbg_out_stat false
% 0.95/1.07
% 0.95/1.07 % ------ General Options
% 0.95/1.07
% 0.95/1.07 % --fof false
% 0.95/1.07 % --time_out_real 150.
% 0.95/1.07 % --time_out_prep_mult 0.2
% 0.95/1.07 % --time_out_virtual -1.
% 0.95/1.07 % --schedule none
% 0.95/1.07 % --ground_splitting input
% 0.95/1.07 % --splitting_nvd 16
% 0.95/1.07 % --non_eq_to_eq false
% 0.95/1.07 % --prep_gs_sim true
% 0.95/1.07 % --prep_unflatten false
% 0.95/1.07 % --prep_res_sim true
% 0.95/1.07 % --prep_upred true
% 0.95/1.07 % --res_sim_input true
% 0.95/1.07 % --clause_weak_htbl true
% 0.95/1.07 % --gc_record_bc_elim false
% 0.95/1.07 % --symbol_type_check false
% 0.95/1.07 % --clausify_out false
% 0.95/1.07 % --large_theory_mode false
% 0.95/1.07 % --prep_sem_filter none
% 0.95/1.07 % --prep_sem_filter_out false
% 0.95/1.07 % --preprocessed_out false
% 0.95/1.07 % --sub_typing false
% 0.95/1.07 % --brand_transform false
% 0.95/1.07 % --pure_diseq_elim true
% 0.95/1.07 % --min_unsat_core false
% 0.95/1.07 % --pred_elim true
% 0.95/1.07 % --add_important_lit false
% 0.95/1.07 % --soft_assumptions false
% 0.95/1.07 % --reset_solvers false
% 0.95/1.07 % --bc_imp_inh []
% 0.95/1.07 % --conj_cone_tolerance 1.5
% 0.95/1.07 % --prolific_symb_bound 500
% 0.95/1.07 % --lt_threshold 2000
% 0.95/1.07
% 0.95/1.07 % ------ SAT Options
% 0.95/1.07
% 0.95/1.07 % --sat_mode false
% 0.95/1.07 % --sat_fm_restart_options ""
% 0.95/1.07 % --sat_gr_def false
% 0.95/1.07 % --sat_epr_types true
% 0.95/1.07 % --sat_non_cyclic_types false
% 0.95/1.07 % --sat_finite_models false
% 0.95/1.07 % --sat_fm_lemmas false
% 0.95/1.07 % --sat_fm_prep false
% 0.95/1.07 % --sat_fm_uc_incr true
% 0.95/1.07 % --sat_out_model small
% 0.95/1.07 % --sat_out_clauses false
% 0.95/1.07
% 0.95/1.07 % ------ QBF Options
% 0.95/1.07
% 0.95/1.07 % --qbf_mode false
% 0.95/1.07 % --qbf_elim_univ true
% 0.95/1.07 % --qbf_sk_in true
% 0.95/1.07 % --qbf_pred_elim true
% 0.95/1.07 % --qbf_split 32
% 0.95/1.07
% 0.95/1.07 % ------ BMC1 Options
% 0.95/1.07
% 0.95/1.07 % --bmc1_incremental false
% 0.95/1.07 % --bmc1_axioms reachable_all
% 0.95/1.07 % --bmc1_min_bound 0
% 0.95/1.07 % --bmc1_max_bound -1
% 0.95/1.07 % --bmc1_max_bound_default -1
% 0.95/1.07 % --bmc1_symbol_reachability true
% 0.95/1.07 % --bmc1_property_lemmas false
% 0.95/1.07 % --bmc1_k_induction false
% 0.95/1.07 % --bmc1_non_equiv_states false
% 0.95/1.07 % --bmc1_deadlock false
% 0.95/1.07 % --bmc1_ucm false
% 0.95/1.07 % --bmc1_add_unsat_core none
% 0.95/1.07 % --bmc1_unsat_core_children false
% 0.95/1.07 % --bmc1_unsat_core_extrapolate_axioms false
% 0.95/1.07 % --bmc1_out_stat full
% 0.95/1.07 % --bmc1_ground_init false
% 0.95/1.07 % --bmc1_pre_inst_next_state false
% 0.95/1.07 % --bmc1_pre_inst_state false
% 0.95/1.07 % --bmc1_pre_inst_reach_state false
% 0.95/1.07 % --bmc1_out_unsat_core false
% 0.95/1.07 % --bmc1_aig_witness_out false
% 0.95/1.07 % --bmc1_verbose false
% 0.95/1.07 % --bmc1_dump_clauses_tptp false
% 11.46/11.66 % --bmc1_dump_unsat_core_tptp false
% 11.46/11.66 % --bmc1_dump_file -
% 11.46/11.66 % --bmc1_ucm_expand_uc_limit 128
% 11.46/11.66 % --bmc1_ucm_n_expand_iterations 6
% 11.46/11.66 % --bmc1_ucm_extend_mode 1
% 11.46/11.66 % --bmc1_ucm_init_mode 2
% 11.46/11.66 % --bmc1_ucm_cone_mode none
% 11.46/11.66 % --bmc1_ucm_reduced_relation_type 0
% 11.46/11.66 % --bmc1_ucm_relax_model 4
% 11.46/11.66 % --bmc1_ucm_full_tr_after_sat true
% 11.46/11.66 % --bmc1_ucm_expand_neg_assumptions false
% 11.46/11.66 % --bmc1_ucm_layered_model none
% 11.46/11.66 % --bmc1_ucm_max_lemma_size 10
% 11.46/11.66
% 11.46/11.66 % ------ AIG Options
% 11.46/11.66
% 11.46/11.66 % --aig_mode false
% 11.46/11.66
% 11.46/11.66 % ------ Instantiation Options
% 11.46/11.66
% 11.46/11.66 % --instantiation_flag true
% 11.46/11.66 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 11.46/11.66 % --inst_solver_per_active 750
% 11.46/11.66 % --inst_solver_calls_frac 0.5
% 11.46/11.66 % --inst_passive_queue_type priority_queues
% 11.46/11.66 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 11.46/11.66 % --inst_passive_queues_freq [25;2]
% 11.46/11.66 % --inst_dismatching true
% 11.46/11.66 % --inst_eager_unprocessed_to_passive true
% 11.46/11.66 % --inst_prop_sim_given true
% 11.46/11.66 % --inst_prop_sim_new false
% 11.46/11.66 % --inst_orphan_elimination true
% 11.46/11.66 % --inst_learning_loop_flag true
% 11.46/11.66 % --inst_learning_start 3000
% 11.46/11.66 % --inst_learning_factor 2
% 11.46/11.66 % --inst_start_prop_sim_after_learn 3
% 11.46/11.66 % --inst_sel_renew solver
% 11.46/11.66 % --inst_lit_activity_flag true
% 11.46/11.66 % --inst_out_proof true
% 11.46/11.66
% 11.46/11.66 % ------ Resolution Options
% 11.46/11.66
% 11.46/11.66 % --resolution_flag true
% 11.46/11.66 % --res_lit_sel kbo_max
% 11.46/11.66 % --res_to_prop_solver none
% 11.46/11.66 % --res_prop_simpl_new false
% 11.46/11.66 % --res_prop_simpl_given false
% 11.46/11.66 % --res_passive_queue_type priority_queues
% 11.46/11.66 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 11.46/11.66 % --res_passive_queues_freq [15;5]
% 11.46/11.66 % --res_forward_subs full
% 11.46/11.66 % --res_backward_subs full
% 11.46/11.66 % --res_forward_subs_resolution true
% 11.46/11.66 % --res_backward_subs_resolution true
% 11.46/11.66 % --res_orphan_elimination false
% 11.46/11.66 % --res_time_limit 1000.
% 11.46/11.66 % --res_out_proof true
% 11.46/11.66 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_25e430.s
% 11.46/11.66 % --modulo true
% 11.46/11.66
% 11.46/11.66 % ------ Combination Options
% 11.46/11.66
% 11.46/11.66 % --comb_res_mult 1000
% 11.46/11.66 % --comb_inst_mult 300
% 11.46/11.66 % ------
% 11.46/11.66
% 11.46/11.66 % ------ Parsing...% successful
% 11.46/11.66
% 11.46/11.66 % ------ 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 %
% 11.46/11.66
% 11.46/11.66 % ------ Proving...
% 11.46/11.66 % ------ Problem Properties
% 11.46/11.66
% 11.46/11.66 %
% 11.46/11.66 % EPR false
% 11.46/11.66 % Horn false
% 11.46/11.66 % Has equality true
% 11.46/11.66
% 11.46/11.66 % % ------ Input Options Time Limit: Unbounded
% 11.46/11.66
% 11.46/11.66
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 Compiling...
% 11.46/11.66 Loading plugin: done.
% 11.46/11.66 % % ------ Current options:
% 11.46/11.66
% 11.46/11.66 % ------ Input Options
% 11.46/11.66
% 11.46/11.66 % --out_options all
% 11.46/11.66 % --tptp_safe_out true
% 11.46/11.66 % --problem_path ""
% 11.46/11.66 % --include_path ""
% 11.46/11.66 % --clausifier .//eprover
% 11.46/11.66 % --clausifier_options --tstp-format
% 11.46/11.66 % --stdin false
% 11.46/11.66 % --dbg_backtrace false
% 11.46/11.66 % --dbg_dump_prop_clauses false
% 11.46/11.66 % --dbg_dump_prop_clauses_file -
% 11.46/11.66 % --dbg_out_stat false
% 11.46/11.66
% 11.46/11.66 % ------ General Options
% 11.46/11.66
% 11.46/11.66 % --fof false
% 11.46/11.66 % --time_out_real 150.
% 11.46/11.66 % --time_out_prep_mult 0.2
% 11.46/11.66 % --time_out_virtual -1.
% 11.46/11.66 % --schedule none
% 11.46/11.66 % --ground_splitting input
% 11.46/11.66 % --splitting_nvd 16
% 11.46/11.66 % --non_eq_to_eq false
% 11.46/11.66 % --prep_gs_sim true
% 11.46/11.66 % --prep_unflatten false
% 11.46/11.66 % --prep_res_sim true
% 11.46/11.66 % --prep_upred true
% 11.46/11.66 % --res_sim_input true
% 11.46/11.66 % --clause_weak_htbl true
% 11.46/11.66 % --gc_record_bc_elim false
% 11.46/11.66 % --symbol_type_check false
% 11.46/11.66 % --clausify_out false
% 11.46/11.66 % --large_theory_mode false
% 11.46/11.66 % --prep_sem_filter none
% 11.46/11.66 % --prep_sem_filter_out false
% 11.46/11.66 % --preprocessed_out false
% 11.46/11.66 % --sub_typing false
% 11.46/11.66 % --brand_transform false
% 11.46/11.66 % --pure_diseq_elim true
% 11.46/11.66 % --min_unsat_core false
% 11.46/11.66 % --pred_elim true
% 11.46/11.66 % --add_important_lit false
% 11.46/11.66 % --soft_assumptions false
% 11.46/11.66 % --reset_solvers false
% 11.46/11.66 % --bc_imp_inh []
% 11.46/11.66 % --conj_cone_tolerance 1.5
% 11.46/11.66 % --prolific_symb_bound 500
% 11.46/11.66 % --lt_threshold 2000
% 11.46/11.66
% 11.46/11.66 % ------ SAT Options
% 11.46/11.66
% 11.46/11.66 % --sat_mode false
% 11.46/11.66 % --sat_fm_restart_options ""
% 11.46/11.66 % --sat_gr_def false
% 11.46/11.66 % --sat_epr_types true
% 11.46/11.66 % --sat_non_cyclic_types false
% 11.46/11.66 % --sat_finite_models false
% 11.46/11.66 % --sat_fm_lemmas false
% 11.46/11.66 % --sat_fm_prep false
% 11.46/11.66 % --sat_fm_uc_incr true
% 11.46/11.66 % --sat_out_model small
% 11.46/11.66 % --sat_out_clauses false
% 11.46/11.66
% 11.46/11.66 % ------ QBF Options
% 11.46/11.66
% 11.46/11.66 % --qbf_mode false
% 11.46/11.66 % --qbf_elim_univ true
% 11.46/11.66 % --qbf_sk_in true
% 11.46/11.66 % --qbf_pred_elim true
% 11.46/11.66 % --qbf_split 32
% 11.46/11.66
% 11.46/11.66 % ------ BMC1 Options
% 11.46/11.66
% 11.46/11.66 % --bmc1_incremental false
% 11.46/11.66 % --bmc1_axioms reachable_all
% 11.46/11.66 % --bmc1_min_bound 0
% 11.46/11.66 % --bmc1_max_bound -1
% 11.46/11.66 % --bmc1_max_bound_default -1
% 11.46/11.66 % --bmc1_symbol_reachability true
% 11.46/11.66 % --bmc1_property_lemmas false
% 11.46/11.66 % --bmc1_k_induction false
% 11.46/11.66 % --bmc1_non_equiv_states false
% 11.46/11.66 % --bmc1_deadlock false
% 11.46/11.66 % --bmc1_ucm false
% 11.46/11.66 % --bmc1_add_unsat_core none
% 11.46/11.66 % --bmc1_unsat_core_children false
% 11.46/11.66 % --bmc1_unsat_core_extrapolate_axioms false
% 11.46/11.66 % --bmc1_out_stat full
% 11.46/11.66 % --bmc1_ground_init false
% 11.46/11.66 % --bmc1_pre_inst_next_state false
% 11.46/11.66 % --bmc1_pre_inst_state false
% 11.46/11.66 % --bmc1_pre_inst_reach_state false
% 11.46/11.66 % --bmc1_out_unsat_core false
% 11.46/11.66 % --bmc1_aig_witness_out false
% 11.46/11.66 % --bmc1_verbose false
% 11.46/11.66 % --bmc1_dump_clauses_tptp false
% 11.46/11.66 % --bmc1_dump_unsat_core_tptp false
% 11.46/11.66 % --bmc1_dump_file -
% 11.46/11.66 % --bmc1_ucm_expand_uc_limit 128
% 11.46/11.66 % --bmc1_ucm_n_expand_iterations 6
% 11.46/11.66 % --bmc1_ucm_extend_mode 1
% 11.46/11.66 % --bmc1_ucm_init_mode 2
% 11.46/11.66 % --bmc1_ucm_cone_mode none
% 11.46/11.66 % --bmc1_ucm_reduced_relation_type 0
% 11.46/11.66 % --bmc1_ucm_relax_model 4
% 11.46/11.66 % --bmc1_ucm_full_tr_after_sat true
% 11.46/11.68 % --bmc1_ucm_expand_neg_assumptions false
% 11.46/11.68 % --bmc1_ucm_layered_model none
% 11.46/11.68 % --bmc1_ucm_max_lemma_size 10
% 11.46/11.68
% 11.46/11.68 % ------ AIG Options
% 11.46/11.68
% 11.46/11.68 % --aig_mode false
% 11.46/11.68
% 11.46/11.68 % ------ Instantiation Options
% 11.46/11.68
% 11.46/11.68 % --instantiation_flag true
% 11.46/11.68 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 11.46/11.68 % --inst_solver_per_active 750
% 11.46/11.68 % --inst_solver_calls_frac 0.5
% 11.46/11.68 % --inst_passive_queue_type priority_queues
% 11.46/11.68 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 11.46/11.68 % --inst_passive_queues_freq [25;2]
% 11.46/11.68 % --inst_dismatching true
% 11.46/11.68 % --inst_eager_unprocessed_to_passive true
% 11.46/11.68 % --inst_prop_sim_given true
% 11.46/11.68 % --inst_prop_sim_new false
% 11.46/11.68 % --inst_orphan_elimination true
% 11.46/11.68 % --inst_learning_loop_flag true
% 11.46/11.68 % --inst_learning_start 3000
% 11.46/11.68 % --inst_learning_factor 2
% 11.46/11.68 % --inst_start_prop_sim_after_learn 3
% 11.46/11.68 % --inst_sel_renew solver
% 11.46/11.68 % --inst_lit_activity_flag true
% 11.46/11.68 % --inst_out_proof true
% 11.46/11.68
% 11.46/11.68 % ------ Resolution Options
% 11.46/11.68
% 11.46/11.68 % --resolution_flag true
% 11.46/11.68 % --res_lit_sel kbo_max
% 11.46/11.68 % --res_to_prop_solver none
% 11.46/11.68 % --res_prop_simpl_new false
% 11.46/11.68 % --res_prop_simpl_given false
% 11.46/11.68 % --res_passive_queue_type priority_queues
% 11.46/11.68 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 11.46/11.68 % --res_passive_queues_freq [15;5]
% 11.46/11.68 % --res_forward_subs full
% 11.46/11.68 % --res_backward_subs full
% 11.46/11.68 % --res_forward_subs_resolution true
% 11.46/11.68 % --res_backward_subs_resolution true
% 11.46/11.68 % --res_orphan_elimination false
% 11.46/11.68 % --res_time_limit 1000.
% 11.46/11.68 % --res_out_proof true
% 11.46/11.68 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_25e430.s
% 11.46/11.68 % --modulo true
% 11.46/11.68
% 11.46/11.68 % ------ Combination Options
% 11.46/11.68
% 11.46/11.68 % --comb_res_mult 1000
% 11.46/11.68 % --comb_inst_mult 300
% 11.46/11.68 % ------
% 11.46/11.68
% 11.46/11.68
% 11.46/11.68
% 11.46/11.68 % ------ Proving...
% 11.46/11.68 %
% 11.46/11.68
% 11.46/11.68
% 11.46/11.68 % Resolution empty clause
% 11.46/11.68
% 11.46/11.68 % ------ Statistics
% 11.46/11.68
% 11.46/11.68 % ------ General
% 11.46/11.68
% 11.46/11.68 % num_of_input_clauses: 3992
% 11.46/11.68 % num_of_input_neg_conjectures: 1
% 11.46/11.68 % num_of_splits: 0
% 11.46/11.68 % num_of_split_atoms: 0
% 11.46/11.68 % num_of_sem_filtered_clauses: 0
% 11.46/11.68 % num_of_subtypes: 0
% 11.46/11.68 % monotx_restored_types: 0
% 11.46/11.68 % sat_num_of_epr_types: 0
% 11.46/11.68 % sat_num_of_non_cyclic_types: 0
% 11.46/11.68 % sat_guarded_non_collapsed_types: 0
% 11.46/11.68 % is_epr: 0
% 11.46/11.68 % is_horn: 0
% 11.46/11.68 % has_eq: 1
% 11.46/11.68 % num_pure_diseq_elim: 0
% 11.46/11.68 % simp_replaced_by: 0
% 11.46/11.68 % res_preprocessed: 2
% 11.46/11.68 % prep_upred: 0
% 11.46/11.68 % prep_unflattend: 0
% 11.46/11.68 % pred_elim_cands: 0
% 11.46/11.68 % pred_elim: 0
% 11.46/11.68 % pred_elim_cl: 0
% 11.46/11.68 % pred_elim_cycles: 0
% 11.46/11.68 % forced_gc_time: 0
% 11.46/11.68 % gc_basic_clause_elim: 0
% 11.46/11.68 % parsing_time: 0.166
% 11.46/11.68 % sem_filter_time: 0.
% 11.46/11.68 % pred_elim_time: 0.
% 11.46/11.68 % out_proof_time: 0.001
% 11.46/11.68 % monotx_time: 0.
% 11.46/11.68 % subtype_inf_time: 0.
% 11.46/11.68 % unif_index_cands_time: 0.
% 11.46/11.68 % unif_index_add_time: 0.003
% 11.46/11.68 % total_time: 10.621
% 11.46/11.68 % num_of_symbols: 231
% 11.46/11.68 % num_of_terms: 9455
% 11.46/11.68
% 11.46/11.68 % ------ Propositional Solver
% 11.46/11.68
% 11.46/11.68 % prop_solver_calls: 1
% 11.46/11.68 % prop_fast_solver_calls: 6
% 11.46/11.68 % prop_num_of_clauses: 3194
% 11.46/11.68 % prop_preprocess_simplified: 12292
% 11.46/11.68 % prop_fo_subsumed: 0
% 11.46/11.68 % prop_solver_time: 0.
% 11.46/11.68 % prop_fast_solver_time: 0.
% 11.46/11.68 % prop_unsat_core_time: 0.
% 11.46/11.68
% 11.46/11.68 % ------ QBF
% 11.46/11.68
% 11.46/11.68 % qbf_q_res: 0
% 11.46/11.68 % qbf_num_tautologies: 0
% 11.46/11.68 % qbf_prep_cycles: 0
% 11.46/11.68
% 11.46/11.68 % ------ BMC1
% 11.46/11.68
% 11.46/11.68 % bmc1_current_bound: -1
% 11.46/11.68 % bmc1_last_solved_bound: -1
% 11.46/11.68 % bmc1_unsat_core_size: -1
% 11.46/11.68 % bmc1_unsat_core_parents_size: -1
% 11.46/11.68 % bmc1_merge_next_fun: 0
% 11.46/11.68 % bmc1_unsat_core_clauses_time: 0.
% 11.46/11.68
% 11.46/11.68 % ------ Instantiation
% 11.46/11.68
% 11.46/11.68 % inst_num_of_clauses: 3689
% 11.46/11.68 % inst_num_in_passive: 0
% 11.46/11.68 % inst_num_in_active: 0
% 11.46/11.68 % inst_num_in_unprocessed: 3992
% 11.46/11.68 % inst_num_of_loops: 0
% 11.46/11.68 % inst_num_of_learning_restarts: 0
% 11.46/11.68 % inst_num_moves_active_passive: 0
% 11.46/11.68 % inst_lit_activity: 0
% 11.46/11.68 % inst_lit_activity_moves: 0
% 11.46/11.68 % inst_num_tautologies: 0
% 11.46/11.68 % inst_num_prop_implied: 0
% 11.46/11.68 % inst_num_existing_simplified: 0
% 11.46/11.68 % inst_num_eq_res_simplified: 0
% 11.46/11.68 % inst_num_child_elim: 0
% 11.46/11.68 % inst_num_of_dismatching_blockings: 0
% 11.46/11.68 % inst_num_of_non_proper_insts: 0
% 11.46/11.68 % inst_num_of_duplicates: 0
% 11.46/11.68 % inst_inst_num_from_inst_to_res: 0
% 11.46/11.68 % inst_dismatching_checking_time: 0.
% 11.46/11.68
% 11.46/11.68 % ------ Resolution
% 11.46/11.68
% 11.46/11.68 % res_num_of_clauses: 4313
% 11.46/11.68 % res_num_in_passive: 163
% 11.46/11.68 % res_num_in_active: 1476
% 11.46/11.68 % res_num_of_loops: 17
% 11.46/11.68 % res_forward_subset_subsumed: 2292
% 11.46/11.68 % res_backward_subset_subsumed: 31
% 11.46/11.68 % res_forward_subsumed: 5
% 11.46/11.68 % res_backward_subsumed: 32
% 11.46/11.68 % res_forward_subsumption_resolution: 5
% 11.46/11.68 % res_backward_subsumption_resolution: 1
% 11.46/11.68 % res_clause_to_clause_subsumption: 115
% 11.46/11.68 % res_orphan_elimination: 0
% 11.46/11.68 % res_tautology_del: 48
% 11.46/11.68 % res_num_eq_res_simplified: 0
% 11.46/11.68 % res_num_sel_changes: 0
% 11.46/11.68 % res_moves_from_active_to_pass: 0
% 11.46/11.68
% 11.46/11.69 % Status Unsatisfiable
% 11.46/11.69 % SZS status Theorem
% 11.46/11.69 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------