TSTP Solution File: LCL774-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : LCL774-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 11:39:28 EDT 2022
% Result : Unsatisfiable 151.69s 152.11s
% Output : CNFRefutation 151.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 384
% Syntax : Number of formulae : 2764 ( 654 unt; 0 def)
% Number of atoms : 6522 (2177 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 7211 (3453 ~;3758 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 3 con; 0-3 aty)
% Number of variables : 7343 ( 329 sgn2931 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X11,X3),X10,X3),X9,X3) ),
file('<stdin>',cls_less__add__iff1_1) ).
fof(c_0_1,axiom,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X11,X3),X9,X3),X3) ),
file('<stdin>',cls_less__add__iff2_1) ).
fof(c_0_2,axiom,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X11,X3),X10,X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3),X3) ),
file('<stdin>',cls_less__add__iff1_0) ).
fof(c_0_3,axiom,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X11,X3),X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3),X3) ),
file('<stdin>',cls_less__add__iff2_0) ).
fof(c_0_4,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_0) ).
fof(c_0_5,axiom,
! [X11,X9,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X11,X3),X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3) ),
file('<stdin>',cls_eq__add__iff2_1) ).
fof(c_0_6,axiom,
! [X11,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X11,X3),X10,X3),X3) ),
file('<stdin>',cls_eq__add__iff1_1) ).
fof(c_0_7,axiom,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__sum__squares__lt__zero_0) ).
fof(c_0_8,axiom,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X11,X3),X10,X3) = X9 ),
file('<stdin>',cls_eq__add__iff1_0) ).
fof(c_0_9,axiom,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3)
| X10 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X11,X3),X9,X3) ),
file('<stdin>',cls_eq__add__iff2_0) ).
fof(c_0_10,axiom,
! [X11,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X10,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X11,X3),X10,X3) ),
file('<stdin>',cls_combine__common__factor_0) ).
fof(c_0_11,axiom,
! [X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X9,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X9,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3)
| X10 = X9
| X2 = X1 ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).
fof(c_0_12,axiom,
! [X8,X6,X7,X20,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X6,X3),c_HOL_Otimes__class_Otimes(X7,X8,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X8,X3),c_HOL_Otimes__class_Otimes(X7,X6,X3),X3)
| X6 = X8
| X20 = X7 ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).
fof(c_0_13,axiom,
! [X16,X13,X14,X12] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X16,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),X13,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X12,X14,tc_nat),X16,tc_nat),X13,tc_nat),
file('<stdin>',cls_left__add__mult__distrib_0) ).
fof(c_0_14,axiom,
! [X8,X6,X7,X20] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X6,tc_nat),c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X8,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| X6 = X8
| X20 = X7 ),
file('<stdin>',cls_natgb_Oadd__mul__solve_0) ).
fof(c_0_15,axiom,
! [X9,X10,X1,X2] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,tc_nat),c_HOL_Otimes__class_Otimes(X1,X9,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X9,tc_nat),c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),tc_nat)
| X10 = X9
| X2 = X1 ),
file('<stdin>',cls_natgb_Onoteq__reduce_0) ).
fof(c_0_16,axiom,
! [X21,X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),c_HOL_Otimes__class_Otimes(X22,X21,X3),X3) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),X21,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).
fof(c_0_17,axiom,
! [X21,X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),c_HOL_Otimes__class_Otimes(X22,X21,X3),X3) = c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X22,X21,X3),X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).
fof(c_0_18,axiom,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),X3)
| X6 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_2) ).
fof(c_0_19,axiom,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),X3)
| X7 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_1) ).
fof(c_0_20,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3) ),
file('<stdin>',cls_mult__less__cancel__left__pos_0) ).
fof(c_0_21,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__neg_0) ).
fof(c_0_22,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_nat__mult__less__cancel1_0) ).
fof(c_0_23,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_0) ).
fof(c_0_24,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_0) ).
fof(c_0_25,axiom,
! [X7,X9,X10,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X10,X3),c_HOL_Otimes__class_Otimes(X7,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X9,X3),c_HOL_Otimes__class_Otimes(X7,X10,X3),X3) ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).
fof(c_0_26,axiom,
! [X8,X6,X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,X3),c_HOL_Otimes__class_Otimes(X7,X8,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X8,X3),c_HOL_Otimes__class_Otimes(X7,X6,X3),X3) ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).
fof(c_0_27,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_1) ).
fof(c_0_28,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_2) ).
fof(c_0_29,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_1) ).
fof(c_0_30,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_2) ).
fof(c_0_31,axiom,
! [X21,X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),c_HOL_Otimes__class_Otimes(X22,X21,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X22,X3),c_HOL_Otimes__class_Otimes(X23,X21,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(c_0_32,axiom,
! [X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(X10,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X10,X3),c_HOL_Oplus__class_Oplus(X1,X9,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_33,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_3) ).
fof(c_0_34,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_3) ).
fof(c_0_35,axiom,
! [X7,X25,X9,X10,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X25,X10,X3),X3) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X25,X9,X3),X3)
| X10 = X9
| X25 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(c_0_36,axiom,
! [X8,X6,X7] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
file('<stdin>',cls_natgb_Oadd__mul__solve_1) ).
fof(c_0_37,axiom,
! [X7,X9,X10] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X10,tc_nat),c_HOL_Otimes__class_Otimes(X7,X9,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X9,tc_nat),c_HOL_Otimes__class_Otimes(X7,X10,tc_nat),tc_nat),
file('<stdin>',cls_natgb_Onoteq__reduce_1) ).
fof(c_0_38,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat),tc_nat) ),
file('<stdin>',cls_Suc__mult__less__cancel1_0) ).
fof(c_0_39,axiom,
! [X7,X25,X9,X10] :
( c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X25,X10,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X25,X9,tc_nat),tc_nat)
| X10 = X9
| X25 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__scale__eq__noteq_0) ).
fof(c_0_40,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X2,X3),c_HOL_Oplus__class_Oplus(X10,X1,X3),X3) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_41,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X10,X3),c_HOL_Oplus__class_Oplus(X1,X10,X3),X3) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_42,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_0) ).
fof(c_0_43,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_0) ).
fof(c_0_44,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X5,tc_nat),c_HOL_Oplus__class_Oplus(X13,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_0) ).
fof(c_0_45,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_1) ).
fof(c_0_46,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_1) ).
fof(c_0_47,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__left__mono__comm_0) ).
fof(c_0_48,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_5) ).
fof(c_0_49,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_4) ).
fof(c_0_50,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__right__mono_0) ).
fof(c_0_51,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_mult__strict__right__mono__neg_0) ).
fof(c_0_52,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_5) ).
fof(c_0_53,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_4) ).
fof(c_0_54,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__left__mono_0) ).
fof(c_0_55,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_mult__strict__left__mono__neg_0) ).
fof(c_0_56,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3) ),
file('<stdin>',cls_mult__less__cancel__left__pos_1) ).
fof(c_0_57,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__neg_1) ).
fof(c_0_58,axiom,
! [X9,X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X10,X3),c_HOL_Oplus__class_Oplus(X1,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(X10,X9,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_59,axiom,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| X7 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).
fof(c_0_60,axiom,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| X6 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).
fof(c_0_61,axiom,
! [X8,X6,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X7,c_HOL_Oplus__class_Oplus(X6,X8,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,X3),c_HOL_Otimes__class_Otimes(X7,X8,X3),X3) ),
file('<stdin>',cls_class__semiring_Omul__d_0) ).
fof(c_0_62,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).
fof(c_0_63,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(c_0_64,axiom,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X5,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).
fof(c_0_65,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_nat__mult__less__cancel1_1) ).
fof(c_0_66,axiom,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X13,tc_nat),c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
file('<stdin>',cls_mult__less__mono1_0) ).
fof(c_0_67,axiom,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X12,tc_nat),c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
file('<stdin>',cls_mult__less__mono2_0) ).
fof(c_0_68,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_2) ).
fof(c_0_69,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_2) ).
fof(c_0_70,axiom,
! [X15,X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),c_HOL_Oplus__class_Oplus(X14,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
file('<stdin>',cls_add__less__mono_0) ).
fof(c_0_71,axiom,
! [X4,X5,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X4,tc_nat),c_HOL_Ominus__class_Ominus(X15,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_diff__less__mono2_0) ).
fof(c_0_72,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__less__mult__pos_0) ).
fof(c_0_73,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
file('<stdin>',cls_zero__less__mult__pos2_0) ).
fof(c_0_74,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(X13,c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat),
file('<stdin>',cls_add__mult__distrib2_0) ).
fof(c_0_75,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X13,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat),
file('<stdin>',cls_add__mult__distrib_0) ).
fof(c_0_76,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat),
file('<stdin>',cls_diff__mult__distrib_0) ).
fof(c_0_77,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(X13,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat),
file('<stdin>',cls_diff__mult__distrib2_0) ).
fof(c_0_78,axiom,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(X12,c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),X14,tc_nat) ),
file('<stdin>',cls_less__diff__conv_1) ).
fof(c_0_79,axiom,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),tc_nat) ),
file('<stdin>',cls_less__diff__conv_0) ).
fof(c_0_80,axiom,
! [X8,X6,X7,X16,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X8,X3),X3) != c_HOL_Oplus__class_Oplus(X6,X16,X3)
| c_HOL_Oplus__class_Oplus(X7,X8,X3) = X16 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_81,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
file('<stdin>',cls_one__less__mult_0) ).
fof(c_0_82,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_Suc__mult__less__cancel1_1) ).
fof(c_0_83,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__neg__pos_0) ).
fof(c_0_84,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_mult__pos__neg_0) ).
fof(c_0_85,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_mult__pos__neg2_0) ).
fof(c_0_86,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_87,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__neg__neg_0) ).
fof(c_0_88,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_mult__pos__pos_0) ).
fof(c_0_89,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_90,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_add__gr__0_0) ).
fof(c_0_91,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
file('<stdin>',cls_n__less__m__mult__n_0) ).
fof(c_0_92,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
file('<stdin>',cls_n__less__n__mult__m_0) ).
fof(c_0_93,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X2,X3),c_HOL_Oplus__class_Oplus(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_94,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X2,X3),c_HOL_Oplus__class_Oplus(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_95,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X10,X3),c_HOL_Oplus__class_Oplus(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_96,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X10,X3),c_HOL_Oplus__class_Oplus(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_97,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X10,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_98,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X5,tc_nat),c_HOL_Oplus__class_Oplus(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_1) ).
fof(c_0_99,axiom,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
file('<stdin>',cls_add__less__mono1_0) ).
fof(c_0_100,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_nat__0__less__mult__iff_2) ).
fof(c_0_101,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_diff__less_0) ).
fof(c_0_102,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_103,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_104,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_105,axiom,
! [X4,X5,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X5),X4,tc_nat),c_Suc(X13),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X13,tc_nat),
file('<stdin>',cls_Suc__diff__diff_0) ).
fof(c_0_106,axiom,
! [X8,X6,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X6,X8,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X7,X6,X3),X8,X3) ),
file('<stdin>',cls_class__semiring_Omul__a_0) ).
fof(c_0_107,axiom,
! [X21,X22,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X22,X21,X3),X3) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X24,X21,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(c_0_108,axiom,
! [X21,X22,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X22,X21,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X22,X3),X21,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(c_0_109,axiom,
! [X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),X22,X3) = c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X23,X22,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).
fof(c_0_110,axiom,
! [X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),X22,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X22,X3),X23,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(c_0_111,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X1,X3),X10,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(c_0_112,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X10,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_113,axiom,
! [X9,X10,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X10,X9,X3),X3) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X2,X9,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_114,axiom,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X10,X3),X1,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_115,axiom,
! [X9,X10,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X10,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X10,X3),X9,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_116,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X10,X3),X3) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_117,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X10,X3),X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X10,X3),X3) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_118,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X10,X3),X3) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_119,axiom,
! [X8,X6,X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X8,X3),X3) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X7,X8,X3),X3) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_120,axiom,
! [X8,X6,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X8,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X6,X3),X8,X3) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_121,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).
fof(c_0_122,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_less__iff__diff__less__0_1) ).
fof(c_0_123,axiom,
! [X18,X6,X19,X7,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X19,X18,X3)
| c_HOL_Oord__class_Oless(X7,X6,X3)
| ~ c_HOL_Oord__class_Oless(X19,X18,X3) ),
file('<stdin>',cls_less__eqI_1) ).
fof(c_0_124,axiom,
! [X18,X6,X19,X7,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X19,X18,X3)
| c_HOL_Oord__class_Oless(X19,X18,X3)
| ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
file('<stdin>',cls_less__eqI_0) ).
fof(c_0_125,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X13,tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat),
file('<stdin>',cls_nat__mult__assoc_0) ).
fof(c_0_126,axiom,
! [X13,X14,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X12,X14,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X12,X13,tc_nat),X14,tc_nat),
file('<stdin>',cls_diff__commute_0) ).
fof(c_0_127,axiom,
! [X4,X5,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X13,X5,tc_nat),c_HOL_Oplus__class_Oplus(X13,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
file('<stdin>',cls_diff__cancel_0) ).
fof(c_0_128,axiom,
! [X4,X5,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X13,tc_nat),c_HOL_Oplus__class_Oplus(X4,X13,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
file('<stdin>',cls_diff__cancel2_0) ).
fof(c_0_129,axiom,
! [X13,X14,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X12,X14,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(X12,c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),tc_nat),
file('<stdin>',cls_diff__diff__left_0) ).
fof(c_0_130,axiom,
! [X4,X5,X13] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X13,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X4,X13,tc_nat),tc_nat),
file('<stdin>',cls_nat__add__assoc_0) ).
fof(c_0_131,axiom,
! [X8,X6,X7] : c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X8,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),tc_nat),
file('<stdin>',cls_nat__add__left__commute_0) ).
fof(c_0_132,axiom,
! [X16,X26,X29,X13] : c_Lambda_Osubstn(c_Lambda_OdB_OApp(X26,X16),X29,X13) = c_Lambda_OdB_OApp(c_Lambda_Osubstn(X26,X29,X13),c_Lambda_Osubstn(X16,X29,X13)),
file('<stdin>',cls_substn_Osimps_I2_J_0) ).
fof(c_0_133,axiom,
! [X26,X29,X4,X13] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X29,X26),X13) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X29,X13),c_Lambda_Oliftn(X4,X26,X13)),
file('<stdin>',cls_liftn_Osimps_I2_J_0) ).
fof(c_0_134,axiom,
! [X16,X26,X29,X13] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X26,X16),X29,X13) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X26,X29,X13),c_Lambda_Osubst(X16,X29,X13)),
file('<stdin>',cls_subst__App_0) ).
fof(c_0_135,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__0__less__mult__iff_0) ).
fof(c_0_136,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__0__less__mult__iff_1) ).
fof(c_0_137,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat) ),
file('<stdin>',cls_zero__less__diff_0) ).
fof(c_0_138,axiom,
! [X4,X5,X15,X13] :
( c_HOL_Oplus__class_Oplus(X5,X15,tc_nat) != c_HOL_Oplus__class_Oplus(X13,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_less__add__eq__less_0) ).
fof(c_0_139,axiom,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(X12,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X14,tc_nat),X13,tc_nat) ),
file('<stdin>',cls_add__lessD1_0) ).
fof(c_0_140,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_141,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_142,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_143,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__square__less__zero_0) ).
fof(c_0_144,axiom,
! [X7,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat)),tc_nat),
file('<stdin>',cls_less__iff__Suc__add_1) ).
fof(c_0_145,axiom,
! [X5,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X5,X12,tc_nat)),tc_nat),
file('<stdin>',cls_less__add__Suc2_0) ).
fof(c_0_146,axiom,
! [X5,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X12,X5,tc_nat)),tc_nat),
file('<stdin>',cls_less__add__Suc1_0) ).
fof(c_0_147,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_less__iff__diff__less__0_0) ).
fof(c_0_148,axiom,
! [X4,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Suc(X12),tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_diff__Suc__less_0) ).
fof(c_0_149,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| X5 = X4 ),
file('<stdin>',cls_nat__mult__eq__cancel1_0) ).
fof(c_0_150,axiom,
! [X26,X29,X25,X12] :
( c_Lambda_Obeta(c_Lambda_Osubst(X25,X26,X12),c_Lambda_Osubst(X29,X26,X12))
| ~ c_Lambda_Obeta(X25,X29) ),
file('<stdin>',cls_subst__preserves__beta_0) ).
fof(c_0_151,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_add__gr__0_1) ).
fof(c_0_152,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_add__gr__0_2) ).
fof(c_0_153,axiom,
! [X14,X12] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X12,tc_nat),X12,tc_nat),
file('<stdin>',cls_not__add__less2_0) ).
fof(c_0_154,axiom,
! [X14,X12] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X14,tc_nat),X12,tc_nat),
file('<stdin>',cls_not__add__less1_0) ).
fof(c_0_155,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_zero__less__diff_1) ).
fof(c_0_156,axiom,
! [X4,X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X4,tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
file('<stdin>',cls_less__imp__diff__less_0) ).
fof(c_0_157,axiom,
! [X5,X14,X12] :
( c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X5,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
file('<stdin>',cls_trans__less__add2_0) ).
fof(c_0_158,axiom,
! [X5,X14,X12] :
( c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X14,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
file('<stdin>',cls_trans__less__add1_0) ).
fof(c_0_159,axiom,
! [X8,X6,X7] :
( c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X6,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I2_J_0) ).
fof(c_0_160,axiom,
! [X8,X6,X7] :
( c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X6,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I1_J_0) ).
fof(c_0_161,axiom,
! [X8,X6,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X8,X7,X3)
| ~ c_HOL_Oord__class_Oless(X8,X6,X3)
| ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_162,axiom,
! [X8,X6,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X7,X8,X3)
| ~ c_HOL_Oord__class_Oless(X6,X8,X3)
| ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_163,axiom,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X3) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
file('<stdin>',cls_of__nat__add_0) ).
fof(c_0_164,axiom,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
file('<stdin>',cls_of__nat__mult_0) ).
fof(c_0_165,axiom,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
file('<stdin>',cls_of__nat__less__iff_0) ).
fof(c_0_166,axiom,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_Suc(X12),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
file('<stdin>',cls_less__trans__Suc_0) ).
fof(c_0_167,axiom,
! [X6,X7,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X7,X6,X3),X3) = c_HOL_Otimes__class_Otimes(X7,X6,X3) ),
file('<stdin>',cls_mult__left__idem_0) ).
fof(c_0_168,axiom,
! [X4] :
( c_Suc(c_HOL_Ominus__class_Ominus(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_Suc__pred_0) ).
fof(c_0_169,axiom,
! [X26,X29,X4] : c_Lambda_Osubstn(X26,X29,X4) = c_Lambda_Osubst(X26,c_Lambda_Oliftn(X4,X29,c_HOL_Ozero__class_Ozero(tc_nat)),X4),
file('<stdin>',cls_substn__subst__n_0) ).
fof(c_0_170,axiom,
! [X4,X13,X12] :
( c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X12),X13) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X12,X4,tc_nat))
| c_HOL_Oord__class_Oless(X12,X13,tc_nat) ),
file('<stdin>',cls_liftn_Osimps_I1_J_1) ).
fof(c_0_171,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(c_Suc(X5),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat),
file('<stdin>',cls_mult__Suc_0) ).
fof(c_0_172,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_Suc(X4),tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat),
file('<stdin>',cls_mult__Suc__right_0) ).
fof(c_0_173,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) = X5
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_add__diff__inverse_0) ).
fof(c_0_174,axiom,
! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
file('<stdin>',cls_of__nat__0__less__iff_0) ).
fof(c_0_175,axiom,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_of__nat__less__iff_1) ).
fof(c_0_176,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat)
| X5 = X4 ),
file('<stdin>',cls_Suc__mult__cancel1_0) ).
fof(c_0_177,axiom,
! [X8,X6,X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X7,X6,X3) != c_HOL_Oplus__class_Oplus(X7,X8,X3)
| X6 = X8 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_178,axiom,
! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_of__nat__0__less__iff_1) ).
fof(c_0_179,axiom,
! [X26,X4,X13] : c_Lambda_Oliftn(c_Suc(X4),X26,X13) = c_Lambda_Olift(c_Lambda_Oliftn(X4,X26,X13),X13),
file('<stdin>',cls_liftn__lift_0) ).
fof(c_0_180,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Oplus__class_Oplus(X10,X2,X3)
| X1 = X10 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_181,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X10,X3)
| X1 = X10 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_182,axiom,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X10,X3)
| X1 = X10 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_183,axiom,
! [X18,X19,X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X7,X7,X3) != c_HOL_Ominus__class_Ominus(X19,X18,X3)
| X19 = X18 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_184,axiom,
! [X6,X17,X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X17,X6,X3) != c_HOL_Ominus__class_Ominus(X7,X7,X3)
| X17 = X6 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_185,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_186,axiom,
! [X6,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X6,X3)
| ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_187,axiom,
! [X6,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X7,X3)
| ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_188,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_189,axiom,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat) ),
file('<stdin>',cls_not__less__eq_1) ).
fof(c_0_190,axiom,
! [X4,X5] :
( c_HOL_Ominus__class_Ominus(X4,X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
file('<stdin>',cls_diffs0__imp__equal_0) ).
fof(c_0_191,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X5,X4),X4,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
file('<stdin>',cls_less__Suc__eq__0__disj_1) ).
fof(c_0_192,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X5,X13,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X13,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
file('<stdin>',cls_mult__cancel2_0) ).
fof(c_0_193,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
file('<stdin>',cls_mult__cancel1_0) ).
fof(c_0_194,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| X5 = X4
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_nat__mult__eq__cancel__disj_0) ).
fof(c_0_195,axiom,
! [X7,X29] :
( c_HOL_Oord__class_Oless(X7,X7,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X7),X29,X7) = c_Lambda_Oliftn(X7,X29,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_substn_Osimps_I1_J_1) ).
fof(c_0_196,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = X2 ),
file('<stdin>',cls_add__diff__cancel_0) ).
fof(c_0_197,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X3),X1,X3) = X2 ),
file('<stdin>',cls_diff__add__cancel_0) ).
fof(c_0_198,axiom,
! [X4,X5,X13] :
( c_HOL_Oplus__class_Oplus(X13,X5,tc_nat) != c_HOL_Oplus__class_Oplus(X13,X4,tc_nat)
| X5 = X4 ),
file('<stdin>',cls_nat__add__left__cancel_0) ).
fof(c_0_199,axiom,
! [X4,X5,X13] :
( c_HOL_Oplus__class_Oplus(X5,X13,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X13,tc_nat)
| X5 = X4 ),
file('<stdin>',cls_nat__add__right__cancel_0) ).
fof(c_0_200,axiom,
! [X8,X6,X7] :
( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X8,tc_nat)
| X6 = X8 ),
file('<stdin>',cls_natgb_Oadd__cancel_0) ).
fof(c_0_201,axiom,
! [X4,X5] : c_HOL_Oplus__class_Oplus(c_Suc(X5),X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)),
file('<stdin>',cls_add__Suc_0) ).
fof(c_0_202,axiom,
! [X4,X5] : c_HOL_Oplus__class_Oplus(X5,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)),
file('<stdin>',cls_add__Suc__right_0) ).
fof(c_0_203,axiom,
! [X26,X29] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X29),X26),c_Lambda_Osubst(X29,X26,c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_beta_0) ).
fof(c_0_204,axiom,
! [X4,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),c_Suc(X5),tc_nat),
file('<stdin>',cls_diff__less__Suc_0) ).
fof(c_0_205,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__add__0_0) ).
fof(c_0_206,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),X4,tc_nat) = X5,
file('<stdin>',cls_diff__add__inverse_0) ).
fof(c_0_207,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X4,tc_nat) = X5,
file('<stdin>',cls_diff__add__inverse2_0) ).
fof(c_0_208,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
file('<stdin>',cls_Suc__less__eq_0) ).
fof(c_0_209,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_Suc__mono_0) ).
fof(c_0_210,axiom,
! [X7,X4] :
( c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X4,tc_nat) ),
file('<stdin>',cls_less__Suc__eq__0__disj_3) ).
fof(c_0_211,axiom,
! [X4,X5] :
( X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
file('<stdin>',cls_less__SucE_0) ).
fof(c_0_212,axiom,
! [X4,X5] :
( X5 = X4
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
file('<stdin>',cls_less__antisym_0) ).
fof(c_0_213,axiom,
! [X4,X5] :
( X4 = X5
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_0) ).
fof(c_0_214,axiom,
! [X16,X14,X12] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X16,X12) = c_Lambda_OdB_OVar(X14)
| ~ c_HOL_Oord__class_Oless(X14,X12,tc_nat) ),
file('<stdin>',cls_subst__lt_0) ).
fof(c_0_215,axiom,
! [X4,X13,X12] :
( c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X12),X13) = c_Lambda_OdB_OVar(X12)
| ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat) ),
file('<stdin>',cls_liftn_Osimps_I1_J_0) ).
fof(c_0_216,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat)
| c_Suc(X5) = X4
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_Suc__lessI_0) ).
fof(c_0_217,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat) ),
file('<stdin>',cls_Suc__lessD_0) ).
fof(c_0_218,axiom,
! [X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_of__nat__less__0__iff_0) ).
fof(c_0_219,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_less__SucI_0) ).
fof(c_0_220,axiom,
! [X25,X14,X12] :
( c_InductTermi_OIT(c_Lambda_Osubst(X25,c_Lambda_OdB_OVar(X12),X14))
| ~ c_InductTermi_OIT(X25) ),
file('<stdin>',cls_subst__Var__IT_0) ).
fof(c_0_221,axiom,
! [X4,X5] :
( X5 = c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X5,X4))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
file('<stdin>',cls_less__Suc__eq__0__disj_0) ).
fof(c_0_222,axiom,
! [X29,X13,X12] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X12),X29,X13) = c_Lambda_OdB_OVar(X12)
| X12 = X13
| c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
file('<stdin>',cls_substn_Osimps_I1_J_2) ).
fof(c_0_223,axiom,
! [X29,X13,X12] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X29,X13) = c_Lambda_OdB_OVar(X12)
| X12 = X13
| c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
file('<stdin>',cls_subst__Var_2) ).
fof(c_0_224,axiom,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X6,X7,X3)
| c_HOL_Oord__class_Oless(X7,X6,X3)
| X7 = X6 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_225,axiom,
! [X6,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X6
| c_HOL_Oord__class_Oless(X6,X7,X3)
| c_HOL_Oord__class_Oless(X7,X6,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_226,axiom,
! [X6,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X6,X7,X3)
| c_HOL_Oord__class_Oless(X7,X6,X3)
| X7 = X6 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_227,axiom,
! [X6,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X6,X7,X3)
| X7 = X6
| c_HOL_Oord__class_Oless(X7,X6,X3) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_228,axiom,
! [X6,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X6
| c_HOL_Oord__class_Oless(X7,X6,X3)
| c_HOL_Oord__class_Oless(X6,X7,X3) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_229,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(c_Suc(X5),c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
file('<stdin>',cls_diff__Suc__Suc_0) ).
fof(c_0_230,axiom,
! [X4,X5] : c_HOL_Oplus__class_Oplus(c_Suc(X5),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_Suc(X4),tc_nat),
file('<stdin>',cls_add__Suc__shift_0) ).
fof(c_0_231,axiom,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X7,X6,X3) = c_HOL_Oplus__class_Oplus(X6,X7,X3) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_232,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_233,axiom,
! [X10,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,X10,X3) = c_HOL_Oplus__class_Oplus(X10,X2,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_234,axiom,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X7,X6,X3) = c_HOL_Otimes__class_Otimes(X6,X7,X3) ),
file('<stdin>',cls_class__semiring_Omul__c_0) ).
fof(c_0_235,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(c_0_236,axiom,
! [X26,X29] : c_Lambda_Osubstn(X26,X29,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X26,X29,c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_substn__subst__0_0) ).
fof(c_0_237,axiom,
! [X7,X29] :
( c_HOL_Oord__class_Oless(X7,X7,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X7),X29,X7) = X29 ),
file('<stdin>',cls_subst__Var_1) ).
fof(c_0_238,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_not__less__eq_0) ).
fof(c_0_239,axiom,
! [X7] :
( c_HOL_Oord__class_Oless(X7,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_1) ).
fof(c_0_240,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_mult__cancel2_1) ).
fof(c_0_241,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('<stdin>',cls_mult__cancel1_1) ).
fof(c_0_242,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_1) ).
fof(c_0_243,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_1) ).
fof(c_0_244,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_no__zero__divirors__neq0_0) ).
fof(c_0_245,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_no__zero__divisors_0) ).
fof(c_0_246,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_0) ).
fof(c_0_247,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| X5 = X4 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_248,axiom,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| X7 = X6 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_249,axiom,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ozero__class_Ozero(X3)
| X7 = X6 ),
file('<stdin>',cls_class__ringb_Osubr0__iff_0) ).
fof(c_0_250,axiom,
! [X13,X12] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X12),X13) = c_Lambda_OdB_OVar(X12)
| ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_0) ).
fof(c_0_251,axiom,
! [X7,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X7 != c_HOL_Oplus__class_Oplus(X7,X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_252,axiom,
! [X4] :
( X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('<stdin>',cls_less__Suc0_0) ).
fof(c_0_253,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_0) ).
fof(c_0_254,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_3) ).
fof(c_0_255,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_0) ).
fof(c_0_256,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_3) ).
fof(c_0_257,axiom,
! [X26,X29,X13] : c_Lambda_Olift(c_Lambda_OdB_OApp(X29,X26),X13) = c_Lambda_OdB_OApp(c_Lambda_Olift(X29,X13),c_Lambda_Olift(X26,X13)),
file('<stdin>',cls_lift_Osimps_I2_J_0) ).
fof(c_0_258,axiom,
! [X4,X5] : c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),
file('<stdin>',cls_nat__add__commute_0) ).
fof(c_0_259,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),
file('<stdin>',cls_nat__mult__commute_0) ).
fof(c_0_260,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_261,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_mult__eq__1__iff_1) ).
fof(c_0_262,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_mult__eq__1__iff_0) ).
fof(c_0_263,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_2) ).
fof(c_0_264,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_2) ).
fof(c_0_265,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = X1 ),
file('<stdin>',cls_eq__iff__diff__eq__0_1) ).
fof(c_0_266,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = X1 ),
file('<stdin>',cls_right__minus__eq_0) ).
fof(c_0_267,axiom,
! [X4] :
( X4 = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X4))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_gr0__conv__Suc_0) ).
fof(c_0_268,axiom,
! [X4] :
( X4 = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X4))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_gr0__implies__Suc_0) ).
fof(c_0_269,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_mult__is__0_0) ).
fof(c_0_270,axiom,
! [X7,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_271,axiom,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_272,axiom,
! [X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_273,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_neq0__conv_1) ).
fof(c_0_274,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_1) ).
fof(c_0_275,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_0) ).
fof(c_0_276,axiom,
! [X16,X26,X29] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X29,X16),c_Lambda_OdB_OApp(X26,X16))
| ~ c_Lambda_Obeta(X29,X26) ),
file('<stdin>',cls_appL_0) ).
fof(c_0_277,axiom,
! [X16,X26,X29] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X16,X29),c_Lambda_OdB_OApp(X16,X26))
| ~ c_Lambda_Obeta(X29,X26) ),
file('<stdin>',cls_appR_0) ).
fof(c_0_278,axiom,
! [X29,X25,X12] :
( c_Lambda_Obeta(c_Lambda_Olift(X25,X12),c_Lambda_Olift(X29,X12))
| ~ c_Lambda_Obeta(X25,X29) ),
file('<stdin>',cls_lift__preserves__beta_0) ).
fof(c_0_279,axiom,
! [X7,X2] :
( X7 != c_HOL_Oplus__class_Oplus(X7,X2,tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).
fof(c_0_280,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != X5
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__self__zero_0) ).
fof(c_0_281,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_not__less0_0) ).
fof(c_0_282,axiom,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_gr__implies__not0_0) ).
fof(c_0_283,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_mult__eq__1__iff_2) ).
fof(c_0_284,axiom,
! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat),
file('<stdin>',cls_nat__less__le_1) ).
fof(c_0_285,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
file('<stdin>',cls_less__not__refl_0) ).
fof(c_0_286,axiom,
! [X26,X29,X13] : c_Lambda_Osubst(c_Lambda_Olift(X26,X13),X29,X13) = X26,
file('<stdin>',cls_subst__lift_0) ).
fof(c_0_287,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_288,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X7 = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_289,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_add__is__1_5) ).
fof(c_0_290,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_one__is__add_4) ).
fof(c_0_291,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('<stdin>',cls_one__is__add_5) ).
fof(c_0_292,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_add__is__1_4) ).
fof(c_0_293,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Osubr0__iff_1) ).
fof(c_0_294,axiom,
! [X29,X25] :
( c_Lambda_Obeta(X25,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X25,X29))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X25),X29) ),
file('<stdin>',cls_beta__cases_I2_J_1) ).
fof(c_0_295,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Omul__0_0) ).
fof(c_0_296,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__zero__left_0) ).
fof(c_0_297,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__zero__right_0) ).
fof(c_0_298,axiom,
! [X1,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_1) ).
fof(c_0_299,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_2) ).
fof(c_0_300,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(c_0_301,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(c_0_302,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_303,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_304,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_305,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_306,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_307,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_308,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X7,X3) = X7 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_309,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
file('<stdin>',cls_diff__0__right_0) ).
fof(c_0_310,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('<stdin>',cls_less__Suc0_1) ).
fof(c_0_311,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_diff__self_0) ).
fof(c_0_312,axiom,
! [X7,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_right__minus__eq_1) ).
fof(c_0_313,axiom,
! [X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_eq__iff__diff__eq__0_0) ).
fof(c_0_314,axiom,
! [X29,X25] :
( X29 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X25,X29))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X25),X29) ),
file('<stdin>',cls_beta__cases_I2_J_0) ).
fof(c_0_315,axiom,
! [X7,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X7,X7,X3) = X7 ),
file('<stdin>',cls_mult__idem_0) ).
fof(c_0_316,axiom,
! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X7),tc_nat),
file('<stdin>',cls_gr0__conv__Suc_1) ).
fof(c_0_317,axiom,
! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X4),tc_nat),
file('<stdin>',cls_zero__less__Suc_0) ).
fof(c_0_318,axiom,
! [X16,X13] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X16,X13) = X16,
file('<stdin>',cls_subst__eq_0) ).
fof(c_0_319,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_add__is__0_2) ).
fof(c_0_320,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_gr0I_0) ).
fof(c_0_321,axiom,
! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
file('<stdin>',cls_lessI_0) ).
fof(c_0_322,axiom,
! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat),
file('<stdin>',cls_less__Suc__eq_2) ).
fof(c_0_323,axiom,
! [X26,X13] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X26,X13) = X26,
file('<stdin>',cls_liftn__0_0) ).
fof(c_0_324,axiom,
! [X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_mult__is__0_2) ).
fof(c_0_325,axiom,
! [X4] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_mult__is__0_1) ).
fof(c_0_326,axiom,
! [X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__0__eq__0_0) ).
fof(c_0_327,axiom,
! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
file('<stdin>',cls_Nat_Oadd__0__right_0) ).
fof(c_0_328,axiom,
! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4,
file('<stdin>',cls_plus__nat_Oadd__0_0) ).
fof(c_0_329,axiom,
! [X7] : X7 = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_natgb_Oadd__r0__iff_1) ).
fof(c_0_330,axiom,
! [X5] : c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
file('<stdin>',cls_minus__nat_Odiff__0_0) ).
fof(c_0_331,axiom,
! [X5] : c_HOL_Ominus__class_Ominus(X5,X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__self__eq__0_0) ).
fof(c_0_332,axiom,
! [X4,X5,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X5,X3) != c_Nat_Osemiring__1__class_Oof__nat(X4,X3)
| X5 = X4 ),
file('<stdin>',cls_of__nat__eq__iff_0) ).
fof(c_0_333,axiom,
! [X26,X29] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X29),c_Lambda_OdB_OAbs(X26))
| ~ c_Lambda_Obeta(X29,X26) ),
file('<stdin>',cls_abs_0) ).
fof(c_0_334,axiom,
! [X34,X32,X35,X33] :
( c_Lambda_OdB_OApp(X33,X32) != c_Lambda_OdB_OApp(X35,X34)
| X32 = X34 ),
file('<stdin>',cls_dB_Osimps_I2_J_1) ).
fof(c_0_335,axiom,
! [X34,X32,X35,X33] :
( c_Lambda_OdB_OApp(X33,X32) != c_Lambda_OdB_OApp(X35,X34)
| X33 = X35 ),
file('<stdin>',cls_dB_Osimps_I2_J_0) ).
fof(c_0_336,axiom,
! [X26,X12] :
( c_InductTermi_OIT(c_Lambda_Olift(X26,X12))
| ~ c_InductTermi_OIT(X26) ),
file('<stdin>',cls_lift__IT_0) ).
fof(c_0_337,axiom,
! [X26,X12] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X12),X26),
file('<stdin>',cls_beta__cases_I1_J_0) ).
fof(c_0_338,axiom,
! [X28,X34,X35] : c_Lambda_OdB_OApp(X35,X34) != c_Lambda_OdB_OVar(X28),
file('<stdin>',cls_dB_Osimps_I5_J_0) ).
fof(c_0_339,axiom,
! [X28,X34,X35] : c_Lambda_OdB_OVar(X28) != c_Lambda_OdB_OApp(X35,X34),
file('<stdin>',cls_dB_Osimps_I4_J_0) ).
fof(c_0_340,axiom,
! [X30,X32,X33] : c_Lambda_OdB_OAbs(X30) != c_Lambda_OdB_OApp(X33,X32),
file('<stdin>',cls_dB_Osimps_I9_J_0) ).
fof(c_0_341,axiom,
! [X30,X32,X33] : c_Lambda_OdB_OApp(X33,X32) != c_Lambda_OdB_OAbs(X30),
file('<stdin>',cls_dB_Osimps_I8_J_0) ).
fof(c_0_342,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_of__nat__0_0) ).
fof(c_0_343,axiom,
! [X25] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X25))
| ~ c_InductTermi_OIT(X25) ),
file('<stdin>',cls_Lambda_0) ).
fof(c_0_344,axiom,
! [X27,X28] :
( c_Lambda_OdB_OVar(X28) != c_Lambda_OdB_OVar(X27)
| X28 = X27 ),
file('<stdin>',cls_dB_Osimps_I1_J_0) ).
fof(c_0_345,axiom,
! [X30,X31] :
( c_Lambda_OdB_OAbs(X31) != c_Lambda_OdB_OAbs(X30)
| X31 = X30 ),
file('<stdin>',cls_dB_Osimps_I3_J_0) ).
fof(c_0_346,axiom,
! [X6,X7] :
( c_Suc(X7) != c_Suc(X6)
| X7 = X6 ),
file('<stdin>',cls_Suc__inject_0) ).
fof(c_0_347,axiom,
! [X27,X28] :
( c_Suc(X28) != c_Suc(X27)
| X28 = X27 ),
file('<stdin>',cls_nat_Oinject_0) ).
fof(c_0_348,axiom,
! [X28,X30] : c_Lambda_OdB_OVar(X28) != c_Lambda_OdB_OAbs(X30),
file('<stdin>',cls_dB_Osimps_I6_J_0) ).
fof(c_0_349,axiom,
! [X28,X30] : c_Lambda_OdB_OAbs(X30) != c_Lambda_OdB_OVar(X28),
file('<stdin>',cls_dB_Osimps_I7_J_0) ).
fof(c_0_350,axiom,
! [X27] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X27),
file('<stdin>',cls_nat_Osimps_I2_J_0) ).
fof(c_0_351,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X5),
file('<stdin>',cls_Zero__neq__Suc_0) ).
fof(c_0_352,axiom,
! [X27] : c_Suc(X27) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_nat_Osimps_I3_J_0) ).
fof(c_0_353,axiom,
! [X5] : c_Suc(X5) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_Suc__neq__Zero_0) ).
fof(c_0_354,axiom,
! [X4] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X4)),
file('<stdin>',cls_Var__IT_0) ).
fof(c_0_355,axiom,
! [X4] : c_Suc(X4) != X4,
file('<stdin>',cls_Suc__n__not__n_0) ).
fof(c_0_356,axiom,
! [X4] : X4 != c_Suc(X4),
file('<stdin>',cls_n__not__Suc__n_0) ).
fof(c_0_357,axiom,
class_Orderings_Oorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Oorder) ).
fof(c_0_358,axiom,
class_Orderings_Olinorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Olinorder) ).
fof(c_0_359,axiom,
class_Orderings_Opreorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Opreorder) ).
fof(c_0_360,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('<stdin>',clsarity_nat__Nat_Osemiring__char__0) ).
fof(c_0_361,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(c_0_362,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(c_0_363,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(c_0_364,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(c_0_365,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_366,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_367,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_368,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_369,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_370,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(c_0_371,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_372,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_373,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_374,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_375,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(c_0_376,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(c_0_377,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(c_0_378,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_379,plain,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X11,X3),X10,X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_380,plain,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X11,X3),X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_381,plain,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X11,X3),X10,X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_382,plain,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X11,X3),X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_383,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_384,plain,
! [X11,X9,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X11,X3),X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_385,plain,
! [X11,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X11,X3),X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_386,plain,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_387,plain,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X11,X3),X10,X3) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_388,plain,
! [X11,X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),X10,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X9,X3)
| X10 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X11,X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_389,plain,
! [X11,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X3),X10,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X11,X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_390,plain,
! [X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X9,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X9,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3)
| X10 = X9
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_391,plain,
! [X8,X6,X7,X20,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X6,X3),c_HOL_Otimes__class_Otimes(X7,X8,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X8,X3),c_HOL_Otimes__class_Otimes(X7,X6,X3),X3)
| X6 = X8
| X20 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_392,axiom,
! [X16,X13,X14,X12] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X16,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),X13,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X12,X14,tc_nat),X16,tc_nat),X13,tc_nat),
c_0_13 ).
fof(c_0_393,axiom,
! [X8,X6,X7,X20] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X6,tc_nat),c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X8,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| X6 = X8
| X20 = X7 ),
c_0_14 ).
fof(c_0_394,axiom,
! [X9,X10,X1,X2] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,tc_nat),c_HOL_Otimes__class_Otimes(X1,X9,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X9,tc_nat),c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),tc_nat)
| X10 = X9
| X2 = X1 ),
c_0_15 ).
fof(c_0_395,plain,
! [X21,X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),c_HOL_Otimes__class_Otimes(X22,X21,X3),X3) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),X21,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_396,plain,
! [X21,X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),c_HOL_Otimes__class_Otimes(X22,X21,X3),X3) = c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X22,X21,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_397,plain,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),X3)
| X6 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_398,plain,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),X3)
| X7 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_399,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_400,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_401,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_402,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_403,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_404,plain,
! [X7,X9,X10,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X10,X3),c_HOL_Otimes__class_Otimes(X7,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X9,X3),c_HOL_Otimes__class_Otimes(X7,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_405,plain,
! [X8,X6,X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,X3),c_HOL_Otimes__class_Otimes(X7,X8,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X8,X3),c_HOL_Otimes__class_Otimes(X7,X6,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_406,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_407,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_408,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_409,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_410,plain,
! [X21,X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),c_HOL_Otimes__class_Otimes(X22,X21,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X22,X3),c_HOL_Otimes__class_Otimes(X23,X21,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_411,plain,
! [X9,X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(X10,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X10,X3),c_HOL_Oplus__class_Oplus(X1,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_412,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_413,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_414,plain,
! [X7,X25,X9,X10,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X25,X10,X3),X3) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X25,X9,X3),X3)
| X10 = X9
| X25 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_415,axiom,
! [X8,X6,X7] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
c_0_36 ).
fof(c_0_416,axiom,
! [X7,X9,X10] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X10,tc_nat),c_HOL_Otimes__class_Otimes(X7,X9,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X9,tc_nat),c_HOL_Otimes__class_Otimes(X7,X10,tc_nat),tc_nat),
c_0_37 ).
fof(c_0_417,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_418,axiom,
! [X7,X25,X9,X10] :
( c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X25,X10,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X25,X9,tc_nat),tc_nat)
| X10 = X9
| X25 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_39 ).
fof(c_0_419,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X2,X3),c_HOL_Oplus__class_Oplus(X10,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_420,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X10,X3),c_HOL_Oplus__class_Oplus(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_421,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_422,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_423,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X5,tc_nat),c_HOL_Oplus__class_Oplus(X13,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_424,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_425,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_426,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_427,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_428,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_429,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_430,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_431,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_432,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_433,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_434,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_435,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_436,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X2,X3),c_HOL_Otimes__class_Otimes(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_437,plain,
! [X9,X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X10,X3),c_HOL_Oplus__class_Oplus(X1,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(X10,X9,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_438,plain,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| X7 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_439,plain,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| X6 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_440,plain,
! [X8,X6,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X7,c_HOL_Oplus__class_Oplus(X6,X8,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,X3),c_HOL_Otimes__class_Otimes(X7,X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_441,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_442,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,X3),c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_443,plain,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_444,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_445,plain,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X13,tc_nat),c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_446,plain,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X12,tc_nat),c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_447,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_448,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_449,plain,
! [X15,X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),c_HOL_Oplus__class_Oplus(X14,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_450,plain,
! [X4,X5,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X4,tc_nat),c_HOL_Ominus__class_Ominus(X15,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_451,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_452,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_453,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(X13,c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat),
c_0_74 ).
fof(c_0_454,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X13,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat),
c_0_75 ).
fof(c_0_455,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat),
c_0_76 ).
fof(c_0_456,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(X13,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat),
c_0_77 ).
fof(c_0_457,plain,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(X12,c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_458,plain,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_459,plain,
! [X8,X6,X7,X16,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X8,X3),X3) != c_HOL_Oplus__class_Oplus(X6,X16,X3)
| c_HOL_Oplus__class_Oplus(X7,X8,X3) = X16 ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_460,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_461,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_462,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_463,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_464,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_465,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_466,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_467,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_468,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_469,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_470,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_471,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_472,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X2,X3),c_HOL_Oplus__class_Oplus(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_473,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X2,X3),c_HOL_Oplus__class_Oplus(X10,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_474,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X10,X3),c_HOL_Oplus__class_Oplus(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_475,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X10,X3),c_HOL_Oplus__class_Oplus(X1,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_476,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X10,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X10,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_477,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X5,tc_nat),c_HOL_Oplus__class_Oplus(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_478,plain,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_479,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_480,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_481,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_482,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_483,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_484,axiom,
! [X4,X5,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X5),X4,tc_nat),c_Suc(X13),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X13,tc_nat),
c_0_105 ).
fof(c_0_485,plain,
! [X8,X6,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X6,X8,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X7,X6,X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_486,plain,
! [X21,X22,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X22,X21,X3),X3) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X24,X21,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_487,plain,
! [X21,X22,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X22,X21,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X22,X3),X21,X3) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_488,plain,
! [X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),X22,X3) = c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X23,X22,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_489,plain,
! [X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X23,X3),X22,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X24,X22,X3),X23,X3) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_490,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X1,X3),X10,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_491,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_492,plain,
! [X9,X10,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X10,X9,X3),X3) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X2,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_493,plain,
! [X10,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X10,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_494,plain,
! [X9,X10,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X10,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X10,X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_495,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_496,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X10,X3),X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_497,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X10,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_498,plain,
! [X8,X6,X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X8,X3),X3) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X7,X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_499,plain,
! [X8,X6,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X8,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X6,X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_500,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_501,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_502,plain,
! [X18,X6,X19,X7,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X19,X18,X3)
| c_HOL_Oord__class_Oless(X7,X6,X3)
| ~ c_HOL_Oord__class_Oless(X19,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_503,plain,
! [X18,X6,X19,X7,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X19,X18,X3)
| c_HOL_Oord__class_Oless(X19,X18,X3)
| ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_504,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X13,tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat),
c_0_125 ).
fof(c_0_505,axiom,
! [X13,X14,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X12,X14,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X12,X13,tc_nat),X14,tc_nat),
c_0_126 ).
fof(c_0_506,axiom,
! [X4,X5,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X13,X5,tc_nat),c_HOL_Oplus__class_Oplus(X13,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
c_0_127 ).
fof(c_0_507,axiom,
! [X4,X5,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X13,tc_nat),c_HOL_Oplus__class_Oplus(X4,X13,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
c_0_128 ).
fof(c_0_508,axiom,
! [X13,X14,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X12,X14,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(X12,c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),tc_nat),
c_0_129 ).
fof(c_0_509,axiom,
! [X4,X5,X13] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X13,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X4,X13,tc_nat),tc_nat),
c_0_130 ).
fof(c_0_510,axiom,
! [X8,X6,X7] : c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X8,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),tc_nat),
c_0_131 ).
fof(c_0_511,axiom,
! [X16,X26,X29,X13] : c_Lambda_Osubstn(c_Lambda_OdB_OApp(X26,X16),X29,X13) = c_Lambda_OdB_OApp(c_Lambda_Osubstn(X26,X29,X13),c_Lambda_Osubstn(X16,X29,X13)),
c_0_132 ).
fof(c_0_512,axiom,
! [X26,X29,X4,X13] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X29,X26),X13) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X29,X13),c_Lambda_Oliftn(X4,X26,X13)),
c_0_133 ).
fof(c_0_513,axiom,
! [X16,X26,X29,X13] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X26,X16),X29,X13) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X26,X29,X13),c_Lambda_Osubst(X16,X29,X13)),
c_0_134 ).
fof(c_0_514,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_515,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_516,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_517,plain,
! [X4,X5,X15,X13] :
( c_HOL_Oplus__class_Oplus(X5,X15,tc_nat) != c_HOL_Oplus__class_Oplus(X13,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_518,plain,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(X12,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X14,tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_519,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_520,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_521,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_522,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_523,axiom,
! [X7,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat)),tc_nat),
c_0_144 ).
fof(c_0_524,axiom,
! [X5,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X5,X12,tc_nat)),tc_nat),
c_0_145 ).
fof(c_0_525,axiom,
! [X5,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X12,X5,tc_nat)),tc_nat),
c_0_146 ).
fof(c_0_526,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_527,plain,
! [X4,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Suc(X12),tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_528,plain,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| X5 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_529,plain,
! [X26,X29,X25,X12] :
( c_Lambda_Obeta(c_Lambda_Osubst(X25,X26,X12),c_Lambda_Osubst(X29,X26,X12))
| ~ c_Lambda_Obeta(X25,X29) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_530,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_531,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_532,plain,
! [X14,X12] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X12,tc_nat),X12,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_533,plain,
! [X14,X12] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X14,tc_nat),X12,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_534,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_535,plain,
! [X4,X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X4,tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_536,plain,
! [X5,X14,X12] :
( c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X5,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_537,plain,
! [X5,X14,X12] :
( c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X14,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_538,plain,
! [X8,X6,X7] :
( c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X6,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_539,plain,
! [X8,X6,X7] :
( c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X6,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_540,plain,
! [X8,X6,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X8,X7,X3)
| ~ c_HOL_Oord__class_Oless(X8,X6,X3)
| ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_541,plain,
! [X8,X6,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X7,X8,X3)
| ~ c_HOL_Oord__class_Oless(X6,X8,X3)
| ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_542,plain,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X3) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_543,plain,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_544,plain,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_545,plain,
! [X13,X14,X12] :
( c_HOL_Oord__class_Oless(c_Suc(X12),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_546,plain,
! [X6,X7,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X7,X6,X3),X3) = c_HOL_Otimes__class_Otimes(X7,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_547,plain,
! [X4] :
( c_Suc(c_HOL_Ominus__class_Ominus(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_548,axiom,
! [X26,X29,X4] : c_Lambda_Osubstn(X26,X29,X4) = c_Lambda_Osubst(X26,c_Lambda_Oliftn(X4,X29,c_HOL_Ozero__class_Ozero(tc_nat)),X4),
c_0_169 ).
fof(c_0_549,axiom,
! [X4,X13,X12] :
( c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X12),X13) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X12,X4,tc_nat))
| c_HOL_Oord__class_Oless(X12,X13,tc_nat) ),
c_0_170 ).
fof(c_0_550,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(c_Suc(X5),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat),
c_0_171 ).
fof(c_0_551,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_Suc(X4),tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat),
c_0_172 ).
fof(c_0_552,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) = X5
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
c_0_173 ).
fof(c_0_553,plain,
! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_554,plain,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_555,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat)
| X5 = X4 ),
c_0_176 ).
fof(c_0_556,plain,
! [X8,X6,X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X7,X6,X3) != c_HOL_Oplus__class_Oplus(X7,X8,X3)
| X6 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_557,plain,
! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_558,axiom,
! [X26,X4,X13] : c_Lambda_Oliftn(c_Suc(X4),X26,X13) = c_Lambda_Olift(c_Lambda_Oliftn(X4,X26,X13),X13),
c_0_179 ).
fof(c_0_559,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Oplus__class_Oplus(X10,X2,X3)
| X1 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_560,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X10,X3)
| X1 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_561,plain,
! [X10,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X10,X3)
| X1 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_562,plain,
! [X18,X19,X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X7,X7,X3) != c_HOL_Ominus__class_Ominus(X19,X18,X3)
| X19 = X18 ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_563,plain,
! [X6,X17,X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X17,X6,X3) != c_HOL_Ominus__class_Ominus(X7,X7,X3)
| X17 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_564,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_565,plain,
! [X6,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X6,X3)
| ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_566,plain,
! [X6,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X7,X3)
| ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_567,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_568,plain,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_569,axiom,
! [X4,X5] :
( c_HOL_Ominus__class_Ominus(X4,X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
c_0_190 ).
fof(c_0_570,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X5,X4),X4,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_571,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X5,X13,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X13,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
c_0_192 ).
fof(c_0_572,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
c_0_193 ).
fof(c_0_573,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| X5 = X4
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_194 ).
fof(c_0_574,axiom,
! [X7,X29] :
( c_HOL_Oord__class_Oless(X7,X7,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X7),X29,X7) = c_Lambda_Oliftn(X7,X29,c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_195 ).
fof(c_0_575,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_576,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X3),X1,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_577,axiom,
! [X4,X5,X13] :
( c_HOL_Oplus__class_Oplus(X13,X5,tc_nat) != c_HOL_Oplus__class_Oplus(X13,X4,tc_nat)
| X5 = X4 ),
c_0_198 ).
fof(c_0_578,axiom,
! [X4,X5,X13] :
( c_HOL_Oplus__class_Oplus(X5,X13,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X13,tc_nat)
| X5 = X4 ),
c_0_199 ).
fof(c_0_579,axiom,
! [X8,X6,X7] :
( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X8,tc_nat)
| X6 = X8 ),
c_0_200 ).
fof(c_0_580,axiom,
! [X4,X5] : c_HOL_Oplus__class_Oplus(c_Suc(X5),X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)),
c_0_201 ).
fof(c_0_581,axiom,
! [X4,X5] : c_HOL_Oplus__class_Oplus(X5,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)),
c_0_202 ).
fof(c_0_582,axiom,
! [X26,X29] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X29),X26),c_Lambda_Osubst(X29,X26,c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_203 ).
fof(c_0_583,axiom,
! [X4,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),c_Suc(X5),tc_nat),
c_0_204 ).
fof(c_0_584,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_205 ).
fof(c_0_585,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),X4,tc_nat) = X5,
c_0_206 ).
fof(c_0_586,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X4,tc_nat) = X5,
c_0_207 ).
fof(c_0_587,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_588,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_589,plain,
! [X7,X4] :
( c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_590,plain,
! [X4,X5] :
( X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_591,plain,
! [X4,X5] :
( X5 = X4
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_592,plain,
! [X4,X5] :
( X4 = X5
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_593,plain,
! [X16,X14,X12] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X16,X12) = c_Lambda_OdB_OVar(X14)
| ~ c_HOL_Oord__class_Oless(X14,X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_594,plain,
! [X4,X13,X12] :
( c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X12),X13) = c_Lambda_OdB_OVar(X12)
| ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_595,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat)
| c_Suc(X5) = X4
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_596,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_597,plain,
! [X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_598,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_599,plain,
! [X25,X14,X12] :
( c_InductTermi_OIT(c_Lambda_Osubst(X25,c_Lambda_OdB_OVar(X12),X14))
| ~ c_InductTermi_OIT(X25) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_600,plain,
! [X4,X5] :
( X5 = c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X5,X4))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_601,axiom,
! [X29,X13,X12] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X12),X29,X13) = c_Lambda_OdB_OVar(X12)
| X12 = X13
| c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
c_0_222 ).
fof(c_0_602,axiom,
! [X29,X13,X12] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X29,X13) = c_Lambda_OdB_OVar(X12)
| X12 = X13
| c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
c_0_223 ).
fof(c_0_603,plain,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X6,X7,X3)
| c_HOL_Oord__class_Oless(X7,X6,X3)
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_604,plain,
! [X6,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X6
| c_HOL_Oord__class_Oless(X6,X7,X3)
| c_HOL_Oord__class_Oless(X7,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_605,plain,
! [X6,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X6,X7,X3)
| c_HOL_Oord__class_Oless(X7,X6,X3)
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_606,plain,
! [X6,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X6,X7,X3)
| X7 = X6
| c_HOL_Oord__class_Oless(X7,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_607,plain,
! [X6,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X6
| c_HOL_Oord__class_Oless(X7,X6,X3)
| c_HOL_Oord__class_Oless(X6,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_608,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(c_Suc(X5),c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
c_0_229 ).
fof(c_0_609,axiom,
! [X4,X5] : c_HOL_Oplus__class_Oplus(c_Suc(X5),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_Suc(X4),tc_nat),
c_0_230 ).
fof(c_0_610,plain,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X7,X6,X3) = c_HOL_Oplus__class_Oplus(X6,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_611,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_612,plain,
! [X10,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,X10,X3) = c_HOL_Oplus__class_Oplus(X10,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_613,plain,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X7,X6,X3) = c_HOL_Otimes__class_Otimes(X6,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_614,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_615,axiom,
! [X26,X29] : c_Lambda_Osubstn(X26,X29,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X26,X29,c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_236 ).
fof(c_0_616,axiom,
! [X7,X29] :
( c_HOL_Oord__class_Oless(X7,X7,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X7),X29,X7) = X29 ),
c_0_237 ).
fof(c_0_617,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
c_0_238 ).
fof(c_0_618,axiom,
! [X7] :
( c_HOL_Oord__class_Oless(X7,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat) ),
c_0_239 ).
fof(c_0_619,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_240 ).
fof(c_0_620,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
c_0_241 ).
fof(c_0_621,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_242 ).
fof(c_0_622,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_243 ).
fof(c_0_623,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_624,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_625,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_626,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| X5 = X4 ),
c_0_247 ).
fof(c_0_627,axiom,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| X7 = X6 ),
c_0_248 ).
fof(c_0_628,plain,
! [X6,X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ozero__class_Ozero(X3)
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_629,plain,
! [X13,X12] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X12),X13) = c_Lambda_OdB_OVar(X12)
| ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_630,plain,
! [X7,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X7 != c_HOL_Oplus__class_Oplus(X7,X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_631,plain,
! [X4] :
( X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_632,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_253 ).
fof(c_0_633,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_254 ).
fof(c_0_634,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_255 ).
fof(c_0_635,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_256 ).
fof(c_0_636,axiom,
! [X26,X29,X13] : c_Lambda_Olift(c_Lambda_OdB_OApp(X29,X26),X13) = c_Lambda_OdB_OApp(c_Lambda_Olift(X29,X13),c_Lambda_Olift(X26,X13)),
c_0_257 ).
fof(c_0_637,axiom,
! [X4,X5] : c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),
c_0_258 ).
fof(c_0_638,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),
c_0_259 ).
fof(c_0_639,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_640,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_261 ).
fof(c_0_641,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_262 ).
fof(c_0_642,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_263 ).
fof(c_0_643,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_264 ).
fof(c_0_644,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_645,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_646,plain,
! [X4] :
( X4 = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X4))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_647,plain,
! [X4] :
( X4 = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X4))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_648,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_269 ).
fof(c_0_649,plain,
! [X7,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_650,plain,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_651,plain,
! [X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_652,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_653,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_274 ).
fof(c_0_654,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_275 ).
fof(c_0_655,plain,
! [X16,X26,X29] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X29,X16),c_Lambda_OdB_OApp(X26,X16))
| ~ c_Lambda_Obeta(X29,X26) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_656,plain,
! [X16,X26,X29] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X16,X29),c_Lambda_OdB_OApp(X16,X26))
| ~ c_Lambda_Obeta(X29,X26) ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_657,plain,
! [X29,X25,X12] :
( c_Lambda_Obeta(c_Lambda_Olift(X25,X12),c_Lambda_Olift(X29,X12))
| ~ c_Lambda_Obeta(X25,X29) ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_658,axiom,
! [X7,X2] :
( X7 != c_HOL_Oplus__class_Oplus(X7,X2,tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_279 ).
fof(c_0_659,axiom,
! [X4,X5] :
( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != X5
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_280 ).
fof(c_0_660,plain,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_661,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_662,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_283 ).
fof(c_0_663,plain,
! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_664,plain,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_665,axiom,
! [X26,X29,X13] : c_Lambda_Osubst(c_Lambda_Olift(X26,X13),X29,X13) = X26,
c_0_286 ).
fof(c_0_666,plain,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_667,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X7 = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_668,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_289 ).
fof(c_0_669,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_290 ).
fof(c_0_670,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_291 ).
fof(c_0_671,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_292 ).
fof(c_0_672,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_673,plain,
! [X29,X25] :
( c_Lambda_Obeta(X25,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X25,X29))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X25),X29) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_674,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_675,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_676,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_677,plain,
! [X1,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_678,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_679,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_680,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_681,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_682,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_683,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_684,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_685,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_686,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_687,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X7,X3) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_688,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_689,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_310 ).
fof(c_0_690,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_691,plain,
! [X7,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_692,plain,
! [X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_693,plain,
! [X29,X25] :
( X29 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X25,X29))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X25),X29) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_694,plain,
! [X7,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X7,X7,X3) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_695,axiom,
! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X7),tc_nat),
c_0_316 ).
fof(c_0_696,axiom,
! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X4),tc_nat),
c_0_317 ).
fof(c_0_697,axiom,
! [X16,X13] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X16,X13) = X16,
c_0_318 ).
fof(c_0_698,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_319 ).
fof(c_0_699,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_320 ).
fof(c_0_700,axiom,
! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
c_0_321 ).
fof(c_0_701,axiom,
! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat),
c_0_322 ).
fof(c_0_702,axiom,
! [X26,X13] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X26,X13) = X26,
c_0_323 ).
fof(c_0_703,axiom,
! [X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_324 ).
fof(c_0_704,axiom,
! [X4] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_325 ).
fof(c_0_705,axiom,
! [X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_326 ).
fof(c_0_706,axiom,
! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
c_0_327 ).
fof(c_0_707,axiom,
! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4,
c_0_328 ).
fof(c_0_708,axiom,
! [X7] : X7 = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_329 ).
fof(c_0_709,axiom,
! [X5] : c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
c_0_330 ).
fof(c_0_710,axiom,
! [X5] : c_HOL_Ominus__class_Ominus(X5,X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_331 ).
fof(c_0_711,plain,
! [X4,X5,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X5,X3) != c_Nat_Osemiring__1__class_Oof__nat(X4,X3)
| X5 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_712,plain,
! [X26,X29] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X29),c_Lambda_OdB_OAbs(X26))
| ~ c_Lambda_Obeta(X29,X26) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_713,axiom,
! [X34,X32,X35,X33] :
( c_Lambda_OdB_OApp(X33,X32) != c_Lambda_OdB_OApp(X35,X34)
| X32 = X34 ),
c_0_334 ).
fof(c_0_714,axiom,
! [X34,X32,X35,X33] :
( c_Lambda_OdB_OApp(X33,X32) != c_Lambda_OdB_OApp(X35,X34)
| X33 = X35 ),
c_0_335 ).
fof(c_0_715,plain,
! [X26,X12] :
( c_InductTermi_OIT(c_Lambda_Olift(X26,X12))
| ~ c_InductTermi_OIT(X26) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_716,plain,
! [X26,X12] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X12),X26),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_717,axiom,
! [X28,X34,X35] : c_Lambda_OdB_OApp(X35,X34) != c_Lambda_OdB_OVar(X28),
c_0_338 ).
fof(c_0_718,axiom,
! [X28,X34,X35] : c_Lambda_OdB_OVar(X28) != c_Lambda_OdB_OApp(X35,X34),
c_0_339 ).
fof(c_0_719,axiom,
! [X30,X32,X33] : c_Lambda_OdB_OAbs(X30) != c_Lambda_OdB_OApp(X33,X32),
c_0_340 ).
fof(c_0_720,axiom,
! [X30,X32,X33] : c_Lambda_OdB_OApp(X33,X32) != c_Lambda_OdB_OAbs(X30),
c_0_341 ).
fof(c_0_721,plain,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_722,plain,
! [X25] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X25))
| ~ c_InductTermi_OIT(X25) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_723,axiom,
! [X27,X28] :
( c_Lambda_OdB_OVar(X28) != c_Lambda_OdB_OVar(X27)
| X28 = X27 ),
c_0_344 ).
fof(c_0_724,axiom,
! [X30,X31] :
( c_Lambda_OdB_OAbs(X31) != c_Lambda_OdB_OAbs(X30)
| X31 = X30 ),
c_0_345 ).
fof(c_0_725,axiom,
! [X6,X7] :
( c_Suc(X7) != c_Suc(X6)
| X7 = X6 ),
c_0_346 ).
fof(c_0_726,axiom,
! [X27,X28] :
( c_Suc(X28) != c_Suc(X27)
| X28 = X27 ),
c_0_347 ).
fof(c_0_727,axiom,
! [X28,X30] : c_Lambda_OdB_OVar(X28) != c_Lambda_OdB_OAbs(X30),
c_0_348 ).
fof(c_0_728,axiom,
! [X28,X30] : c_Lambda_OdB_OAbs(X30) != c_Lambda_OdB_OVar(X28),
c_0_349 ).
fof(c_0_729,axiom,
! [X27] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X27),
c_0_350 ).
fof(c_0_730,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X5),
c_0_351 ).
fof(c_0_731,axiom,
! [X27] : c_Suc(X27) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_352 ).
fof(c_0_732,axiom,
! [X5] : c_Suc(X5) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_353 ).
fof(c_0_733,axiom,
! [X4] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X4)),
c_0_354 ).
fof(c_0_734,axiom,
! [X4] : c_Suc(X4) != X4,
c_0_355 ).
fof(c_0_735,axiom,
! [X4] : X4 != c_Suc(X4),
c_0_356 ).
fof(c_0_736,axiom,
class_Orderings_Oorder(tc_nat),
c_0_357 ).
fof(c_0_737,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_358 ).
fof(c_0_738,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_359 ).
fof(c_0_739,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_360 ).
fof(c_0_740,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_361 ).
fof(c_0_741,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_362 ).
fof(c_0_742,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_363 ).
fof(c_0_743,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_364 ).
fof(c_0_744,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_365 ).
fof(c_0_745,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_366 ).
fof(c_0_746,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_367 ).
fof(c_0_747,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_368 ).
fof(c_0_748,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_369 ).
fof(c_0_749,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_370 ).
fof(c_0_750,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_371 ).
fof(c_0_751,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_372 ).
fof(c_0_752,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_373 ).
fof(c_0_753,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_374 ).
fof(c_0_754,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_375 ).
fof(c_0_755,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_376 ).
fof(c_0_756,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_377 ).
fof(c_0_757,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_378 ).
fof(c_0_758,plain,
! [X12,X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Opordered__ring(X17)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X12,X17),X14,X17),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,X17),X13,X17),X17)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X15,X17),X12,X17),X14,X17),X13,X17) ),
inference(variable_rename,[status(thm)],[c_0_379]) ).
fof(c_0_759,plain,
! [X12,X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Opordered__ring(X17)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X12,X17),X14,X17),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,X17),X13,X17),X17)
| ~ c_HOL_Oord__class_Oless(X14,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X15,X16,X17),X12,X17),X13,X17),X17) ),
inference(variable_rename,[status(thm)],[c_0_380]) ).
fof(c_0_760,plain,
! [X12,X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Opordered__ring(X17)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X15,X17),X12,X17),X14,X17),X13,X17)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X12,X17),X14,X17),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,X17),X13,X17),X17) ),
inference(variable_rename,[status(thm)],[c_0_381]) ).
fof(c_0_761,plain,
! [X12,X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Opordered__ring(X17)
| c_HOL_Oord__class_Oless(X14,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X15,X16,X17),X12,X17),X13,X17),X17)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X12,X17),X14,X17),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,X17),X13,X17),X17) ),
inference(variable_rename,[status(thm)],[c_0_382]) ).
fof(c_0_762,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_383]) ).
fof(c_0_763,plain,
! [X12,X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Oring(X16)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,X16),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X15,X16),X12,X16),X13,X16),X16) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X12,X16),X13,X16) ),
inference(variable_rename,[status(thm)],[c_0_384]) ).
fof(c_0_764,plain,
! [X12,X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Oring(X16)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,X16),X13,X16) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X12,X16),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X15,X14,X16),X12,X16),X13,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_385]) ).
fof(c_0_765,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_386]) ).
fof(c_0_766,plain,
! [X12,X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Oring(X17)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X12,X17),X14,X17) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,X17),X13,X17)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X15,X17),X12,X17),X14,X17) = X13 ),
inference(variable_rename,[status(thm)],[c_0_387]) ).
fof(c_0_767,plain,
! [X12,X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Oring(X17)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X12,X17),X14,X17) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,X17),X13,X17)
| X14 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X15,X16,X17),X12,X17),X13,X17) ),
inference(variable_rename,[status(thm)],[c_0_388]) ).
fof(c_0_768,plain,
! [X12,X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Osemiring(X16)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,X16),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X12,X16),X13,X16),X16) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X15,X14,X16),X12,X16),X13,X16) ),
inference(variable_rename,[status(thm)],[c_0_389]) ).
fof(c_0_769,plain,
! [X11,X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| ~ class_Int_Onumber__ring(X15)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X11,X15),X15) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X11,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15)
| X12 = X11
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_390]) ).
fof(c_0_770,plain,
! [X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Oidom(X25)
| ~ class_Int_Onumber__ring(X25)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X22,X25),c_HOL_Otimes__class_Otimes(X23,X21,X25),X25) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X25),c_HOL_Otimes__class_Otimes(X23,X22,X25),X25)
| X22 = X21
| X24 = X23 ),
inference(variable_rename,[status(thm)],[c_0_391]) ).
fof(c_0_771,plain,
! [X17,X18,X19,X20] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X17,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X17,tc_nat),X18,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X20,X19,tc_nat),X17,tc_nat),X18,tc_nat),
inference(variable_rename,[status(thm)],[c_0_392]) ).
fof(c_0_772,plain,
! [X21,X22,X23,X24] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X22,tc_nat),c_HOL_Otimes__class_Otimes(X23,X21,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,tc_nat),c_HOL_Otimes__class_Otimes(X23,X22,tc_nat),tc_nat)
| X22 = X21
| X24 = X23 ),
inference(variable_rename,[status(thm)],[c_0_393]) ).
fof(c_0_773,plain,
! [X11,X12,X13,X14] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X12,tc_nat),c_HOL_Otimes__class_Otimes(X13,X11,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X11,tc_nat),c_HOL_Otimes__class_Otimes(X13,X12,tc_nat),tc_nat)
| X12 = X11
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_394]) ).
fof(c_0_774,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),c_HOL_Otimes__class_Otimes(X26,X25,X29),X29) = c_HOL_Otimes__class_Otimes(X26,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),X25,X29),X29) ),
inference(variable_rename,[status(thm)],[c_0_395]) ).
fof(c_0_775,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),c_HOL_Otimes__class_Otimes(X26,X25,X29),X29) = c_HOL_Otimes__class_Otimes(X28,c_HOL_Otimes__class_Otimes(X27,c_HOL_Otimes__class_Otimes(X26,X25,X29),X29),X29) ),
inference(variable_rename,[status(thm)],[c_0_396]) ).
fof(c_0_776,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),X10)
| X8 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_397]) ).
fof(c_0_777,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_398]) ).
fof(c_0_778,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_399]) ).
fof(c_0_779,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(X12,X13,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_400]) ).
fof(c_0_780,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_401])])]) ).
fof(c_0_781,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X14),X14)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_402]) ).
fof(c_0_782,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X14),X14)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_403]) ).
fof(c_0_783,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oidom(X14)
| ~ class_Int_Onumber__ring(X14)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X12,X14),c_HOL_Otimes__class_Otimes(X11,X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_404]) ).
fof(c_0_784,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| ~ class_Int_Onumber__ring(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X10,X12),c_HOL_Otimes__class_Otimes(X11,X9,X12),X12) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_405]) ).
fof(c_0_785,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(X12,X13,X14)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_406]) ).
fof(c_0_786,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X14),X14)
| c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_407]) ).
fof(c_0_787,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(X12,X13,X14)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_408]) ).
fof(c_0_788,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X14),X14)
| c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_409]) ).
fof(c_0_789,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),c_HOL_Otimes__class_Otimes(X26,X25,X29),X29) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X26,X29),c_HOL_Otimes__class_Otimes(X27,X25,X29),X29) ),
inference(variable_rename,[status(thm)],[c_0_410]) ).
fof(c_0_790,plain,
! [X11,X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X14,X13,X15),c_HOL_Oplus__class_Oplus(X12,X11,X15),X15) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X14,X12,X15),c_HOL_Oplus__class_Oplus(X13,X11,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_411]) ).
fof(c_0_791,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(X12,X13,X14)
| c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_412]) ).
fof(c_0_792,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(X12,X13,X14)
| c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_413]) ).
fof(c_0_793,plain,
! [X26,X27,X28,X29,X30] :
( ~ class_Ring__and__Field_Oidom(X30)
| ~ class_Int_Onumber__ring(X30)
| c_HOL_Oplus__class_Oplus(X26,c_HOL_Otimes__class_Otimes(X27,X29,X30),X30) != c_HOL_Oplus__class_Oplus(X26,c_HOL_Otimes__class_Otimes(X27,X28,X30),X30)
| X29 = X28
| X27 = c_HOL_Ozero__class_Ozero(X30) ),
inference(variable_rename,[status(thm)],[c_0_414]) ).
fof(c_0_794,plain,
! [X9,X10,X11] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_415]) ).
fof(c_0_795,plain,
! [X11,X12,X13] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X13,tc_nat),c_HOL_Otimes__class_Otimes(X11,X12,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X12,tc_nat),c_HOL_Otimes__class_Otimes(X11,X13,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_416]) ).
fof(c_0_796,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X16),X15,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X16),X14,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_417])])]) ).
fof(c_0_797,plain,
! [X26,X27,X28,X29] :
( c_HOL_Oplus__class_Oplus(X26,c_HOL_Otimes__class_Otimes(X27,X29,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X26,c_HOL_Otimes__class_Otimes(X27,X28,tc_nat),tc_nat)
| X29 = X28
| X27 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_418]) ).
fof(c_0_798,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X14)
| c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,X14),c_HOL_Oplus__class_Oplus(X11,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_419]) ).
fof(c_0_799,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X14)
| c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,X14),c_HOL_Oplus__class_Oplus(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_420]) ).
fof(c_0_800,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_421]) ).
fof(c_0_801,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_422]) ).
fof(c_0_802,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X14,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_423])])]) ).
fof(c_0_803,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_424])])]) ).
fof(c_0_804,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_425])])]) ).
fof(c_0_805,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_426]) ).
fof(c_0_806,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14)
| ~ c_HOL_Oord__class_Oless(X12,X13,X14)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_427]) ).
fof(c_0_807,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_428]) ).
fof(c_0_808,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_429]) ).
fof(c_0_809,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_HOL_Oord__class_Oless(X12,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_430]) ).
fof(c_0_810,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(X12,X13,X14)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_431]) ).
fof(c_0_811,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_432]) ).
fof(c_0_812,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_433]) ).
fof(c_0_813,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_HOL_Oord__class_Oless(X12,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_434]) ).
fof(c_0_814,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_435]) ).
fof(c_0_815,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,X14),c_HOL_Otimes__class_Otimes(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(X12,X13,X14)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_436]) ).
fof(c_0_816,plain,
! [X11,X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X15)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X12,X15),c_HOL_Oplus__class_Oplus(X13,X11,X15),X15)
| ~ c_HOL_Oord__class_Oless(X12,X11,X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_437]) ).
fof(c_0_817,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10) != c_HOL_Ozero__class_Ozero(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_438]) ).
fof(c_0_818,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10) != c_HOL_Ozero__class_Ozero(X10)
| X8 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_439]) ).
fof(c_0_819,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Otimes__class_Otimes(X11,c_HOL_Oplus__class_Oplus(X10,X9,X12),X12) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X10,X12),c_HOL_Otimes__class_Otimes(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_440]) ).
fof(c_0_820,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring(X14)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X13,X12,X14),X11,X14) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_441]) ).
fof(c_0_821,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X13,X12,X14),X11,X14) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_442]) ).
fof(c_0_822,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X6,X9),c_HOL_Otimes__class_Otimes(X7,X6,X9),X9) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X7,X9),X6,X9) ),
inference(variable_rename,[status(thm)],[c_0_443]) ).
fof(c_0_823,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_444]) ).
fof(c_0_824,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_445]) ).
fof(c_0_825,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X17,tc_nat),c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_446]) ).
fof(c_0_826,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_447]) ).
fof(c_0_827,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_448]) ).
fof(c_0_828,plain,
! [X16,X17,X18,X19] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X17,tc_nat),c_HOL_Oplus__class_Oplus(X18,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_449]) ).
fof(c_0_829,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X16,tc_nat),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_450]) ).
fof(c_0_830,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_451]) ).
fof(c_0_831,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X4,X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_452]) ).
fof(c_0_832,plain,
! [X14,X15,X16] : c_HOL_Otimes__class_Otimes(X16,c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_453]) ).
fof(c_0_833,plain,
! [X14,X15,X16] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),X16,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_454]) ).
fof(c_0_834,plain,
! [X14,X15,X16] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),X16,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_455]) ).
fof(c_0_835,plain,
! [X14,X15,X16] : c_HOL_Otimes__class_Otimes(X16,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_456]) ).
fof(c_0_836,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_457]) ).
fof(c_0_837,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_458]) ).
fof(c_0_838,plain,
! [X17,X18,X19,X20,X21] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_HOL_Oplus__class_Oplus(X19,c_HOL_Oplus__class_Oplus(X18,X17,X21),X21) != c_HOL_Oplus__class_Oplus(X18,X20,X21)
| c_HOL_Oplus__class_Oplus(X19,X17,X21) = X20 ),
inference(variable_rename,[status(thm)],[c_0_459]) ).
fof(c_0_839,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_460]) ).
fof(c_0_840,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X16),X15,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X16),X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_461])])]) ).
fof(c_0_841,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_462]) ).
fof(c_0_842,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_463]) ).
fof(c_0_843,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_464]) ).
fof(c_0_844,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_465]) ).
fof(c_0_845,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_466]) ).
fof(c_0_846,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_467]) ).
fof(c_0_847,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_468]) ).
fof(c_0_848,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_469])])]) ).
fof(c_0_849,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_470]) ).
fof(c_0_850,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_471]) ).
fof(c_0_851,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X14)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,X14),c_HOL_Oplus__class_Oplus(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_472]) ).
fof(c_0_852,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X14)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,X14),c_HOL_Oplus__class_Oplus(X11,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_473]) ).
fof(c_0_853,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X14)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,X14),c_HOL_Oplus__class_Oplus(X12,X11,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_474]) ).
fof(c_0_854,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X14)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,X14),c_HOL_Oplus__class_Oplus(X12,X11,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_475]) ).
fof(c_0_855,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X13,X11,X14),X14)
| ~ c_HOL_Oord__class_Oless(X12,X11,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_476]) ).
fof(c_0_856,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_477])])]) ).
fof(c_0_857,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_478]) ).
fof(c_0_858,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_479]) ).
fof(c_0_859,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_480]) ).
fof(c_0_860,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_481]) ).
fof(c_0_861,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_482]) ).
fof(c_0_862,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X4,X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_483]) ).
fof(c_0_863,plain,
! [X14,X15,X16] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X15),X14,tc_nat),c_Suc(X16),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),X16,tc_nat),
inference(variable_rename,[status(thm)],[c_0_484]) ).
fof(c_0_864,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Otimes__class_Otimes(X11,c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X10,X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_485]) ).
fof(c_0_865,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| c_HOL_Otimes__class_Otimes(X27,c_HOL_Otimes__class_Otimes(X26,X25,X28),X28) = c_HOL_Otimes__class_Otimes(X26,c_HOL_Otimes__class_Otimes(X27,X25,X28),X28) ),
inference(variable_rename,[status(thm)],[c_0_486]) ).
fof(c_0_866,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| c_HOL_Otimes__class_Otimes(X27,c_HOL_Otimes__class_Otimes(X26,X25,X28),X28) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X27,X26,X28),X25,X28) ),
inference(variable_rename,[status(thm)],[c_0_487]) ).
fof(c_0_867,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X27,X26,X28),X25,X28) = c_HOL_Otimes__class_Otimes(X27,c_HOL_Otimes__class_Otimes(X26,X25,X28),X28) ),
inference(variable_rename,[status(thm)],[c_0_488]) ).
fof(c_0_868,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X27,X26,X28),X25,X28) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X27,X25,X28),X26,X28) ),
inference(variable_rename,[status(thm)],[c_0_489]) ).
fof(c_0_869,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X14)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X13,X12,X14),X11,X14) = c_HOL_Otimes__class_Otimes(X13,c_HOL_Otimes__class_Otimes(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_490]) ).
fof(c_0_870,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X13,X12,X14),X11,X14) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Oplus__class_Oplus(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_491]) ).
fof(c_0_871,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Oplus__class_Oplus(X13,c_HOL_Oplus__class_Oplus(X12,X11,X14),X14) = c_HOL_Oplus__class_Oplus(X12,c_HOL_Oplus__class_Oplus(X13,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_492]) ).
fof(c_0_872,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X13,X12,X14),X11,X14) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X13,X11,X14),X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_493]) ).
fof(c_0_873,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Oplus__class_Oplus(X13,c_HOL_Oplus__class_Oplus(X12,X11,X14),X14) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X13,X12,X14),X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_874,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Oab__semigroup__add(X14)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X13,X12,X14),X11,X14) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Oplus__class_Oplus(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_875,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X14)
| c_HOL_Oplus__class_Oplus(X13,c_HOL_Oplus__class_Oplus(X12,X11,X14),X14) = c_HOL_Oplus__class_Oplus(X12,c_HOL_Oplus__class_Oplus(X13,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_496]) ).
fof(c_0_876,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X14)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X13,X12,X14),X11,X14) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Oplus__class_Oplus(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_877,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Oab__group__add(X12)
| c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X10,X9,X12),X12) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_498]) ).
fof(c_0_878,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X10,X9,X12),X12) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_499]) ).
fof(c_0_879,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_500]) ).
fof(c_0_880,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_501]) ).
fof(c_0_881,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X24)
| c_HOL_Ominus__class_Ominus(X23,X21,X24) != c_HOL_Ominus__class_Ominus(X22,X20,X24)
| c_HOL_Oord__class_Oless(X23,X21,X24)
| ~ c_HOL_Oord__class_Oless(X22,X20,X24) ),
inference(variable_rename,[status(thm)],[c_0_502]) ).
fof(c_0_882,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X24)
| c_HOL_Ominus__class_Ominus(X23,X21,X24) != c_HOL_Ominus__class_Ominus(X22,X20,X24)
| c_HOL_Oord__class_Oless(X22,X20,X24)
| ~ c_HOL_Oord__class_Oless(X23,X21,X24) ),
inference(variable_rename,[status(thm)],[c_0_503]) ).
fof(c_0_883,plain,
! [X14,X15,X16] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X14,tc_nat),X16,tc_nat) = c_HOL_Otimes__class_Otimes(X15,c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_504]) ).
fof(c_0_884,plain,
! [X15,X16,X17] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X17,X15,tc_nat),X16,tc_nat),
inference(variable_rename,[status(thm)],[c_0_505]) ).
fof(c_0_885,plain,
! [X14,X15,X16] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X14,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),
inference(variable_rename,[status(thm)],[c_0_506]) ).
fof(c_0_886,plain,
! [X14,X15,X16] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),c_HOL_Oplus__class_Oplus(X14,X16,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),
inference(variable_rename,[status(thm)],[c_0_507]) ).
fof(c_0_887,plain,
! [X15,X16,X17] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(X17,c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_508]) ).
fof(c_0_888,plain,
! [X14,X15,X16] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),X16,tc_nat) = c_HOL_Oplus__class_Oplus(X15,c_HOL_Oplus__class_Oplus(X14,X16,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_509]) ).
fof(c_0_889,plain,
! [X9,X10,X11] : c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X11,X9,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_510]) ).
fof(c_0_890,plain,
! [X30,X31,X32,X33] : c_Lambda_Osubstn(c_Lambda_OdB_OApp(X31,X30),X32,X33) = c_Lambda_OdB_OApp(c_Lambda_Osubstn(X31,X32,X33),c_Lambda_Osubstn(X30,X32,X33)),
inference(variable_rename,[status(thm)],[c_0_511]) ).
fof(c_0_891,plain,
! [X30,X31,X32,X33] : c_Lambda_Oliftn(X32,c_Lambda_OdB_OApp(X31,X30),X33) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X32,X31,X33),c_Lambda_Oliftn(X32,X30,X33)),
inference(variable_rename,[status(thm)],[c_0_512]) ).
fof(c_0_892,plain,
! [X30,X31,X32,X33] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X31,X30),X32,X33) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X31,X32,X33),c_Lambda_Osubst(X30,X32,X33)),
inference(variable_rename,[status(thm)],[c_0_513]) ).
fof(c_0_893,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_514]) ).
fof(c_0_894,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_515])])]) ).
fof(c_0_895,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_516]) ).
fof(c_0_896,plain,
! [X16,X17,X18,X19] :
( c_HOL_Oplus__class_Oplus(X17,X18,tc_nat) != c_HOL_Oplus__class_Oplus(X19,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
| c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_517]) ).
fof(c_0_897,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X17,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_518]) ).
fof(c_0_898,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_519]) ).
fof(c_0_899,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_520]) ).
fof(c_0_900,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X4,X4,X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_521]) ).
fof(c_0_901,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_522]) ).
fof(c_0_902,plain,
! [X8,X9] : c_HOL_Oord__class_Oless(X9,c_Suc(c_HOL_Oplus__class_Oplus(X9,X8,tc_nat)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_523]) ).
fof(c_0_903,plain,
! [X13,X14] : c_HOL_Oord__class_Oless(X14,c_Suc(c_HOL_Oplus__class_Oplus(X13,X14,tc_nat)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_524]) ).
fof(c_0_904,plain,
! [X13,X14] : c_HOL_Oord__class_Oless(X14,c_Suc(c_HOL_Oplus__class_Oplus(X14,X13,tc_nat)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_525]) ).
fof(c_0_905,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_526]) ).
fof(c_0_906,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,c_Suc(X14),tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_527])])]) ).
fof(c_0_907,plain,
! [X14,X15,X16] :
( c_HOL_Otimes__class_Otimes(X16,X15,tc_nat) != c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_528]) ).
fof(c_0_908,plain,
! [X30,X31,X32,X33] :
( c_Lambda_Obeta(c_Lambda_Osubst(X32,X30,X33),c_Lambda_Osubst(X31,X30,X33))
| ~ c_Lambda_Obeta(X32,X31) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_529])])]) ).
fof(c_0_909,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_530]) ).
fof(c_0_910,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_531])])]) ).
fof(c_0_911,plain,
! [X15,X16] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),X16,tc_nat),
inference(variable_rename,[status(thm)],[c_0_532]) ).
fof(c_0_912,plain,
! [X15,X16] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),X16,tc_nat),
inference(variable_rename,[status(thm)],[c_0_533]) ).
fof(c_0_913,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_534]) ).
fof(c_0_914,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X15,tc_nat),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_535]) ).
fof(c_0_915,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_536]) ).
fof(c_0_916,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_537]) ).
fof(c_0_917,plain,
! [X9,X10,X11] :
( c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X9,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_538]) ).
fof(c_0_918,plain,
! [X9,X10,X11] :
( c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X10,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_539]) ).
fof(c_0_919,plain,
! [X9,X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_HOL_Oord__class_Oless(X9,X11,X12)
| ~ c_HOL_Oord__class_Oless(X9,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_920,plain,
! [X9,X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_HOL_Oord__class_Oless(X11,X9,X12)
| ~ c_HOL_Oord__class_Oless(X10,X9,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_921,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),X8) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_922,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X8) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_923,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_924,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_Suc(X17),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_925,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X10)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Otimes__class_Otimes(X9,X8,X10),X10) = c_HOL_Otimes__class_Otimes(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_546]) ).
fof(c_0_926,plain,
! [X5] :
( c_Suc(c_HOL_Ominus__class_Ominus(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X5
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_927,plain,
! [X30,X31,X32] : c_Lambda_Osubstn(X30,X31,X32) = c_Lambda_Osubst(X30,c_Lambda_Oliftn(X32,X31,c_HOL_Ozero__class_Ozero(tc_nat)),X32),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_928,plain,
! [X14,X15,X16] :
( c_Lambda_Oliftn(X14,c_Lambda_OdB_OVar(X16),X15) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X16,X14,tc_nat))
| c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_929,plain,
! [X6,X7] : c_HOL_Otimes__class_Otimes(c_Suc(X7),X6,tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_930,plain,
! [X6,X7] : c_HOL_Otimes__class_Otimes(X7,c_Suc(X6),tc_nat) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_931,plain,
! [X6,X7] :
( c_HOL_Oplus__class_Oplus(X6,c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) = X7
| c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_932,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_933,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_934,plain,
! [X14,X15,X16] :
( c_HOL_Otimes__class_Otimes(c_Suc(X16),X15,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X16),X14,tc_nat)
| X15 = X14 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_555])])]) ).
fof(c_0_935,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| ~ class_Int_Onumber__ring(X12)
| c_HOL_Oplus__class_Oplus(X11,X10,X12) != c_HOL_Oplus__class_Oplus(X11,X9,X12)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_936,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_937,plain,
! [X27,X28,X29] : c_Lambda_Oliftn(c_Suc(X28),X27,X29) = c_Lambda_Olift(c_Lambda_Oliftn(X28,X27,X29),X29),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_938,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X14)
| c_HOL_Oplus__class_Oplus(X12,X13,X14) != c_HOL_Oplus__class_Oplus(X11,X13,X14)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_939,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X14)
| c_HOL_Oplus__class_Oplus(X13,X12,X14) != c_HOL_Oplus__class_Oplus(X13,X11,X14)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_560]) ).
fof(c_0_940,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X14)
| c_HOL_Oplus__class_Oplus(X13,X12,X14) != c_HOL_Oplus__class_Oplus(X13,X11,X14)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_561]) ).
fof(c_0_941,plain,
! [X20,X21,X22,X23] :
( ~ class_OrderedGroup_Oab__group__add(X23)
| c_HOL_Ominus__class_Ominus(X22,X22,X23) != c_HOL_Ominus__class_Ominus(X21,X20,X23)
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_942,plain,
! [X18,X19,X20,X21] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_HOL_Ominus__class_Ominus(X19,X18,X21) != c_HOL_Ominus__class_Ominus(X20,X20,X21)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_943,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ c_HOL_Oord__class_Oless(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_564]) ).
fof(c_0_944,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10)
| ~ c_HOL_Oord__class_Oless(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_945,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Opreorder(X10)
| ~ c_HOL_Oord__class_Oless(X8,X9,X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_946,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Opreorder(X6)
| ~ c_HOL_Oord__class_Oless(X4,X5,X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_947,plain,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_568]) ).
fof(c_0_948,plain,
! [X6,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_949,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X7,X6),X6,tc_nat)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,c_Suc(X6),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_950,plain,
! [X14,X15,X16] :
( c_HOL_Otimes__class_Otimes(X15,X16,tc_nat) != c_HOL_Otimes__class_Otimes(X14,X16,tc_nat)
| X16 = c_HOL_Ozero__class_Ozero(tc_nat)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_951,plain,
! [X14,X15,X16] :
( c_HOL_Otimes__class_Otimes(X16,X15,tc_nat) != c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)
| X16 = c_HOL_Ozero__class_Ozero(tc_nat)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_952,plain,
! [X14,X15,X16] :
( c_HOL_Otimes__class_Otimes(X16,X15,tc_nat) != c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)
| X15 = X14
| X16 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_953,plain,
! [X30,X31] :
( c_HOL_Oord__class_Oless(X30,X30,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X30),X31,X30) = c_Lambda_Oliftn(X30,X31,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_574])])]) ).
fof(c_0_954,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X4,X6),X4,X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_955,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X4,X6),X4,X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_956,plain,
! [X14,X15,X16] :
( c_HOL_Oplus__class_Oplus(X16,X15,tc_nat) != c_HOL_Oplus__class_Oplus(X16,X14,tc_nat)
| X15 = X14 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_577])])]) ).
fof(c_0_957,plain,
! [X14,X15,X16] :
( c_HOL_Oplus__class_Oplus(X15,X16,tc_nat) != c_HOL_Oplus__class_Oplus(X14,X16,tc_nat)
| X15 = X14 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_578])])]) ).
fof(c_0_958,plain,
! [X9,X10,X11] :
( c_HOL_Oplus__class_Oplus(X11,X10,tc_nat) != c_HOL_Oplus__class_Oplus(X11,X9,tc_nat)
| X10 = X9 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_579])])]) ).
fof(c_0_959,plain,
! [X6,X7] : c_HOL_Oplus__class_Oplus(c_Suc(X7),X6,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_580]) ).
fof(c_0_960,plain,
! [X6,X7] : c_HOL_Oplus__class_Oplus(X7,c_Suc(X6),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_581]) ).
fof(c_0_961,plain,
! [X30,X31] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X31),X30),c_Lambda_Osubst(X31,X30,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_582]) ).
fof(c_0_962,plain,
! [X6,X7] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),c_Suc(X7),tc_nat),
inference(variable_rename,[status(thm)],[c_0_583]) ).
fof(c_0_963,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_584]) ).
fof(c_0_964,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),X6,tc_nat) = X7,
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_965,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),X6,tc_nat) = X7,
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_966,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(X6),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_967,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_968,plain,
! [X8,X9] :
( c_HOL_Oord__class_Oless(c_Suc(X8),c_Suc(X9),tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_969,plain,
! [X6,X7] :
( X7 = X6
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,c_Suc(X6),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_970,plain,
! [X6,X7] :
( X7 = X6
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_971,plain,
! [X6,X7] :
( X6 = X7
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_592]) ).
fof(c_0_972,plain,
! [X17,X18,X19] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X18),X17,X19) = c_Lambda_OdB_OVar(X18)
| ~ c_HOL_Oord__class_Oless(X18,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_593]) ).
fof(c_0_973,plain,
! [X14,X15,X16] :
( c_Lambda_Oliftn(X14,c_Lambda_OdB_OVar(X16),X15) = c_Lambda_OdB_OVar(X16)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_974,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Suc(X7),X6,tc_nat)
| c_Suc(X7) = X6
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_595]) ).
fof(c_0_975,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X7),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_596]) ).
fof(c_0_976,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X6,X7),c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_977,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X7,c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_598]) ).
fof(c_0_978,plain,
! [X26,X27,X28] :
( c_InductTermi_OIT(c_Lambda_Osubst(X26,c_Lambda_OdB_OVar(X28),X27))
| ~ c_InductTermi_OIT(X26) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_599])])]) ).
fof(c_0_979,plain,
! [X6,X7] :
( X7 = c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X7,X6))
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,c_Suc(X6),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_980,plain,
! [X30,X31,X32] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X32),X30,X31) = c_Lambda_OdB_OVar(X32)
| X32 = X31
| c_HOL_Oord__class_Oless(X31,X32,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_981,plain,
! [X30,X31,X32] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X32),X30,X31) = c_Lambda_OdB_OVar(X32)
| X32 = X31
| c_HOL_Oord__class_Oless(X31,X32,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_602]) ).
fof(c_0_982,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X10)
| c_HOL_Oord__class_Oless(X8,X9,X10)
| c_HOL_Oord__class_Oless(X9,X8,X10)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_603]) ).
fof(c_0_983,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| X9 = X8
| c_HOL_Oord__class_Oless(X8,X9,X10)
| c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_604]) ).
fof(c_0_984,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_HOL_Oord__class_Oless(X8,X9,X10)
| c_HOL_Oord__class_Oless(X9,X8,X10)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_605]) ).
fof(c_0_985,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_HOL_Oord__class_Oless(X8,X9,X10)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_986,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X10)
| c_HOL_Oord__class_Oless(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_987,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(c_Suc(X7),c_Suc(X6),tc_nat) = c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_608]) ).
fof(c_0_988,plain,
! [X6,X7] : c_HOL_Oplus__class_Oplus(c_Suc(X7),X6,tc_nat) = c_HOL_Oplus__class_Oplus(X7,c_Suc(X6),tc_nat),
inference(variable_rename,[status(thm)],[c_0_609]) ).
fof(c_0_989,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_HOL_Oplus__class_Oplus(X9,X8,X10) = c_HOL_Oplus__class_Oplus(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_990,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
| c_HOL_Oplus__class_Oplus(X5,X4,X6) = c_HOL_Oplus__class_Oplus(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_611]) ).
fof(c_0_991,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| c_HOL_Oplus__class_Oplus(X12,X11,X13) = c_HOL_Oplus__class_Oplus(X11,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_612]) ).
fof(c_0_992,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_HOL_Otimes__class_Otimes(X9,X8,X10) = c_HOL_Otimes__class_Otimes(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_993,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) = c_HOL_Otimes__class_Otimes(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_994,plain,
! [X30,X31] : c_Lambda_Osubstn(X30,X31,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X30,X31,c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_615]) ).
fof(c_0_995,plain,
! [X30,X31] :
( c_HOL_Oord__class_Oless(X30,X30,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X30),X31,X30) = X31 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_616])])]) ).
fof(c_0_996,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_617]) ).
fof(c_0_997,plain,
! [X8] :
( c_HOL_Oord__class_Oless(X8,X8,tc_nat)
| c_HOL_Oord__class_Oless(X8,c_Suc(X8),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_618]) ).
fof(c_0_998,plain,
! [X6,X7] : c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_999,plain,
! [X6,X7] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_1000,plain,
! [X6,X7] :
( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1001,plain,
! [X6,X7] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1002,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6)
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1003,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_1004,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_625]) ).
fof(c_0_1005,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_626]) ).
fof(c_0_1006,plain,
! [X8,X9] :
( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,X8,tc_nat)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1007,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oidom(X10)
| ~ class_Int_Onumber__ring(X10)
| c_HOL_Ominus__class_Ominus(X9,X8,X10) != c_HOL_Ozero__class_Ozero(X10)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1008,plain,
! [X14,X15] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X15),X14) = c_Lambda_OdB_OVar(X15)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_1009,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oidom(X10)
| ~ class_Int_Onumber__ring(X10)
| X8 != c_HOL_Oplus__class_Oplus(X8,X9,X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1010,plain,
! [X5] :
( X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_1011,plain,
! [X6,X7] :
( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1012,plain,
! [X6,X7] :
( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_633])])]) ).
fof(c_0_1013,plain,
! [X6,X7] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1014,plain,
! [X6,X7] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_635])])]) ).
fof(c_0_1015,plain,
! [X30,X31,X32] : c_Lambda_Olift(c_Lambda_OdB_OApp(X31,X30),X32) = c_Lambda_OdB_OApp(c_Lambda_Olift(X31,X32),c_Lambda_Olift(X30,X32)),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1016,plain,
! [X6,X7] : c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) = c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1017,plain,
! [X6,X7] : c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) = c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1018,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1019,plain,
! [X6,X7] :
( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_640])])]) ).
fof(c_0_1020,plain,
! [X6,X7] :
( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1021,plain,
! [X6,X7] :
( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1022,plain,
! [X6,X7] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1023,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_HOL_Ominus__class_Ominus(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1024,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ominus__class_Ominus(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1025,plain,
! [X5] :
( X5 = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X5))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_646]) ).
fof(c_0_1026,plain,
! [X5] :
( X5 = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X5))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1027,plain,
! [X6,X7] :
( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_648]) ).
fof(c_0_1028,plain,
! [X8,X9] :
( ~ class_Orderings_Oorder(X9)
| ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1029,plain,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X9)
| ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1030,plain,
! [X8,X9] :
( ~ class_Orderings_Opreorder(X9)
| ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1031,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_652 ).
fof(c_0_1032,plain,
! [X6,X7] :
( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_653])])]) ).
fof(c_0_1033,plain,
! [X6,X7] :
( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1034,plain,
! [X30,X31,X32] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X32,X30),c_Lambda_OdB_OApp(X31,X30))
| ~ c_Lambda_Obeta(X32,X31) ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1035,plain,
! [X30,X31,X32] :
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X30,X32),c_Lambda_OdB_OApp(X30,X31))
| ~ c_Lambda_Obeta(X32,X31) ),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1036,plain,
! [X30,X31,X32] :
( c_Lambda_Obeta(c_Lambda_Olift(X31,X32),c_Lambda_Olift(X30,X32))
| ~ c_Lambda_Obeta(X31,X30) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_657])])]) ).
fof(c_0_1037,plain,
! [X8,X9] :
( X8 != c_HOL_Oplus__class_Oplus(X8,X9,tc_nat)
| X9 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1038,plain,
! [X6,X7] :
( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != X7
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_659])])]) ).
fof(c_0_1039,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1040,plain,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1041,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_662 ).
fof(c_0_1042,plain,
! [X8] : ~ c_HOL_Oord__class_Oless(X8,X8,tc_nat),
inference(variable_rename,[status(thm)],[c_0_663]) ).
fof(c_0_1043,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat),
inference(variable_rename,[status(thm)],[c_0_664]) ).
fof(c_0_1044,plain,
! [X30,X31,X32] : c_Lambda_Osubst(c_Lambda_Olift(X30,X32),X31,X32) = X30,
inference(variable_rename,[status(thm)],[c_0_665]) ).
fof(c_0_1045,plain,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1046,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| X8 = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1047,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_668 ).
fof(c_0_1048,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_669 ).
fof(c_0_1049,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_670 ).
fof(c_0_1050,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_671 ).
fof(c_0_1051,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| c_HOL_Ominus__class_Ominus(X8,X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1052,plain,
! [X30,X31] :
( c_Lambda_Obeta(X31,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X31,X30))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X31),X30) ),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1053,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X9),X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1054,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1055,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1056,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1057,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1058,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1059,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_680]) ).
fof(c_0_1060,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_681]) ).
fof(c_0_1061,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_682]) ).
fof(c_0_1062,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_683]) ).
fof(c_0_1063,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1064,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1065,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1066,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X9),X8,X9) = X8 ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1067,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1068,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_689 ).
fof(c_0_1069,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1070,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X8,X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1071,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X8,X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1072,plain,
! [X30,X31] :
( X30 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X31,X30))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X31),X30) ),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1073,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X9)
| c_HOL_Otimes__class_Otimes(X8,X8,X9) = X8 ),
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1074,plain,
! [X8] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X8),tc_nat),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1075,plain,
! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1076,plain,
! [X17,X18] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X18),X17,X18) = X17,
inference(variable_rename,[status(thm)],[c_0_697]) ).
fof(c_0_1077,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_698 ).
fof(c_0_1078,plain,
! [X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1079,plain,
! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1080,plain,
! [X8] : c_HOL_Oord__class_Oless(X8,c_Suc(X8),tc_nat),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1081,plain,
! [X27,X28] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X27,X28) = X27,
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1082,plain,
! [X6] : c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1083,plain,
! [X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1084,plain,
! [X5] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1085,plain,
! [X6] : c_HOL_Oplus__class_Oplus(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6,
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1086,plain,
! [X5] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = X5,
inference(variable_rename,[status(thm)],[c_0_707]) ).
fof(c_0_1087,plain,
! [X8] : X8 = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1088,plain,
! [X6] : c_HOL_Ominus__class_Ominus(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6,
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1089,plain,
! [X6] : c_HOL_Ominus__class_Ominus(X6,X6,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1090,plain,
! [X6,X7,X8] :
( ~ class_Nat_Osemiring__char__0(X8)
| c_Nat_Osemiring__1__class_Oof__nat(X7,X8) != c_Nat_Osemiring__1__class_Oof__nat(X6,X8)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1091,plain,
! [X30,X31] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X31),c_Lambda_OdB_OAbs(X30))
| ~ c_Lambda_Obeta(X31,X30) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1092,plain,
! [X36,X37,X38,X39] :
( c_Lambda_OdB_OApp(X39,X37) != c_Lambda_OdB_OApp(X38,X36)
| X37 = X36 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_713])])]) ).
fof(c_0_1093,plain,
! [X36,X37,X38,X39] :
( c_Lambda_OdB_OApp(X39,X37) != c_Lambda_OdB_OApp(X38,X36)
| X39 = X38 ),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1094,plain,
! [X27,X28] :
( c_InductTermi_OIT(c_Lambda_Olift(X27,X28))
| ~ c_InductTermi_OIT(X27) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_715])])]) ).
fof(c_0_1095,plain,
! [X27,X28] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X28),X27),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1096,plain,
! [X36,X37,X38] : c_Lambda_OdB_OApp(X38,X37) != c_Lambda_OdB_OVar(X36),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1097,plain,
! [X36,X37,X38] : c_Lambda_OdB_OVar(X36) != c_Lambda_OdB_OApp(X38,X37),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1098,plain,
! [X34,X35,X36] : c_Lambda_OdB_OAbs(X34) != c_Lambda_OdB_OApp(X36,X35),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1099,plain,
! [X34,X35,X36] : c_Lambda_OdB_OApp(X36,X35) != c_Lambda_OdB_OAbs(X34),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1100,plain,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1101,plain,
! [X26] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X26))
| ~ c_InductTermi_OIT(X26) ),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1102,plain,
! [X29,X30] :
( c_Lambda_OdB_OVar(X30) != c_Lambda_OdB_OVar(X29)
| X30 = X29 ),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1103,plain,
! [X32,X33] :
( c_Lambda_OdB_OAbs(X33) != c_Lambda_OdB_OAbs(X32)
| X33 = X32 ),
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1104,plain,
! [X8,X9] :
( c_Suc(X9) != c_Suc(X8)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_725]) ).
fof(c_0_1105,plain,
! [X29,X30] :
( c_Suc(X30) != c_Suc(X29)
| X30 = X29 ),
inference(variable_rename,[status(thm)],[c_0_726]) ).
fof(c_0_1106,plain,
! [X31,X32] : c_Lambda_OdB_OVar(X31) != c_Lambda_OdB_OAbs(X32),
inference(variable_rename,[status(thm)],[c_0_727]) ).
fof(c_0_1107,plain,
! [X31,X32] : c_Lambda_OdB_OAbs(X32) != c_Lambda_OdB_OVar(X31),
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1108,plain,
! [X28] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X28),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1109,plain,
! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X6),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1110,plain,
! [X28] : c_Suc(X28) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1111,plain,
! [X6] : c_Suc(X6) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1112,plain,
! [X5] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X5)),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1113,plain,
! [X5] : c_Suc(X5) != X5,
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1114,plain,
! [X5] : X5 != c_Suc(X5),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1115,axiom,
class_Orderings_Oorder(tc_nat),
c_0_736 ).
fof(c_0_1116,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_737 ).
fof(c_0_1117,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_738 ).
fof(c_0_1118,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_739 ).
fof(c_0_1119,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_740 ).
fof(c_0_1120,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_741 ).
fof(c_0_1121,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_742 ).
fof(c_0_1122,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_743 ).
fof(c_0_1123,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_744 ).
fof(c_0_1124,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_745 ).
fof(c_0_1125,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_746 ).
fof(c_0_1126,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_747 ).
fof(c_0_1127,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_748 ).
fof(c_0_1128,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_749 ).
fof(c_0_1129,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_750 ).
fof(c_0_1130,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_751 ).
fof(c_0_1131,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_752 ).
fof(c_0_1132,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_753 ).
fof(c_0_1133,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_754 ).
fof(c_0_1134,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_755 ).
fof(c_0_1135,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_756 ).
fof(c_0_1136,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_757 ).
cnf(c_0_1137,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_758]) ).
cnf(c_0_1138,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(split_conjunct,[status(thm)],[c_0_759]) ).
cnf(c_0_1139,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_760]) ).
cnf(c_0_1140,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_761]) ).
cnf(c_0_1141,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_762]) ).
cnf(c_0_1142,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_763]) ).
cnf(c_0_1143,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_764]) ).
cnf(c_0_1144,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_765]) ).
cnf(c_0_1145,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_766]) ).
cnf(c_0_1146,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(split_conjunct,[status(thm)],[c_0_767]) ).
cnf(c_0_1147,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_768]) ).
cnf(c_0_1148,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_769]) ).
cnf(c_0_1149,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_770]) ).
cnf(c_0_1150,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_771]) ).
cnf(c_0_1151,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_772]) ).
cnf(c_0_1152,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_773]) ).
cnf(c_0_1153,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_774]) ).
cnf(c_0_1154,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_775]) ).
cnf(c_0_1155,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_776]) ).
cnf(c_0_1156,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_777]) ).
cnf(c_0_1157,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_778]) ).
cnf(c_0_1158,plain,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_779]) ).
cnf(c_0_1159,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_780]) ).
cnf(c_0_1160,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_781]) ).
cnf(c_0_1161,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_782]) ).
cnf(c_0_1162,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_783]) ).
cnf(c_0_1163,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_784]) ).
cnf(c_0_1164,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_785]) ).
cnf(c_0_1165,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_786]) ).
cnf(c_0_1166,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_787]) ).
cnf(c_0_1167,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_788]) ).
cnf(c_0_1168,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_789]) ).
cnf(c_0_1169,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_790]) ).
cnf(c_0_1170,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_791]) ).
cnf(c_0_1171,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_792]) ).
cnf(c_0_1172,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_793]) ).
cnf(c_0_1173,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_794]) ).
cnf(c_0_1174,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_795]) ).
cnf(c_0_1175,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_796]) ).
cnf(c_0_1176,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_797]) ).
cnf(c_0_1177,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_798]) ).
cnf(c_0_1178,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_799]) ).
cnf(c_0_1179,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_800]) ).
cnf(c_0_1180,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_801]) ).
cnf(c_0_1181,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_802]) ).
cnf(c_0_1182,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_803]) ).
cnf(c_0_1183,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_804]) ).
cnf(c_0_1184,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_805]) ).
cnf(c_0_1185,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_806]) ).
cnf(c_0_1186,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_807]) ).
cnf(c_0_1187,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_808]) ).
cnf(c_0_1188,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1189,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_810]) ).
cnf(c_0_1190,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_811]) ).
cnf(c_0_1191,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_812]) ).
cnf(c_0_1192,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_813]) ).
cnf(c_0_1193,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_814]) ).
cnf(c_0_1194,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_815]) ).
cnf(c_0_1195,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1196,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_817]) ).
cnf(c_0_1197,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_818]) ).
cnf(c_0_1198,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_819]) ).
cnf(c_0_1199,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1200,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1201,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_822]) ).
cnf(c_0_1202,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_823]) ).
cnf(c_0_1203,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1204,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_825]) ).
cnf(c_0_1205,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1206,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_827]) ).
cnf(c_0_1207,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_828]) ).
cnf(c_0_1208,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_829]) ).
cnf(c_0_1209,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_830]) ).
cnf(c_0_1210,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_831]) ).
cnf(c_0_1211,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_832]) ).
cnf(c_0_1212,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_833]) ).
cnf(c_0_1213,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_834]) ).
cnf(c_0_1214,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_835]) ).
cnf(c_0_1215,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_836]) ).
cnf(c_0_1216,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_837]) ).
cnf(c_0_1217,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_838]) ).
cnf(c_0_1218,plain,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_839]) ).
cnf(c_0_1219,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_840]) ).
cnf(c_0_1220,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_841]) ).
cnf(c_0_1221,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_842]) ).
cnf(c_0_1222,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_843]) ).
cnf(c_0_1223,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_844]) ).
cnf(c_0_1224,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_845]) ).
cnf(c_0_1225,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_846]) ).
cnf(c_0_1226,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_847]) ).
cnf(c_0_1227,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_848]) ).
cnf(c_0_1228,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_849]) ).
cnf(c_0_1229,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_850]) ).
cnf(c_0_1230,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_851]) ).
cnf(c_0_1231,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_852]) ).
cnf(c_0_1232,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_853]) ).
cnf(c_0_1233,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_854]) ).
cnf(c_0_1234,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_855]) ).
cnf(c_0_1235,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_856]) ).
cnf(c_0_1236,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_857]) ).
cnf(c_0_1237,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_858]) ).
cnf(c_0_1238,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_859]) ).
cnf(c_0_1239,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_860]) ).
cnf(c_0_1240,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_861]) ).
cnf(c_0_1241,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_862]) ).
cnf(c_0_1242,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_863]) ).
cnf(c_0_1243,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_864]) ).
cnf(c_0_1244,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1245,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_866]) ).
cnf(c_0_1246,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1247,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1248,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_869]) ).
cnf(c_0_1249,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_870]) ).
cnf(c_0_1250,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_871]) ).
cnf(c_0_1251,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_872]) ).
cnf(c_0_1252,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_873]) ).
cnf(c_0_1253,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_874]) ).
cnf(c_0_1254,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_875]) ).
cnf(c_0_1255,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_876]) ).
cnf(c_0_1256,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_877]) ).
cnf(c_0_1257,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_878]) ).
cnf(c_0_1258,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_879]) ).
cnf(c_0_1259,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_880]) ).
cnf(c_0_1260,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_881]) ).
cnf(c_0_1261,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_882]) ).
cnf(c_0_1262,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_883]) ).
cnf(c_0_1263,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_884]) ).
cnf(c_0_1264,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_885]) ).
cnf(c_0_1265,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_886]) ).
cnf(c_0_1266,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_887]) ).
cnf(c_0_1267,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_888]) ).
cnf(c_0_1268,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_889]) ).
cnf(c_0_1269,plain,
c_Lambda_Osubstn(c_Lambda_OdB_OApp(X1,X2),X3,X4) = c_Lambda_OdB_OApp(c_Lambda_Osubstn(X1,X3,X4),c_Lambda_Osubstn(X2,X3,X4)),
inference(split_conjunct,[status(thm)],[c_0_890]) ).
cnf(c_0_1270,plain,
c_Lambda_Oliftn(X1,c_Lambda_OdB_OApp(X2,X3),X4) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X1,X2,X4),c_Lambda_Oliftn(X1,X3,X4)),
inference(split_conjunct,[status(thm)],[c_0_891]) ).
cnf(c_0_1271,plain,
c_Lambda_Osubst(c_Lambda_OdB_OApp(X1,X2),X3,X4) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4)),
inference(split_conjunct,[status(thm)],[c_0_892]) ).
cnf(c_0_1272,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_893]) ).
cnf(c_0_1273,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_894]) ).
cnf(c_0_1274,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_895]) ).
cnf(c_0_1275,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_896]) ).
cnf(c_0_1276,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_897]) ).
cnf(c_0_1277,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_898]) ).
cnf(c_0_1278,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_899]) ).
cnf(c_0_1279,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_900]) ).
cnf(c_0_1280,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_901]) ).
cnf(c_0_1281,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_902]) ).
cnf(c_0_1282,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_903]) ).
cnf(c_0_1283,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_904]) ).
cnf(c_0_1284,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_905]) ).
cnf(c_0_1285,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_906]) ).
cnf(c_0_1286,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_907]) ).
cnf(c_0_1287,plain,
( c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_908]) ).
cnf(c_0_1288,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_909]) ).
cnf(c_0_1289,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_910]) ).
cnf(c_0_1290,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_911]) ).
cnf(c_0_1291,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_912]) ).
cnf(c_0_1292,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_913]) ).
cnf(c_0_1293,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_914]) ).
cnf(c_0_1294,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_915]) ).
cnf(c_0_1295,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_916]) ).
cnf(c_0_1296,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_917]) ).
cnf(c_0_1297,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_918]) ).
cnf(c_0_1298,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_919]) ).
cnf(c_0_1299,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_920]) ).
cnf(c_0_1300,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_921]) ).
cnf(c_0_1301,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_922]) ).
cnf(c_0_1302,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_923]) ).
cnf(c_0_1303,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_924]) ).
cnf(c_0_1304,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_925]) ).
cnf(c_0_1305,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_926]) ).
cnf(c_0_1306,plain,
c_Lambda_Osubstn(X1,X2,X3) = c_Lambda_Osubst(X1,c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3),
inference(split_conjunct,[status(thm)],[c_0_927]) ).
cnf(c_0_1307,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_928]) ).
cnf(c_0_1308,plain,
c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_929]) ).
cnf(c_0_1309,plain,
c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_930]) ).
cnf(c_0_1310,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_931]) ).
cnf(c_0_1311,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_932]) ).
cnf(c_0_1312,plain,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_933]) ).
cnf(c_0_1313,plain,
( X1 = X2
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_934]) ).
cnf(c_0_1314,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(split_conjunct,[status(thm)],[c_0_935]) ).
cnf(c_0_1315,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_936]) ).
cnf(c_0_1316,plain,
c_Lambda_Oliftn(c_Suc(X1),X2,X3) = c_Lambda_Olift(c_Lambda_Oliftn(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_937]) ).
cnf(c_0_1317,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_938]) ).
cnf(c_0_1318,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_939]) ).
cnf(c_0_1319,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_940]) ).
cnf(c_0_1320,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_941]) ).
cnf(c_0_1321,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_942]) ).
cnf(c_0_1322,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_943]) ).
cnf(c_0_1323,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_944]) ).
cnf(c_0_1324,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_945]) ).
cnf(c_0_1325,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_946]) ).
cnf(c_0_1326,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_947]) ).
cnf(c_0_1327,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_948]) ).
cnf(c_0_1328,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X1,X2),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_949]) ).
cnf(c_0_1329,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_950]) ).
cnf(c_0_1330,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_951]) ).
cnf(c_0_1331,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_952]) ).
cnf(c_0_1332,plain,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_953]) ).
cnf(c_0_1333,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_954]) ).
cnf(c_0_1334,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_955]) ).
cnf(c_0_1335,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_956]) ).
cnf(c_0_1336,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_957]) ).
cnf(c_0_1337,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_958]) ).
cnf(c_0_1338,plain,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_959]) ).
cnf(c_0_1339,plain,
c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_960]) ).
cnf(c_0_1340,plain,
c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X1),X2),c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_961]) ).
cnf(c_0_1341,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_962]) ).
cnf(c_0_1342,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_963]) ).
cnf(c_0_1343,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
inference(split_conjunct,[status(thm)],[c_0_964]) ).
cnf(c_0_1344,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_965]) ).
cnf(c_0_1345,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_966]) ).
cnf(c_0_1346,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_967]) ).
cnf(c_0_1347,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_968]) ).
cnf(c_0_1348,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_969]) ).
cnf(c_0_1349,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_970]) ).
cnf(c_0_1350,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_971]) ).
cnf(c_0_1351,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_972]) ).
cnf(c_0_1352,plain,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_973]) ).
cnf(c_0_1353,plain,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_974]) ).
cnf(c_0_1354,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_975]) ).
cnf(c_0_1355,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_976]) ).
cnf(c_0_1356,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_977]) ).
cnf(c_0_1357,plain,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))
| ~ c_InductTermi_OIT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_978]) ).
cnf(c_0_1358,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X1,X2))
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_979]) ).
cnf(c_0_1359,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_980]) ).
cnf(c_0_1360,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_981]) ).
cnf(c_0_1361,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_982]) ).
cnf(c_0_1362,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_983]) ).
cnf(c_0_1363,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_984]) ).
cnf(c_0_1364,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_985]) ).
cnf(c_0_1365,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_986]) ).
cnf(c_0_1366,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_987]) ).
cnf(c_0_1367,plain,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1368,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_989]) ).
cnf(c_0_1369,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_990]) ).
cnf(c_0_1370,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_991]) ).
cnf(c_0_1371,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_992]) ).
cnf(c_0_1372,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_993]) ).
cnf(c_0_1373,plain,
c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_994]) ).
cnf(c_0_1374,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_995]) ).
cnf(c_0_1375,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1376,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1377,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_998]) ).
cnf(c_0_1378,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_999]) ).
cnf(c_0_1379,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1000]) ).
cnf(c_0_1380,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1001]) ).
cnf(c_0_1381,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1002]) ).
cnf(c_0_1382,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1003]) ).
cnf(c_0_1383,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1004]) ).
cnf(c_0_1384,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1005]) ).
cnf(c_0_1385,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1386,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1387,plain,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1388,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 != c_HOL_Oplus__class_Oplus(X3,X1,X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1389,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1010]) ).
cnf(c_0_1390,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1011]) ).
cnf(c_0_1391,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1012]) ).
cnf(c_0_1392,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1013]) ).
cnf(c_0_1393,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1014]) ).
cnf(c_0_1394,plain,
c_Lambda_Olift(c_Lambda_OdB_OApp(X1,X2),X3) = c_Lambda_OdB_OApp(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1015]) ).
cnf(c_0_1395,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1016]) ).
cnf(c_0_1396,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1017]) ).
cnf(c_0_1397,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1018]) ).
cnf(c_0_1398,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1019]) ).
cnf(c_0_1399,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1020]) ).
cnf(c_0_1400,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1021]) ).
cnf(c_0_1401,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1022]) ).
cnf(c_0_1402,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1023]) ).
cnf(c_0_1403,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1024]) ).
cnf(c_0_1404,plain,
( X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X1))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1025]) ).
cnf(c_0_1405,plain,
( X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X1))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1026]) ).
cnf(c_0_1406,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1027]) ).
cnf(c_0_1407,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1028]) ).
cnf(c_0_1408,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1029]) ).
cnf(c_0_1409,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1030]) ).
cnf(c_0_1410,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1031]) ).
cnf(c_0_1411,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1032]) ).
cnf(c_0_1412,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1033]) ).
cnf(c_0_1413,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1034]) ).
cnf(c_0_1414,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1035]) ).
cnf(c_0_1415,plain,
( c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1036]) ).
cnf(c_0_1416,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1037]) ).
cnf(c_0_1417,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1038]) ).
cnf(c_0_1418,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1039]) ).
cnf(c_0_1419,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1040]) ).
cnf(c_0_1420,plain,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1041]) ).
cnf(c_0_1421,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1042]) ).
cnf(c_0_1422,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1043]) ).
cnf(c_0_1423,plain,
c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1044]) ).
cnf(c_0_1424,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1045]) ).
cnf(c_0_1425,plain,
( X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1046]) ).
cnf(c_0_1426,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1047]) ).
cnf(c_0_1427,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1048]) ).
cnf(c_0_1428,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1049]) ).
cnf(c_0_1429,plain,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1050]) ).
cnf(c_0_1430,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1051]) ).
cnf(c_0_1431,plain,
( c_Lambda_Obeta(X1,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1052]) ).
cnf(c_0_1432,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1053]) ).
cnf(c_0_1433,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1054]) ).
cnf(c_0_1434,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1055]) ).
cnf(c_0_1435,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1056]) ).
cnf(c_0_1436,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1057]) ).
cnf(c_0_1437,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1058]) ).
cnf(c_0_1438,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1059]) ).
cnf(c_0_1439,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1060]) ).
cnf(c_0_1440,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1061]) ).
cnf(c_0_1441,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1062]) ).
cnf(c_0_1442,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1063]) ).
cnf(c_0_1443,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1064]) ).
cnf(c_0_1444,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1065]) ).
cnf(c_0_1445,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1446,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1447,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1068]) ).
cnf(c_0_1448,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1069]) ).
cnf(c_0_1449,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1070]) ).
cnf(c_0_1450,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1071]) ).
cnf(c_0_1451,plain,
( X2 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1072]) ).
cnf(c_0_1452,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1073]) ).
cnf(c_0_1453,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1074]) ).
cnf(c_0_1454,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1075]) ).
cnf(c_0_1455,plain,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1076]) ).
cnf(c_0_1456,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1077]) ).
cnf(c_0_1457,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1078]) ).
cnf(c_0_1458,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1079]) ).
cnf(c_0_1459,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1080]) ).
cnf(c_0_1460,plain,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1081]) ).
cnf(c_0_1461,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1082]) ).
cnf(c_0_1462,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1083]) ).
cnf(c_0_1463,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1084]) ).
cnf(c_0_1464,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1085]) ).
cnf(c_0_1465,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1086]) ).
cnf(c_0_1466,plain,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1087]) ).
cnf(c_0_1467,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1088]) ).
cnf(c_0_1468,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1089]) ).
cnf(c_0_1469,plain,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1090]) ).
cnf(c_0_1470,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1091]) ).
cnf(c_0_1471,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1092]) ).
cnf(c_0_1472,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1093]) ).
cnf(c_0_1473,plain,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1474,plain,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
inference(split_conjunct,[status(thm)],[c_0_1095]) ).
cnf(c_0_1475,plain,
c_Lambda_OdB_OApp(X1,X2) != c_Lambda_OdB_OVar(X3),
inference(split_conjunct,[status(thm)],[c_0_1096]) ).
cnf(c_0_1476,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OApp(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1097]) ).
cnf(c_0_1477,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OApp(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1098]) ).
cnf(c_0_1478,plain,
c_Lambda_OdB_OApp(X1,X2) != c_Lambda_OdB_OAbs(X3),
inference(split_conjunct,[status(thm)],[c_0_1099]) ).
cnf(c_0_1479,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1100]) ).
cnf(c_0_1480,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1101]) ).
cnf(c_0_1481,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1482,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1103]) ).
cnf(c_0_1483,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1484,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1485,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1486,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1487,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1488,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1489,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1490,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1491,plain,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X1)),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1492,plain,
c_Suc(X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_1113]) ).
cnf(c_0_1493,plain,
X1 != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1114]) ).
cnf(c_0_1494,plain,
class_Orderings_Oorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1495,plain,
class_Orderings_Olinorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1496,plain,
class_Orderings_Opreorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1117]) ).
cnf(c_0_1497,plain,
class_Nat_Osemiring__char__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1118]) ).
cnf(c_0_1498,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1499,plain,
class_Ring__and__Field_Osemiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1120]) ).
cnf(c_0_1500,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1501,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1502,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1503,plain,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1504,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1505,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1506,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1507,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1508,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1509,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1510,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1511,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1512,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1133]) ).
cnf(c_0_1513,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1134]) ).
cnf(c_0_1514,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1515,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1136]) ).
cnf(c_0_1516,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_1137,
[final] ).
cnf(c_0_1517,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
c_0_1138,
[final] ).
cnf(c_0_1518,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_1139,
[final] ).
cnf(c_0_1519,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_1140,
[final] ).
cnf(c_0_1520,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1141,
[final] ).
cnf(c_0_1521,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_1142,
[final] ).
cnf(c_0_1522,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_1143,
[final] ).
cnf(c_0_1523,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1144,
[final] ).
cnf(c_0_1524,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_1145,
[final] ).
cnf(c_0_1525,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
c_0_1146,
[final] ).
cnf(c_0_1526,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
c_0_1147,
[final] ).
cnf(c_0_1527,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_1148,
[final] ).
cnf(c_0_1528,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_1149,
[final] ).
cnf(c_0_1529,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
c_0_1150,
[final] ).
cnf(c_0_1530,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
c_0_1151,
[final] ).
cnf(c_0_1531,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
c_0_1152,
[final] ).
cnf(c_0_1532,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1153,
[final] ).
cnf(c_0_1533,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1154,
[final] ).
cnf(c_0_1534,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1155,
[final] ).
cnf(c_0_1535,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1156,
[final] ).
cnf(c_0_1536,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1157,
[final] ).
cnf(c_0_1537,plain,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1158,
[final] ).
cnf(c_0_1538,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_1159,
[final] ).
cnf(c_0_1539,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1160,
[final] ).
cnf(c_0_1540,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1161,
[final] ).
cnf(c_0_1541,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1162,
[final] ).
cnf(c_0_1542,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1163,
[final] ).
cnf(c_0_1543,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1164,
[final] ).
cnf(c_0_1544,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1165,
[final] ).
cnf(c_0_1545,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1166,
[final] ).
cnf(c_0_1546,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1167,
[final] ).
cnf(c_0_1547,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1168,
[final] ).
cnf(c_0_1548,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1169,
[final] ).
cnf(c_0_1549,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1170,
[final] ).
cnf(c_0_1550,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1171,
[final] ).
cnf(c_0_1551,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1172,
[final] ).
cnf(c_0_1552,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
c_0_1173,
[final] ).
cnf(c_0_1553,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
c_0_1174,
[final] ).
cnf(c_0_1554,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
c_0_1175,
[final] ).
cnf(c_0_1555,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_1176,
[final] ).
cnf(c_0_1556,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_1177,
[final] ).
cnf(c_0_1557,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_1178,
[final] ).
cnf(c_0_1558,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_1179,
[final] ).
cnf(c_0_1559,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
c_0_1180,
[final] ).
cnf(c_0_1560,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
c_0_1181,
[final] ).
cnf(c_0_1561,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
c_0_1182,
[final] ).
cnf(c_0_1562,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_1183,
[final] ).
cnf(c_0_1563,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
c_0_1184,
[final] ).
cnf(c_0_1564,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1185,
[final] ).
cnf(c_0_1565,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1186,
[final] ).
cnf(c_0_1566,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_1187,
[final] ).
cnf(c_0_1567,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1188,
[final] ).
cnf(c_0_1568,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1189,
[final] ).
cnf(c_0_1569,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1190,
[final] ).
cnf(c_0_1570,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_1191,
[final] ).
cnf(c_0_1571,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1192,
[final] ).
cnf(c_0_1572,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1193,
[final] ).
cnf(c_0_1573,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1194,
[final] ).
cnf(c_0_1574,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1195,
[final] ).
cnf(c_0_1575,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1196,
[final] ).
cnf(c_0_1576,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1197,
[final] ).
cnf(c_0_1577,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1198,
[final] ).
cnf(c_0_1578,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
c_0_1199,
[final] ).
cnf(c_0_1579,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1200,
[final] ).
cnf(c_0_1580,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1201,
[final] ).
cnf(c_0_1581,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1202,
[final] ).
cnf(c_0_1582,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
c_0_1203,
[final] ).
cnf(c_0_1583,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
c_0_1204,
[final] ).
cnf(c_0_1584,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1205,
[final] ).
cnf(c_0_1585,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1206,
[final] ).
cnf(c_0_1586,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
c_0_1207,
[final] ).
cnf(c_0_1587,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
c_0_1208,
[final] ).
cnf(c_0_1588,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1209,
[final] ).
cnf(c_0_1589,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1210,
[final] ).
cnf(c_0_1590,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
c_0_1211,
[final] ).
cnf(c_0_1591,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),
c_0_1212,
[final] ).
cnf(c_0_1592,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
c_0_1213,
[final] ).
cnf(c_0_1593,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat),
c_0_1214,
[final] ).
cnf(c_0_1594,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_1215,
[final] ).
cnf(c_0_1595,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
c_0_1216,
[final] ).
cnf(c_0_1596,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1217,
[final] ).
cnf(c_0_1597,plain,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_1218,
[final] ).
cnf(c_0_1598,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1219,
[final] ).
cnf(c_0_1599,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
c_0_1220,
[final] ).
cnf(c_0_1600,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1221,
[final] ).
cnf(c_0_1601,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1222,
[final] ).
cnf(c_0_1602,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_1223,
[final] ).
cnf(c_0_1603,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1224,
[final] ).
cnf(c_0_1604,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1225,
[final] ).
cnf(c_0_1605,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_1226,
[final] ).
cnf(c_0_1606,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
c_0_1227,
[final] ).
cnf(c_0_1607,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_1228,
[final] ).
cnf(c_0_1608,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_1229,
[final] ).
cnf(c_0_1609,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_1230,
[final] ).
cnf(c_0_1610,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1231,
[final] ).
cnf(c_0_1611,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_1232,
[final] ).
cnf(c_0_1612,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1233,
[final] ).
cnf(c_0_1613,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1234,
[final] ).
cnf(c_0_1614,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1235,
[final] ).
cnf(c_0_1615,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1236,
[final] ).
cnf(c_0_1616,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
c_0_1237,
[final] ).
cnf(c_0_1617,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
c_0_1238,
[final] ).
cnf(c_0_1618,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_1239,
[final] ).
cnf(c_0_1619,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1240,
[final] ).
cnf(c_0_1620,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1241,
[final] ).
cnf(c_0_1621,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
c_0_1242,
[final] ).
cnf(c_0_1622,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1243,
[final] ).
cnf(c_0_1623,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1244,
[final] ).
cnf(c_0_1624,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1245,
[final] ).
cnf(c_0_1625,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1246,
[final] ).
cnf(c_0_1626,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1247,
[final] ).
cnf(c_0_1627,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
c_0_1248,
[final] ).
cnf(c_0_1628,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1249,
[final] ).
cnf(c_0_1629,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1250,
[final] ).
cnf(c_0_1630,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1251,
[final] ).
cnf(c_0_1631,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1252,
[final] ).
cnf(c_0_1632,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
c_0_1253,
[final] ).
cnf(c_0_1633,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
c_0_1254,
[final] ).
cnf(c_0_1634,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
c_0_1255,
[final] ).
cnf(c_0_1635,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_1256,
[final] ).
cnf(c_0_1636,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1257,
[final] ).
cnf(c_0_1637,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1258,
[final] ).
cnf(c_0_1638,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1259,
[final] ).
cnf(c_0_1639,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1260,
[final] ).
cnf(c_0_1640,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1261,
[final] ).
cnf(c_0_1641,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
c_0_1262,
[final] ).
cnf(c_0_1642,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
c_0_1263,
[final] ).
cnf(c_0_1643,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
c_0_1264,
[final] ).
cnf(c_0_1644,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
c_0_1265,
[final] ).
cnf(c_0_1645,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
c_0_1266,
[final] ).
cnf(c_0_1646,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
c_0_1267,
[final] ).
cnf(c_0_1647,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
c_0_1268,
[final] ).
cnf(c_0_1648,plain,
c_Lambda_OdB_OApp(c_Lambda_Osubstn(X1,X3,X4),c_Lambda_Osubstn(X2,X3,X4)) = c_Lambda_Osubstn(c_Lambda_OdB_OApp(X1,X2),X3,X4),
c_0_1269,
[final] ).
cnf(c_0_1649,plain,
c_Lambda_OdB_OApp(c_Lambda_Oliftn(X1,X2,X4),c_Lambda_Oliftn(X1,X3,X4)) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OApp(X2,X3),X4),
c_0_1270,
[final] ).
cnf(c_0_1650,plain,
c_Lambda_OdB_OApp(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4)) = c_Lambda_Osubst(c_Lambda_OdB_OApp(X1,X2),X3,X4),
c_0_1271,
[final] ).
cnf(c_0_1651,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
c_0_1272,
[final] ).
cnf(c_0_1652,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
c_0_1273,
[final] ).
cnf(c_0_1653,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
c_0_1274,
[final] ).
cnf(c_0_1654,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
c_0_1275,
[final] ).
cnf(c_0_1655,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_1276,
[final] ).
cnf(c_0_1656,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_1277,
[final] ).
cnf(c_0_1657,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1278,
[final] ).
cnf(c_0_1658,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1279,
[final] ).
cnf(c_0_1659,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1280,
[final] ).
cnf(c_0_1660,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
c_0_1281,
[final] ).
cnf(c_0_1661,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
c_0_1282,
[final] ).
cnf(c_0_1662,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
c_0_1283,
[final] ).
cnf(c_0_1663,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1284,
[final] ).
cnf(c_0_1664,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1285,
[final] ).
cnf(c_0_1665,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
c_0_1286,
[final] ).
cnf(c_0_1666,plain,
( c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_1287,
[final] ).
cnf(c_0_1667,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1288,
[final] ).
cnf(c_0_1668,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1289,
[final] ).
cnf(c_0_1669,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
c_0_1290,
[final] ).
cnf(c_0_1670,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
c_0_1291,
[final] ).
cnf(c_0_1671,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1292,
[final] ).
cnf(c_0_1672,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1293,
[final] ).
cnf(c_0_1673,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1294,
[final] ).
cnf(c_0_1674,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1295,
[final] ).
cnf(c_0_1675,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1296,
[final] ).
cnf(c_0_1676,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1297,
[final] ).
cnf(c_0_1677,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1298,
[final] ).
cnf(c_0_1678,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1299,
[final] ).
cnf(c_0_1679,plain,
( c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
c_0_1300,
[final] ).
cnf(c_0_1680,plain,
( c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
c_0_1301,
[final] ).
cnf(c_0_1681,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1302,
[final] ).
cnf(c_0_1682,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1303,
[final] ).
cnf(c_0_1683,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
c_0_1304,
[final] ).
cnf(c_0_1684,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1305,
[final] ).
cnf(c_0_1685,plain,
c_Lambda_Osubst(X1,c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3) = c_Lambda_Osubstn(X1,X2,X3),
c_0_1306,
[final] ).
cnf(c_0_1686,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat)) ),
c_0_1307,
[final] ).
cnf(c_0_1687,plain,
c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),
c_0_1308,
[final] ).
cnf(c_0_1688,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat),
c_0_1309,
[final] ).
cnf(c_0_1689,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1 ),
c_0_1310,
[final] ).
cnf(c_0_1690,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1311,
[final] ).
cnf(c_0_1691,plain,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_1312,
[final] ).
cnf(c_0_1692,plain,
( X1 = X2
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
c_0_1313,
[final] ).
cnf(c_0_1693,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
c_0_1314,
[final] ).
cnf(c_0_1694,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1315,
[final] ).
cnf(c_0_1695,plain,
c_Lambda_Olift(c_Lambda_Oliftn(X1,X2,X3),X3) = c_Lambda_Oliftn(c_Suc(X1),X2,X3),
c_0_1316,
[final] ).
cnf(c_0_1696,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
c_0_1317,
[final] ).
cnf(c_0_1697,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
c_0_1318,
[final] ).
cnf(c_0_1698,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
c_0_1319,
[final] ).
cnf(c_0_1699,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_1320,
[final] ).
cnf(c_0_1700,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1321,
[final] ).
cnf(c_0_1701,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1322,
[final] ).
cnf(c_0_1702,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1323,
[final] ).
cnf(c_0_1703,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1324,
[final] ).
cnf(c_0_1704,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1325,
[final] ).
cnf(c_0_1705,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1326,
[final] ).
cnf(c_0_1706,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1327,
[final] ).
cnf(c_0_1707,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X1,X2),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1328,
[final] ).
cnf(c_0_1708,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
c_0_1329,
[final] ).
cnf(c_0_1709,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
c_0_1330,
[final] ).
cnf(c_0_1710,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
c_0_1331,
[final] ).
cnf(c_0_1711,plain,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1332,
[final] ).
cnf(c_0_1712,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1333,
[final] ).
cnf(c_0_1713,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1334,
[final] ).
cnf(c_0_1714,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
c_0_1335,
[final] ).
cnf(c_0_1715,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
c_0_1336,
[final] ).
cnf(c_0_1716,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
c_0_1337,
[final] ).
cnf(c_0_1717,plain,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat),
c_0_1338,
[final] ).
cnf(c_0_1718,plain,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
c_0_1339,
[final] ).
cnf(c_0_1719,plain,
c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X1),X2),c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_1340,
[final] ).
cnf(c_0_1720,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
c_0_1341,
[final] ).
cnf(c_0_1721,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1342,
[final] ).
cnf(c_0_1722,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
c_0_1343,
[final] ).
cnf(c_0_1723,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
c_0_1344,
[final] ).
cnf(c_0_1724,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
c_0_1345,
[final] ).
cnf(c_0_1725,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1346,
[final] ).
cnf(c_0_1726,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1347,
[final] ).
cnf(c_0_1727,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1348,
[final] ).
cnf(c_0_1728,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1349,
[final] ).
cnf(c_0_1729,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1350,
[final] ).
cnf(c_0_1730,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1351,
[final] ).
cnf(c_0_1731,plain,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1352,
[final] ).
cnf(c_0_1732,plain,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1353,
[final] ).
cnf(c_0_1733,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
c_0_1354,
[final] ).
cnf(c_0_1734,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1355,
[final] ).
cnf(c_0_1735,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1356,
[final] ).
cnf(c_0_1736,plain,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))
| ~ c_InductTermi_OIT(X1) ),
c_0_1357,
[final] ).
cnf(c_0_1737,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X1,X2)) = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1358,
[final] ).
cnf(c_0_1738,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
c_0_1359,
[final] ).
cnf(c_0_1739,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
c_0_1360,
[final] ).
cnf(c_0_1740,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1361,
[final] ).
cnf(c_0_1741,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
c_0_1362,
[final] ).
cnf(c_0_1742,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1363,
[final] ).
cnf(c_0_1743,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1364,
[final] ).
cnf(c_0_1744,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
c_0_1365,
[final] ).
cnf(c_0_1745,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
c_0_1366,
[final] ).
cnf(c_0_1746,plain,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
c_0_1367,
[final] ).
cnf(c_0_1747,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1368,
[final] ).
cnf(c_0_1748,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
c_0_1369,
[final] ).
cnf(c_0_1749,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1370,
[final] ).
cnf(c_0_1750,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1371,
[final] ).
cnf(c_0_1751,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1372,
[final] ).
cnf(c_0_1752,plain,
c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1373,
[final] ).
cnf(c_0_1753,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1374,
[final] ).
cnf(c_0_1754,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
c_0_1375,
[final] ).
cnf(c_0_1755,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1376,
[final] ).
cnf(c_0_1756,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1377,
[final] ).
cnf(c_0_1757,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
c_0_1378,
[final] ).
cnf(c_0_1758,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1379,
[final] ).
cnf(c_0_1759,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1380,
[final] ).
cnf(c_0_1760,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
c_0_1381,
[final] ).
cnf(c_0_1761,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
c_0_1382,
[final] ).
cnf(c_0_1762,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
c_0_1383,
[final] ).
cnf(c_0_1763,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1384,
[final] ).
cnf(c_0_1764,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1385,
[final] ).
cnf(c_0_1765,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1386,
[final] ).
cnf(c_0_1766,plain,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1387,
[final] ).
cnf(c_0_1767,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1388,
[final] ).
cnf(c_0_1768,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
c_0_1389,
[final] ).
cnf(c_0_1769,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1390,
[final] ).
cnf(c_0_1770,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1391,
[final] ).
cnf(c_0_1771,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1392,
[final] ).
cnf(c_0_1772,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1393,
[final] ).
cnf(c_0_1773,plain,
c_Lambda_OdB_OApp(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3)) = c_Lambda_Olift(c_Lambda_OdB_OApp(X1,X2),X3),
c_0_1394,
[final] ).
cnf(c_0_1774,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
c_0_1395,
[final] ).
cnf(c_0_1775,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
c_0_1396,
[final] ).
cnf(c_0_1776,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1397,
[final] ).
cnf(c_0_1777,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1398,
[final] ).
cnf(c_0_1778,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1399,
[final] ).
cnf(c_0_1779,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1400,
[final] ).
cnf(c_0_1780,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1401,
[final] ).
cnf(c_0_1781,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1402,
[final] ).
cnf(c_0_1782,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1403,
[final] ).
cnf(c_0_1783,plain,
( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X1)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1404,
[final] ).
cnf(c_0_1784,plain,
( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X1)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1405,
[final] ).
cnf(c_0_1785,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1406,
[final] ).
cnf(c_0_1786,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1407,
[final] ).
cnf(c_0_1787,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1408,
[final] ).
cnf(c_0_1788,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1409,
[final] ).
cnf(c_0_1789,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1410,
[final] ).
cnf(c_0_1790,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1411,
[final] ).
cnf(c_0_1791,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1412,
[final] ).
cnf(c_0_1792,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_1413,
[final] ).
cnf(c_0_1793,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_1414,
[final] ).
cnf(c_0_1794,plain,
( c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_1415,
[final] ).
cnf(c_0_1795,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
c_0_1416,
[final] ).
cnf(c_0_1796,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
c_0_1417,
[final] ).
cnf(c_0_1797,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1418,
[final] ).
cnf(c_0_1798,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1419,
[final] ).
cnf(c_0_1799,plain,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1420,
[final] ).
cnf(c_0_1800,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_1421,
[final] ).
cnf(c_0_1801,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_1422,
[final] ).
cnf(c_0_1802,plain,
c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
c_0_1423,
[final] ).
cnf(c_0_1803,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1424,
[final] ).
cnf(c_0_1804,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1425,
[final] ).
cnf(c_0_1805,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1426,
[final] ).
cnf(c_0_1806,plain,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1427,
[final] ).
cnf(c_0_1807,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1428,
[final] ).
cnf(c_0_1808,plain,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1429,
[final] ).
cnf(c_0_1809,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1430,
[final] ).
cnf(c_0_1810,plain,
( c_Lambda_Obeta(X1,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
c_0_1431,
[final] ).
cnf(c_0_1811,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1432,
[final] ).
cnf(c_0_1812,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
c_0_1433,
[final] ).
cnf(c_0_1813,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2) ),
c_0_1434,
[final] ).
cnf(c_0_1814,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
c_0_1435,
[final] ).
cnf(c_0_1815,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
c_0_1436,
[final] ).
cnf(c_0_1816,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_1437,
[final] ).
cnf(c_0_1817,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1438,
[final] ).
cnf(c_0_1818,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1439,
[final] ).
cnf(c_0_1819,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_1440,
[final] ).
cnf(c_0_1820,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
c_0_1441,
[final] ).
cnf(c_0_1821,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1442,
[final] ).
cnf(c_0_1822,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
c_0_1443,
[final] ).
cnf(c_0_1823,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1444,
[final] ).
cnf(c_0_1824,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1445,
[final] ).
cnf(c_0_1825,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1446,
[final] ).
cnf(c_0_1826,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_1447,
[final] ).
cnf(c_0_1827,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1448,
[final] ).
cnf(c_0_1828,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1449,
[final] ).
cnf(c_0_1829,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_1450,
[final] ).
cnf(c_0_1830,plain,
( c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)) = X2
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
c_0_1451,
[final] ).
cnf(c_0_1831,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
c_0_1452,
[final] ).
cnf(c_0_1832,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_1453,
[final] ).
cnf(c_0_1833,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_1454,
[final] ).
cnf(c_0_1834,plain,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
c_0_1455,
[final] ).
cnf(c_0_1835,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1456,
[final] ).
cnf(c_0_1836,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1457,
[final] ).
cnf(c_0_1837,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_1458,
[final] ).
cnf(c_0_1838,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_1459,
[final] ).
cnf(c_0_1839,plain,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
c_0_1460,
[final] ).
cnf(c_0_1840,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1461,
[final] ).
cnf(c_0_1841,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1462,
[final] ).
cnf(c_0_1842,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1463,
[final] ).
cnf(c_0_1843,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_1464,
[final] ).
cnf(c_0_1844,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
c_0_1465,
[final] ).
cnf(c_0_1845,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_1466,
[final] ).
cnf(c_0_1846,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_1467,
[final] ).
cnf(c_0_1847,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1468,
[final] ).
cnf(c_0_1848,plain,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
c_0_1469,
[final] ).
cnf(c_0_1849,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_1470,
[final] ).
cnf(c_0_1850,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
c_0_1471,
[final] ).
cnf(c_0_1851,plain,
( X1 = X2
| c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
c_0_1472,
[final] ).
cnf(c_0_1852,plain,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
c_0_1473,
[final] ).
cnf(c_0_1853,plain,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
c_0_1474,
[final] ).
cnf(c_0_1854,plain,
c_Lambda_OdB_OApp(X1,X2) != c_Lambda_OdB_OVar(X3),
c_0_1475,
[final] ).
cnf(c_0_1855,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OApp(X2,X3),
c_0_1476,
[final] ).
cnf(c_0_1856,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OApp(X2,X3),
c_0_1477,
[final] ).
cnf(c_0_1857,plain,
c_Lambda_OdB_OApp(X1,X2) != c_Lambda_OdB_OAbs(X3),
c_0_1478,
[final] ).
cnf(c_0_1858,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
c_0_1479,
[final] ).
cnf(c_0_1859,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
c_0_1480,
[final] ).
cnf(c_0_1860,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
c_0_1481,
[final] ).
cnf(c_0_1861,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
c_0_1482,
[final] ).
cnf(c_0_1862,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_1483,
[final] ).
cnf(c_0_1863,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_1484,
[final] ).
cnf(c_0_1864,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
c_0_1485,
[final] ).
cnf(c_0_1865,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
c_0_1486,
[final] ).
cnf(c_0_1866,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1487,
[final] ).
cnf(c_0_1867,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1488,
[final] ).
cnf(c_0_1868,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1489,
[final] ).
cnf(c_0_1869,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1490,
[final] ).
cnf(c_0_1870,plain,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X1)),
c_0_1491,
[final] ).
cnf(c_0_1871,plain,
c_Suc(X1) != X1,
c_0_1492,
[final] ).
cnf(c_0_1872,plain,
c_Suc(X1) != X1,
c_0_1493,
[final] ).
cnf(c_0_1873,plain,
class_Orderings_Oorder(tc_nat),
c_0_1494,
[final] ).
cnf(c_0_1874,plain,
class_Orderings_Olinorder(tc_nat),
c_0_1495,
[final] ).
cnf(c_0_1875,plain,
class_Orderings_Opreorder(tc_nat),
c_0_1496,
[final] ).
cnf(c_0_1876,plain,
class_Nat_Osemiring__char__0(tc_nat),
c_0_1497,
[final] ).
cnf(c_0_1877,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_1498,
[final] ).
cnf(c_0_1878,plain,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_1499,
[final] ).
cnf(c_0_1879,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_1500,
[final] ).
cnf(c_0_1880,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_1501,
[final] ).
cnf(c_0_1881,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_1502,
[final] ).
cnf(c_0_1882,plain,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_1503,
[final] ).
cnf(c_0_1883,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_1504,
[final] ).
cnf(c_0_1884,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_1505,
[final] ).
cnf(c_0_1885,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_1506,
[final] ).
cnf(c_0_1886,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_1507,
[final] ).
cnf(c_0_1887,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_1508,
[final] ).
cnf(c_0_1888,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_1509,
[final] ).
cnf(c_0_1889,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_1510,
[final] ).
cnf(c_0_1890,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_1511,
[final] ).
cnf(c_0_1891,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_1512,
[final] ).
cnf(c_0_1892,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_1513,
[final] ).
cnf(c_0_1893,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_1514,
[final] ).
cnf(c_0_1894,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_1515,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1516_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1516]) ).
cnf(c_0_1516_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1516]) ).
cnf(c_0_1516_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1516]) ).
cnf(c_0_1517_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1517]) ).
cnf(c_0_1517_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1517]) ).
cnf(c_0_1517_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1517]) ).
cnf(c_0_1518_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1518]) ).
cnf(c_0_1518_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1518]) ).
cnf(c_0_1518_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1518]) ).
cnf(c_0_1519_0,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1519]) ).
cnf(c_0_1519_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1519]) ).
cnf(c_0_1519_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1519]) ).
cnf(c_0_1520_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1520]) ).
cnf(c_0_1520_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1520]) ).
cnf(c_0_1521_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1521]) ).
cnf(c_0_1521_1,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1521]) ).
cnf(c_0_1522_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1522]) ).
cnf(c_0_1522_1,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1522]) ).
cnf(c_0_1523_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1523]) ).
cnf(c_0_1523_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1523]) ).
cnf(c_0_1524_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1524]) ).
cnf(c_0_1524_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1524]) ).
cnf(c_0_1524_2,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6 ),
inference(literals_permutation,[status(thm)],[c_0_1524]) ).
cnf(c_0_1525_0,axiom,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1525]) ).
cnf(c_0_1525_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1525]) ).
cnf(c_0_1525_2,axiom,
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1525]) ).
cnf(c_0_1526_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1526]) ).
cnf(c_0_1526_1,axiom,
( ~ class_Ring__and__Field_Osemiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1526]) ).
cnf(c_0_1527_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1527]) ).
cnf(c_0_1527_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1527]) ).
cnf(c_0_1527_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1527]) ).
cnf(c_0_1527_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1527]) ).
cnf(c_0_1527_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1527]) ).
cnf(c_0_1528_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1528]) ).
cnf(c_0_1528_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1528]) ).
cnf(c_0_1528_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1528]) ).
cnf(c_0_1528_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1528]) ).
cnf(c_0_1528_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1528]) ).
cnf(c_0_1530_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1530]) ).
cnf(c_0_1530_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1530]) ).
cnf(c_0_1530_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1530]) ).
cnf(c_0_1531_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1531]) ).
cnf(c_0_1531_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1531]) ).
cnf(c_0_1531_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1531]) ).
cnf(c_0_1532_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1532]) ).
cnf(c_0_1532_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1532]) ).
cnf(c_0_1533_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1533]) ).
cnf(c_0_1533_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1533]) ).
cnf(c_0_1534_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1534]) ).
cnf(c_0_1534_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1534]) ).
cnf(c_0_1534_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1534]) ).
cnf(c_0_1535_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1535]) ).
cnf(c_0_1535_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1535]) ).
cnf(c_0_1535_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1535]) ).
cnf(c_0_1536_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1536]) ).
cnf(c_0_1536_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1536]) ).
cnf(c_0_1536_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1536]) ).
cnf(c_0_1536_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1536]) ).
cnf(c_0_1537_0,axiom,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1537]) ).
cnf(c_0_1537_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1537]) ).
cnf(c_0_1537_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1537]) ).
cnf(c_0_1537_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1537]) ).
cnf(c_0_1538_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1538]) ).
cnf(c_0_1538_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1538]) ).
cnf(c_0_1538_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1538]) ).
cnf(c_0_1539_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1539]) ).
cnf(c_0_1539_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1539]) ).
cnf(c_0_1539_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1539]) ).
cnf(c_0_1539_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1539]) ).
cnf(c_0_1540_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1540]) ).
cnf(c_0_1540_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1540]) ).
cnf(c_0_1540_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1540]) ).
cnf(c_0_1540_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1540]) ).
cnf(c_0_1541_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1541]) ).
cnf(c_0_1541_1,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1541]) ).
cnf(c_0_1541_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1541]) ).
cnf(c_0_1542_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1542]) ).
cnf(c_0_1542_1,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1542]) ).
cnf(c_0_1542_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1542]) ).
cnf(c_0_1543_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1543]) ).
cnf(c_0_1543_1,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1543]) ).
cnf(c_0_1543_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1543]) ).
cnf(c_0_1543_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1543]) ).
cnf(c_0_1544_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1544]) ).
cnf(c_0_1544_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1544]) ).
cnf(c_0_1544_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1544]) ).
cnf(c_0_1544_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1544]) ).
cnf(c_0_1545_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1545]) ).
cnf(c_0_1545_1,axiom,
( c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1545]) ).
cnf(c_0_1545_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1545]) ).
cnf(c_0_1545_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1545]) ).
cnf(c_0_1546_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1546]) ).
cnf(c_0_1546_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1546]) ).
cnf(c_0_1546_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1546]) ).
cnf(c_0_1546_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1546]) ).
cnf(c_0_1547_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1547]) ).
cnf(c_0_1547_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1547]) ).
cnf(c_0_1548_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1548]) ).
cnf(c_0_1548_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1548]) ).
cnf(c_0_1549_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1549]) ).
cnf(c_0_1549_1,axiom,
( c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1549]) ).
cnf(c_0_1549_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1549]) ).
cnf(c_0_1549_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1549]) ).
cnf(c_0_1550_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1550_1,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1550_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1550_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1551_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1551_1,axiom,
( X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1551_2,axiom,
( c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1551_3,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1551_4,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1554_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1554]) ).
cnf(c_0_1554_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1554]) ).
cnf(c_0_1555_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1555]) ).
cnf(c_0_1555_1,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1555]) ).
cnf(c_0_1555_2,axiom,
( c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1555]) ).
cnf(c_0_1556_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1556]) ).
cnf(c_0_1556_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1556]) ).
cnf(c_0_1556_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1556]) ).
cnf(c_0_1557_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1557]) ).
cnf(c_0_1557_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1557]) ).
cnf(c_0_1557_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1557]) ).
cnf(c_0_1558_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1558]) ).
cnf(c_0_1558_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1558]) ).
cnf(c_0_1559_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1559]) ).
cnf(c_0_1559_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1559]) ).
cnf(c_0_1560_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1561_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1562_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1563_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_3,axiom,
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1564_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1565_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1566_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1567_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1568_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1569_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1570_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1571_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1572_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1573_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1574_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1575_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1576_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1577_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1578_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1579_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1580_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1581_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1582_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1583_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1584_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1585_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1586_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1587_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1588_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1589_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1594_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1595_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1595_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1596_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1596_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1596_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1597_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1597]) ).
cnf(c_0_1597_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1597]) ).
cnf(c_0_1597_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1597]) ).
cnf(c_0_1598_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1598]) ).
cnf(c_0_1598_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1598]) ).
cnf(c_0_1599_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1600_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1600_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1600_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1600_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1601_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1601_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1601_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1601_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1602_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1603_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1604_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1605_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1606_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1607_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1608_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1609_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1610_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1611_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1612_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1613_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1614_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1614_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1615_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1615_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1616_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1617_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1618_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1618_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1618_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1619_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1619_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1619_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1620_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1620_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1620_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1622_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1622_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1623_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1623_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1624_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1625_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1626_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1627_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1628_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1629_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1630_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1631_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1631]) ).
cnf(c_0_1631_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1631]) ).
cnf(c_0_1632_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1632_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1633_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1634_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1635_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1636_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1636_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1637_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1637_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1638_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1639_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_2,axiom,
( c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1640_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_2,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1651_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1651_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1652_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1652_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1653_0,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1653_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1654_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_1,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1655_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1656_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1657_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1657_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1657_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1658_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1659_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1659_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1663_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1663_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1663_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1664_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1664_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1665_0,axiom,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| X1 = X2
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_2,axiom,
( c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1666_0,axiom,
( c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1667_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1667_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1668_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1668_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1671_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1672_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1672_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1673_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1674_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1675_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1675_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1676_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1677_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1678_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1679_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1679_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1680_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1681_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1681_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1681_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1682_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1682_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1682_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1683_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1684_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1684_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1686_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_1,axiom,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat))
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1689_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1689_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1690_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1691_0,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1692_0,axiom,
( X1 = X2
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1692_1,axiom,
( c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1693_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1693_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1693_2,axiom,
( ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1693_3,axiom,
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1694_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1694_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1694_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1696_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1696_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1696_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1697_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1697_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1697_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1698_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_2,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1699_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_1,axiom,
( c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1700_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1700_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1700_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1701_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1702_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1703_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1704_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1705_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1705_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1706_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_2,axiom,
( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1707_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X1,X2),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_1,axiom,
( c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X1,X2),X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X1,X2),X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1708_0,axiom,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1708_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1708_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1709_0,axiom,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_2,axiom,
( c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1710_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_1,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1711_0,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1712_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1712_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1713_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1713_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1714_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1715_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1715_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1716_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1724_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1725_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1726_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1726_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1727_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1728_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1728_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1728_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1729_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1730_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1731_0,axiom,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1732_0,axiom,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_1,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1733_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1733_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1734_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1735_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1736_0,axiom,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))
| ~ c_InductTermi_OIT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_1,axiom,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1737_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X1,X2)) = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_1,axiom,
( c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X1,X2)) = X1
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X1,X2)) = X1
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1738_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_2,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1739_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_2,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1740_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1740_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1740_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1740_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1741_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_2,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1742_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1743_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1744_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1744_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1744_2,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1744_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1747_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1747_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1748_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1749_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1750_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1750_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1751_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1751_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1753_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1753_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1754_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1754_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1755_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1755_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1758_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1758_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1758_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1759_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1760_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_2,axiom,
( c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1761_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1762_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_3,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1763_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1763_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1763_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1764_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1764_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1764_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1765_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1765_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1765_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1765_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1766_0,axiom,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1766_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1767_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1767_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1767_2,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1767_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1768_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1768_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1769_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1769_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1769_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1770_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1770_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1770_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1771_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1772_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1776_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1776_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1776_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1777_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1777_1,axiom,
( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1778_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1778_1,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1779_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1779]) ).
cnf(c_0_1779_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1779]) ).
cnf(c_0_1779_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1779]) ).
cnf(c_0_1780_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1780_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1780_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1781_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1781_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1781_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1782_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1783_0,axiom,
( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X1)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1784_0,axiom,
( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X1)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1785_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1786_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1787_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1788_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1790_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1791_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1792_0,axiom,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1793_0,axiom,
( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1794_0,axiom,
( c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1795_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1796_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1803_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1804_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1804_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1804_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1809_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1809_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1809_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1810_0,axiom,
( c_Lambda_Obeta(X1,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1810_1,axiom,
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2)
| c_Lambda_Obeta(X1,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1811_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1812_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1812_1,axiom,
( ~ class_Ring__and__Field_Omult__zero(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1813_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1813_1,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1814_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1814_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1815_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1815_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1816_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1817_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1818_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1818_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1819_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1819_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1820_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1820_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1821_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1821_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1822_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1823_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1823_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1824_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1825_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1827_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1828_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1829_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1830_0,axiom,
( c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)) = X2
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_1,axiom,
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),X2)
| c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1831_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2)
| c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1836_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1836_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1848_0,axiom,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_1,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| X1 = X2
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_2,axiom,
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1849_0,axiom,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1850_0,axiom,
( X1 = X2
| c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_1,axiom,
( c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1851_0,axiom,
( X1 = X2
| c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1851_1,axiom,
( c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1852_0,axiom,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1852_1,axiom,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_Olift(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1858_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1858_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X1)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1859_0,axiom,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_1,axiom,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1860_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1860_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1861_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1861_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1862_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1863_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1669_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1670_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1789_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1797_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1798_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1800_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1801_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1853_0,axiom,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1854_0,axiom,
c_Lambda_OdB_OApp(X1,X2) != c_Lambda_OdB_OVar(X3),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1855_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OApp(X2,X3),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1856_0,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OApp(X2,X3),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1857_0,axiom,
c_Lambda_OdB_OApp(X1,X2) != c_Lambda_OdB_OAbs(X3),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1864_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1865_0,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1866_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1867_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1868_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1869_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1871_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1872_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1529_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1529]) ).
cnf(c_0_1552_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1552]) ).
cnf(c_0_1553_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1553]) ).
cnf(c_0_1590_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1591_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1592_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1593_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1621_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1641_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1642_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1643_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1644_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1645_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1646_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1647_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1648_0,axiom,
c_Lambda_OdB_OApp(c_Lambda_Osubstn(X1,X3,X4),c_Lambda_Osubstn(X2,X3,X4)) = c_Lambda_Osubstn(c_Lambda_OdB_OApp(X1,X2),X3,X4),
inference(literals_permutation,[status(thm)],[c_0_1648]) ).
cnf(c_0_1649_0,axiom,
c_Lambda_OdB_OApp(c_Lambda_Oliftn(X1,X2,X4),c_Lambda_Oliftn(X1,X3,X4)) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OApp(X2,X3),X4),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1650_0,axiom,
c_Lambda_OdB_OApp(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4)) = c_Lambda_Osubst(c_Lambda_OdB_OApp(X1,X2),X3,X4),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1660_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1661_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1662_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1685_0,axiom,
c_Lambda_Osubst(X1,c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3) = c_Lambda_Osubstn(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1687_0,axiom,
c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1688_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1695_0,axiom,
c_Lambda_Olift(c_Lambda_Oliftn(X1,X2,X3),X3) = c_Lambda_Oliftn(c_Suc(X1),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1717_0,axiom,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1718_0,axiom,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1719_0,axiom,
c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X1),X2),c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1720_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1721_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1722_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1723_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1745_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1745]) ).
cnf(c_0_1746_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1752_0,axiom,
c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1756_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1757_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1773_0,axiom,
c_Lambda_OdB_OApp(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3)) = c_Lambda_Olift(c_Lambda_OdB_OApp(X1,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1774_0,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1775_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1775]) ).
cnf(c_0_1799_0,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1802_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1805_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1806_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1807_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1808_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1808]) ).
cnf(c_0_1826_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1832_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1833_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1834_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1835_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1837_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1838_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1839_0,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1840_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1841_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1842_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1843_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1844_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1845_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1846_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1847_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1870_0,axiom,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X1)),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1873_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1874_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1875_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1876_0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1877_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1878_0,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1879_0,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1880_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1881_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1882_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1883_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1884_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1885_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1886_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1887_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1888_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1889_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1890_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1891_0,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1892_0,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1893_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1894_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_r,c_Lambda_OdB_OVar(v_i))),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_1_002,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
file('<stdin>',cls_conjecture_2) ).
fof(c_0_2_003,negated_conjecture,
c_InductTermi_OIT(v_r),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_3_004,negated_conjecture,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_r,c_Lambda_OdB_OVar(v_i))),
c_0_0 ).
fof(c_0_4_005,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_5_006,negated_conjecture,
c_InductTermi_OIT(v_r),
c_0_2 ).
fof(c_0_6_007,negated_conjecture,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_r,c_Lambda_OdB_OVar(v_i))),
c_0_3 ).
fof(c_0_7_008,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
c_0_4 ).
fof(c_0_8_009,negated_conjecture,
c_InductTermi_OIT(v_r),
c_0_5 ).
cnf(c_0_9_010,negated_conjecture,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_r,c_Lambda_OdB_OVar(v_i))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10_011,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11_012,negated_conjecture,
c_InductTermi_OIT(v_r),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12_013,negated_conjecture,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_r,c_Lambda_OdB_OVar(v_i))),
c_0_9,
[final] ).
cnf(c_0_13_014,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
c_0_10,
[final] ).
cnf(c_0_14_015,negated_conjecture,
c_InductTermi_OIT(v_r),
c_0_11,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_845,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
file('/export/starexec/sandbox/tmp/iprover_modulo_5c69df.p',c_0_13) ).
cnf(c_1092,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
inference(copy,[status(esa)],[c_845]) ).
cnf(c_1104,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
inference(copy,[status(esa)],[c_1092]) ).
cnf(c_1109,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
inference(copy,[status(esa)],[c_1104]) ).
cnf(c_1110,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
inference(copy,[status(esa)],[c_1109]) ).
cnf(c_3607,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
inference(copy,[status(esa)],[c_1110]) ).
cnf(c_22,plain,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X0)),
file('/export/starexec/sandbox/tmp/iprover_modulo_5c69df.p',c_0_1870_0) ).
cnf(c_2005,plain,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X0)),
inference(copy,[status(esa)],[c_22]) ).
cnf(c_3622,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3607,c_2005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL774-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 19:25:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.18/0.44 % Orienting using strategy Equiv(ClausalAll)
% 0.18/0.44 % Orientation found
% 0.18/0.44 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0cf017.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_5c69df.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_81743a | grep -v "SZS"
% 0.18/0.46
% 0.18/0.46 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.18/0.46
% 0.18/0.46 %
% 0.18/0.46 % ------ iProver source info
% 0.18/0.46
% 0.18/0.46 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.18/0.46 % git: non_committed_changes: true
% 0.18/0.46 % git: last_make_outside_of_git: true
% 0.18/0.46
% 0.18/0.46 %
% 0.18/0.46 % ------ Input Options
% 0.18/0.46
% 0.18/0.46 % --out_options all
% 0.18/0.46 % --tptp_safe_out true
% 0.18/0.46 % --problem_path ""
% 0.18/0.46 % --include_path ""
% 0.18/0.46 % --clausifier .//eprover
% 0.18/0.46 % --clausifier_options --tstp-format
% 0.18/0.46 % --stdin false
% 0.18/0.46 % --dbg_backtrace false
% 0.18/0.46 % --dbg_dump_prop_clauses false
% 0.18/0.46 % --dbg_dump_prop_clauses_file -
% 0.18/0.46 % --dbg_out_stat false
% 0.18/0.46
% 0.18/0.46 % ------ General Options
% 0.18/0.46
% 0.18/0.46 % --fof false
% 0.18/0.46 % --time_out_real 150.
% 0.18/0.46 % --time_out_prep_mult 0.2
% 0.18/0.46 % --time_out_virtual -1.
% 0.18/0.46 % --schedule none
% 0.18/0.46 % --ground_splitting input
% 0.18/0.46 % --splitting_nvd 16
% 0.18/0.46 % --non_eq_to_eq false
% 0.18/0.46 % --prep_gs_sim true
% 0.18/0.46 % --prep_unflatten false
% 0.18/0.46 % --prep_res_sim true
% 0.18/0.46 % --prep_upred true
% 0.18/0.46 % --res_sim_input true
% 0.18/0.46 % --clause_weak_htbl true
% 0.18/0.46 % --gc_record_bc_elim false
% 0.18/0.46 % --symbol_type_check false
% 0.18/0.46 % --clausify_out false
% 0.18/0.46 % --large_theory_mode false
% 0.18/0.46 % --prep_sem_filter none
% 0.18/0.46 % --prep_sem_filter_out false
% 0.18/0.46 % --preprocessed_out false
% 0.18/0.46 % --sub_typing false
% 0.18/0.46 % --brand_transform false
% 0.18/0.46 % --pure_diseq_elim true
% 0.18/0.46 % --min_unsat_core false
% 0.18/0.46 % --pred_elim true
% 0.18/0.46 % --add_important_lit false
% 0.18/0.46 % --soft_assumptions false
% 0.18/0.46 % --reset_solvers false
% 0.18/0.46 % --bc_imp_inh []
% 0.18/0.46 % --conj_cone_tolerance 1.5
% 0.18/0.46 % --prolific_symb_bound 500
% 0.18/0.46 % --lt_threshold 2000
% 0.18/0.46
% 0.18/0.46 % ------ SAT Options
% 0.18/0.46
% 0.18/0.46 % --sat_mode false
% 0.18/0.46 % --sat_fm_restart_options ""
% 0.18/0.46 % --sat_gr_def false
% 0.18/0.46 % --sat_epr_types true
% 0.18/0.46 % --sat_non_cyclic_types false
% 0.18/0.46 % --sat_finite_models false
% 0.18/0.46 % --sat_fm_lemmas false
% 0.18/0.46 % --sat_fm_prep false
% 0.18/0.46 % --sat_fm_uc_incr true
% 0.18/0.46 % --sat_out_model small
% 0.18/0.46 % --sat_out_clauses false
% 0.18/0.46
% 0.18/0.46 % ------ QBF Options
% 0.18/0.46
% 0.18/0.46 % --qbf_mode false
% 0.18/0.46 % --qbf_elim_univ true
% 0.18/0.46 % --qbf_sk_in true
% 0.18/0.46 % --qbf_pred_elim true
% 0.18/0.46 % --qbf_split 32
% 0.18/0.46
% 0.18/0.46 % ------ BMC1 Options
% 0.18/0.46
% 0.18/0.46 % --bmc1_incremental false
% 0.18/0.46 % --bmc1_axioms reachable_all
% 0.18/0.46 % --bmc1_min_bound 0
% 0.18/0.46 % --bmc1_max_bound -1
% 0.18/0.46 % --bmc1_max_bound_default -1
% 0.18/0.46 % --bmc1_symbol_reachability true
% 0.18/0.46 % --bmc1_property_lemmas false
% 0.18/0.46 % --bmc1_k_induction false
% 0.18/0.46 % --bmc1_non_equiv_states false
% 0.18/0.46 % --bmc1_deadlock false
% 0.18/0.46 % --bmc1_ucm false
% 0.18/0.46 % --bmc1_add_unsat_core none
% 0.18/0.46 % --bmc1_unsat_core_children false
% 0.18/0.46 % --bmc1_unsat_core_extrapolate_axioms false
% 0.18/0.46 % --bmc1_out_stat full
% 0.18/0.46 % --bmc1_ground_init false
% 0.18/0.46 % --bmc1_pre_inst_next_state false
% 0.18/0.46 % --bmc1_pre_inst_state false
% 0.18/0.46 % --bmc1_pre_inst_reach_state false
% 0.18/0.46 % --bmc1_out_unsat_core false
% 0.18/0.46 % --bmc1_aig_witness_out false
% 0.18/0.46 % --bmc1_verbose false
% 0.18/0.46 % --bmc1_dump_clauses_tptp false
% 150.24/150.46 % --bmc1_dump_unsat_core_tptp false
% 150.24/150.46 % --bmc1_dump_file -
% 150.24/150.46 % --bmc1_ucm_expand_uc_limit 128
% 150.24/150.46 % --bmc1_ucm_n_expand_iterations 6
% 150.24/150.46 % --bmc1_ucm_extend_mode 1
% 150.24/150.46 % --bmc1_ucm_init_mode 2
% 150.24/150.46 % --bmc1_ucm_cone_mode none
% 150.24/150.46 % --bmc1_ucm_reduced_relation_type 0
% 150.24/150.46 % --bmc1_ucm_relax_model 4
% 150.24/150.46 % --bmc1_ucm_full_tr_after_sat true
% 150.24/150.46 % --bmc1_ucm_expand_neg_assumptions false
% 150.24/150.46 % --bmc1_ucm_layered_model none
% 150.24/150.46 % --bmc1_ucm_max_lemma_size 10
% 150.24/150.46
% 150.24/150.46 % ------ AIG Options
% 150.24/150.46
% 150.24/150.46 % --aig_mode false
% 150.24/150.46
% 150.24/150.46 % ------ Instantiation Options
% 150.24/150.46
% 150.24/150.46 % --instantiation_flag true
% 150.24/150.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.24/150.46 % --inst_solver_per_active 750
% 150.24/150.46 % --inst_solver_calls_frac 0.5
% 150.24/150.46 % --inst_passive_queue_type priority_queues
% 150.24/150.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.24/150.46 % --inst_passive_queues_freq [25;2]
% 150.24/150.46 % --inst_dismatching true
% 150.24/150.46 % --inst_eager_unprocessed_to_passive true
% 150.24/150.46 % --inst_prop_sim_given true
% 150.24/150.46 % --inst_prop_sim_new false
% 150.24/150.46 % --inst_orphan_elimination true
% 150.24/150.46 % --inst_learning_loop_flag true
% 150.24/150.46 % --inst_learning_start 3000
% 150.24/150.46 % --inst_learning_factor 2
% 150.24/150.46 % --inst_start_prop_sim_after_learn 3
% 150.24/150.46 % --inst_sel_renew solver
% 150.24/150.46 % --inst_lit_activity_flag true
% 150.24/150.46 % --inst_out_proof true
% 150.24/150.46
% 150.24/150.46 % ------ Resolution Options
% 150.24/150.46
% 150.24/150.46 % --resolution_flag true
% 150.24/150.46 % --res_lit_sel kbo_max
% 150.24/150.46 % --res_to_prop_solver none
% 150.24/150.46 % --res_prop_simpl_new false
% 150.24/150.46 % --res_prop_simpl_given false
% 150.24/150.46 % --res_passive_queue_type priority_queues
% 150.24/150.46 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.24/150.46 % --res_passive_queues_freq [15;5]
% 150.24/150.46 % --res_forward_subs full
% 150.24/150.46 % --res_backward_subs full
% 150.24/150.46 % --res_forward_subs_resolution true
% 150.24/150.46 % --res_backward_subs_resolution true
% 150.24/150.46 % --res_orphan_elimination false
% 150.24/150.46 % --res_time_limit 1000.
% 150.24/150.46 % --res_out_proof true
% 150.24/150.46 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0cf017.s
% 150.24/150.46 % --modulo true
% 150.24/150.46
% 150.24/150.46 % ------ Combination Options
% 150.24/150.46
% 150.24/150.46 % --comb_res_mult 1000
% 150.24/150.46 % --comb_inst_mult 300
% 150.24/150.46 % ------
% 150.24/150.46
% 150.24/150.46 % ------ Parsing...% successful
% 150.24/150.46
% 150.24/150.46 % ------ 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 %
% 150.24/150.46
% 150.24/150.46 % ------ Proving...
% 150.24/150.46 % ------ Problem Properties
% 150.24/150.46
% 150.24/150.46 %
% 150.24/150.46 % EPR false
% 150.24/150.46 % Horn false
% 150.24/150.46 % Has equality true
% 150.24/150.46
% 150.24/150.46 % % ------ Input Options Time Limit: Unbounded
% 150.24/150.46
% 150.24/150.46
% 150.24/150.46 Compiling...
% 150.24/150.46 Loading plugin: done.
% 150.24/150.46 %
% 150.24/150.46
% 150.24/150.46
% 150.24/150.46 % Time Out Real
% 150.24/150.46
% 150.24/150.46 % ------ Statistics
% 150.24/150.46
% 150.24/150.46 % ------ General
% 150.24/150.46
% 150.24/150.46 % num_of_input_clauses: 848
% 150.24/150.46 % num_of_input_neg_conjectures: 3
% 150.24/150.46 % num_of_splits: 0
% 150.24/150.46 % num_of_split_atoms: 0
% 150.24/150.46 % num_of_sem_filtered_clauses: 0
% 150.24/150.46 % num_of_subtypes: 0
% 150.24/150.46 % monotx_restored_types: 0
% 150.24/150.46 % sat_num_of_epr_types: 0
% 150.24/150.46 % sat_num_of_non_cyclic_types: 0
% 150.24/150.46 % sat_guarded_non_collapsed_types: 0
% 150.24/150.46 % is_epr: 0
% 150.24/150.46 % is_horn: 0
% 150.24/150.46 % has_eq: 1
% 150.24/150.46 % num_pure_diseq_elim: 0
% 150.24/150.46 % simp_replaced_by: 0
% 150.24/150.46 % res_preprocessed: 6
% 150.24/150.46 % prep_upred: 0
% 150.24/150.46 % prep_unflattend: 0
% 150.24/150.46 % pred_elim_cands: 0
% 150.24/150.46 % pred_elim: 0
% 150.24/150.46 % pred_elim_cl: 0
% 150.24/150.46 % pred_elim_cycles: 0
% 150.24/150.46 % forced_gc_time: 0
% 150.24/150.46 % gc_basic_clause_elim: 0
% 150.24/150.46 % parsing_time: 0.029
% 150.24/150.46 % sem_filter_time: 0.
% 150.24/150.46 % pred_elim_time: 0.
% 150.24/150.46 % out_proof_time: 0.
% 150.24/150.46 % monotx_time: 0.
% 150.24/150.46 % subtype_inf_time: 0.
% 150.24/150.46 % unif_index_cands_time: 0.
% 150.24/150.46 % unif_index_add_time: 0.
% 150.24/150.46 % total_time: 150.011
% 150.24/150.46 % num_of_symbols: 82
% 150.24/150.46 % num_of_terms: 2239
% 150.24/150.46
% 150.24/150.46 % ------ Propositional Solver
% 150.24/150.46
% 150.24/150.46 % prop_solver_calls: 1
% 150.24/150.46 % prop_fast_solver_calls: 9
% 150.24/150.46 % prop_num_of_clauses: 733
% 150.24/150.46 % prop_preprocess_simplified: 2617
% 150.24/150.46 % prop_fo_subsumed: 0
% 150.24/150.46 % prop_solver_time: 0.
% 150.24/150.46 % prop_fast_solver_time: 0.
% 150.24/150.46 % prop_unsat_core_time: 0.
% 150.24/150.46
% 150.24/150.46 % ------ QBF
% 150.24/150.46
% 150.24/150.46 % qbf_q_res: 0
% 150.24/150.46 % qbf_num_tautologies: 0
% 150.24/150.46 % qbf_prep_cycles: 0
% 150.24/150.46
% 150.24/150.46 % ------ BMC1
% 150.24/150.46
% 150.24/150.46 % bmc1_current_bound: -1
% 150.24/150.46 % bmc1_last_solved_bound: -1
% 150.24/150.46 % bmc1_unsat_core_size: -1
% 150.24/150.46 % bmc1_unsat_core_parents_size: -1
% 150.24/150.46 % bmc1_merge_next_fun: 0
% 150.24/150.46 % bmc1_unsat_core_clauses_time: 0.
% 150.24/150.46
% 150.24/150.46 % ------ Instantiation
% 150.24/150.46
% 150.24/150.46 % inst_num_of_clauses: 750
% 150.24/150.46 % inst_num_in_passive: 0
% 150.24/150.46 % inst_num_in_active: 0
% 150.24/150.46 % inst_num_in_unprocessed: 848
% 150.24/150.46 % inst_num_of_loops: 0
% 150.24/150.46 % inst_num_of_learning_restarts: 0
% 150.24/150.46 % inst_num_moves_active_passive: 0
% 150.24/150.46 % inst_lit_activity: 0
% 150.24/150.46 % inst_lit_activity_moves: 0
% 150.24/150.46 % inst_num_tautologies: 0
% 150.24/150.46 % inst_num_prop_implied: 0
% 150.24/150.46 % inst_num_existing_simplified: 0
% 150.24/150.46 % inst_num_eq_res_simplified: 0
% 150.24/150.46 % inst_num_child_elim: 0
% 150.24/150.46 % inst_num_of_dismatching_blockings: 0
% 150.24/150.46 % inst_num_of_non_proper_insts: 0
% 150.24/150.46 % inst_num_of_duplicates: 0
% 150.24/150.46 % inst_inst_num_from_inst_to_res: 0
% 150.24/150.46 % inst_dismatching_checking_time: 0.
% 150.24/150.46
% 150.24/150.46 % ------ Resolution
% 150.24/150.46
% 150.24/150.46 % res_num_of_clauses: 732
% 150.24/150.46 % res_num_in_passive: 0
% 150.24/150.46 % res_num_in_active: 271
% 150.24/150.46 % res_num_of_loops: 0
% 150.24/150.46 % res_forward_subset_subsumed: 470
% 150.24/150.46 % res_backward_subset_subsumed: 0
% 150.24/150.46 % res_forward_subsumed: 0
% 150.24/150.46 % res_backward_subsumed: 0
% 150.24/150.46 % res_forward_subsumption_resolution: 0
% 150.24/150.46 % res_backward_subsumption_resolution: 0
% 150.24/150.46 % res_clause_to_clause_subsumption: 0
% 150.24/150.46 % res_orphan_elimination: 0
% 150.24/150.46 % res_tautology_del: 0
% 150.24/150.46 % res_num_eq_res_simplified: 0
% 150.24/150.46 % res_num_sel_changes: 0
% 150.24/150.46 % res_moves_from_active_to_pass: 0
% 150.24/150.46
% 150.24/150.46 % Status Unknown
% 150.32/150.54 % Orienting using strategy ClausalAll
% 150.32/150.54 % Orientation found
% 150.32/150.54 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0cf017.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_5c69df.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_0d8c5b | grep -v "SZS"
% 150.32/150.55
% 150.32/150.55 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.32/150.55
% 150.32/150.55 %
% 150.32/150.55 % ------ iProver source info
% 150.32/150.55
% 150.32/150.55 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.32/150.55 % git: non_committed_changes: true
% 150.32/150.55 % git: last_make_outside_of_git: true
% 150.32/150.55
% 150.32/150.55 %
% 150.32/150.55 % ------ Input Options
% 150.32/150.55
% 150.32/150.55 % --out_options all
% 150.32/150.55 % --tptp_safe_out true
% 150.32/150.55 % --problem_path ""
% 150.32/150.55 % --include_path ""
% 150.32/150.55 % --clausifier .//eprover
% 150.32/150.55 % --clausifier_options --tstp-format
% 150.32/150.55 % --stdin false
% 150.32/150.55 % --dbg_backtrace false
% 150.32/150.55 % --dbg_dump_prop_clauses false
% 150.32/150.55 % --dbg_dump_prop_clauses_file -
% 150.32/150.55 % --dbg_out_stat false
% 150.32/150.55
% 150.32/150.55 % ------ General Options
% 150.32/150.55
% 150.32/150.55 % --fof false
% 150.32/150.55 % --time_out_real 150.
% 150.32/150.55 % --time_out_prep_mult 0.2
% 150.32/150.55 % --time_out_virtual -1.
% 150.32/150.55 % --schedule none
% 150.32/150.55 % --ground_splitting input
% 150.32/150.55 % --splitting_nvd 16
% 150.32/150.55 % --non_eq_to_eq false
% 150.32/150.55 % --prep_gs_sim true
% 150.32/150.55 % --prep_unflatten false
% 150.32/150.55 % --prep_res_sim true
% 150.32/150.55 % --prep_upred true
% 150.32/150.55 % --res_sim_input true
% 150.32/150.55 % --clause_weak_htbl true
% 150.32/150.55 % --gc_record_bc_elim false
% 150.32/150.55 % --symbol_type_check false
% 150.32/150.55 % --clausify_out false
% 150.32/150.55 % --large_theory_mode false
% 150.32/150.55 % --prep_sem_filter none
% 150.32/150.55 % --prep_sem_filter_out false
% 150.32/150.55 % --preprocessed_out false
% 150.32/150.55 % --sub_typing false
% 150.32/150.55 % --brand_transform false
% 150.32/150.55 % --pure_diseq_elim true
% 150.32/150.55 % --min_unsat_core false
% 150.32/150.55 % --pred_elim true
% 150.32/150.55 % --add_important_lit false
% 150.32/150.55 % --soft_assumptions false
% 150.32/150.55 % --reset_solvers false
% 150.32/150.55 % --bc_imp_inh []
% 150.32/150.55 % --conj_cone_tolerance 1.5
% 150.32/150.55 % --prolific_symb_bound 500
% 150.32/150.55 % --lt_threshold 2000
% 150.32/150.55
% 150.32/150.55 % ------ SAT Options
% 150.32/150.55
% 150.32/150.55 % --sat_mode false
% 150.32/150.55 % --sat_fm_restart_options ""
% 150.32/150.55 % --sat_gr_def false
% 150.32/150.55 % --sat_epr_types true
% 150.32/150.55 % --sat_non_cyclic_types false
% 150.32/150.55 % --sat_finite_models false
% 150.32/150.55 % --sat_fm_lemmas false
% 150.32/150.55 % --sat_fm_prep false
% 150.32/150.55 % --sat_fm_uc_incr true
% 150.32/150.55 % --sat_out_model small
% 150.32/150.55 % --sat_out_clauses false
% 150.32/150.55
% 150.32/150.55 % ------ QBF Options
% 150.32/150.55
% 150.32/150.55 % --qbf_mode false
% 150.32/150.55 % --qbf_elim_univ true
% 150.32/150.55 % --qbf_sk_in true
% 150.32/150.55 % --qbf_pred_elim true
% 150.32/150.55 % --qbf_split 32
% 150.32/150.55
% 150.32/150.55 % ------ BMC1 Options
% 150.32/150.56
% 150.32/150.56 % --bmc1_incremental false
% 150.32/150.56 % --bmc1_axioms reachable_all
% 150.32/150.56 % --bmc1_min_bound 0
% 150.32/150.56 % --bmc1_max_bound -1
% 150.32/150.56 % --bmc1_max_bound_default -1
% 150.32/150.56 % --bmc1_symbol_reachability true
% 150.32/150.56 % --bmc1_property_lemmas false
% 150.32/150.56 % --bmc1_k_induction false
% 150.32/150.56 % --bmc1_non_equiv_states false
% 150.32/150.56 % --bmc1_deadlock false
% 150.32/150.56 % --bmc1_ucm false
% 150.32/150.56 % --bmc1_add_unsat_core none
% 150.32/150.56 % --bmc1_unsat_core_children false
% 150.32/150.56 % --bmc1_unsat_core_extrapolate_axioms false
% 150.32/150.56 % --bmc1_out_stat full
% 150.32/150.56 % --bmc1_ground_init false
% 150.32/150.56 % --bmc1_pre_inst_next_state false
% 150.32/150.56 % --bmc1_pre_inst_state false
% 150.32/150.56 % --bmc1_pre_inst_reach_state false
% 150.32/150.56 % --bmc1_out_unsat_core false
% 150.32/150.56 % --bmc1_aig_witness_out false
% 150.32/150.56 % --bmc1_verbose false
% 150.32/150.56 % --bmc1_dump_clauses_tptp false
% 151.69/152.10 % --bmc1_dump_unsat_core_tptp false
% 151.69/152.10 % --bmc1_dump_file -
% 151.69/152.10 % --bmc1_ucm_expand_uc_limit 128
% 151.69/152.10 % --bmc1_ucm_n_expand_iterations 6
% 151.69/152.10 % --bmc1_ucm_extend_mode 1
% 151.69/152.10 % --bmc1_ucm_init_mode 2
% 151.69/152.10 % --bmc1_ucm_cone_mode none
% 151.69/152.10 % --bmc1_ucm_reduced_relation_type 0
% 151.69/152.10 % --bmc1_ucm_relax_model 4
% 151.69/152.10 % --bmc1_ucm_full_tr_after_sat true
% 151.69/152.10 % --bmc1_ucm_expand_neg_assumptions false
% 151.69/152.10 % --bmc1_ucm_layered_model none
% 151.69/152.10 % --bmc1_ucm_max_lemma_size 10
% 151.69/152.10
% 151.69/152.10 % ------ AIG Options
% 151.69/152.10
% 151.69/152.10 % --aig_mode false
% 151.69/152.10
% 151.69/152.10 % ------ Instantiation Options
% 151.69/152.10
% 151.69/152.10 % --instantiation_flag true
% 151.69/152.10 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 151.69/152.10 % --inst_solver_per_active 750
% 151.69/152.10 % --inst_solver_calls_frac 0.5
% 151.69/152.10 % --inst_passive_queue_type priority_queues
% 151.69/152.10 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 151.69/152.10 % --inst_passive_queues_freq [25;2]
% 151.69/152.10 % --inst_dismatching true
% 151.69/152.10 % --inst_eager_unprocessed_to_passive true
% 151.69/152.10 % --inst_prop_sim_given true
% 151.69/152.10 % --inst_prop_sim_new false
% 151.69/152.10 % --inst_orphan_elimination true
% 151.69/152.10 % --inst_learning_loop_flag true
% 151.69/152.10 % --inst_learning_start 3000
% 151.69/152.10 % --inst_learning_factor 2
% 151.69/152.10 % --inst_start_prop_sim_after_learn 3
% 151.69/152.10 % --inst_sel_renew solver
% 151.69/152.10 % --inst_lit_activity_flag true
% 151.69/152.10 % --inst_out_proof true
% 151.69/152.10
% 151.69/152.10 % ------ Resolution Options
% 151.69/152.10
% 151.69/152.10 % --resolution_flag true
% 151.69/152.10 % --res_lit_sel kbo_max
% 151.69/152.10 % --res_to_prop_solver none
% 151.69/152.10 % --res_prop_simpl_new false
% 151.69/152.10 % --res_prop_simpl_given false
% 151.69/152.10 % --res_passive_queue_type priority_queues
% 151.69/152.10 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 151.69/152.10 % --res_passive_queues_freq [15;5]
% 151.69/152.10 % --res_forward_subs full
% 151.69/152.10 % --res_backward_subs full
% 151.69/152.10 % --res_forward_subs_resolution true
% 151.69/152.10 % --res_backward_subs_resolution true
% 151.69/152.10 % --res_orphan_elimination false
% 151.69/152.10 % --res_time_limit 1000.
% 151.69/152.10 % --res_out_proof true
% 151.69/152.10 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0cf017.s
% 151.69/152.10 % --modulo true
% 151.69/152.10
% 151.69/152.10 % ------ Combination Options
% 151.69/152.10
% 151.69/152.10 % --comb_res_mult 1000
% 151.69/152.10 % --comb_inst_mult 300
% 151.69/152.10 % ------
% 151.69/152.10
% 151.69/152.10 % ------ Parsing...% successful
% 151.69/152.10
% 151.69/152.10 % ------ 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 %
% 151.69/152.10
% 151.69/152.10 % ------ Proving...
% 151.69/152.10 % ------ Problem Properties
% 151.69/152.10
% 151.69/152.10 %
% 151.69/152.10 % EPR false
% 151.69/152.10 % Horn false
% 151.69/152.10 % Has equality true
% 151.69/152.10
% 151.69/152.10 % % ------ Input Options Time Limit: Unbounded
% 151.69/152.10
% 151.69/152.10
% 151.69/152.10 Compiling...
% 151.69/152.10 Loading plugin: done.
% 151.69/152.10 Compiling...
% 151.69/152.10 Loading plugin: done.
% 151.69/152.10 Compiling...
% 151.69/152.10 Loading plugin: done.
% 151.69/152.10 Compiling...
% 151.69/152.10 Loading plugin: done.
% 151.69/152.10 Compiling...
% 151.69/152.10 Loading plugin: done.
% 151.69/152.10 Compiling...
% 151.69/152.10 Loading plugin: done.
% 151.69/152.10 Compiling...
% 151.69/152.10 Loading plugin: done.
% 151.69/152.10 Compiling...
% 151.69/152.10 Loading plugin: done.
% 151.69/152.10 Compiling...
% 151.69/152.10 Loading plugin: done.
% 151.69/152.10 Compiling...
% 151.69/152.10 Loading plugin: done.
% 151.69/152.10 % % ------ Current options:
% 151.69/152.10
% 151.69/152.10 % ------ Input Options
% 151.69/152.10
% 151.69/152.10 % --out_options all
% 151.69/152.10 % --tptp_safe_out true
% 151.69/152.10 % --problem_path ""
% 151.69/152.10 % --include_path ""
% 151.69/152.10 % --clausifier .//eprover
% 151.69/152.10 % --clausifier_options --tstp-format
% 151.69/152.10 % --stdin false
% 151.69/152.10 % --dbg_backtrace false
% 151.69/152.10 % --dbg_dump_prop_clauses false
% 151.69/152.10 % --dbg_dump_prop_clauses_file -
% 151.69/152.10 % --dbg_out_stat false
% 151.69/152.10
% 151.69/152.10 % ------ General Options
% 151.69/152.10
% 151.69/152.10 % --fof false
% 151.69/152.10 % --time_out_real 150.
% 151.69/152.10 % --time_out_prep_mult 0.2
% 151.69/152.10 % --time_out_virtual -1.
% 151.69/152.10 % --schedule none
% 151.69/152.10 % --ground_splitting input
% 151.69/152.10 % --splitting_nvd 16
% 151.69/152.10 % --non_eq_to_eq false
% 151.69/152.10 % --prep_gs_sim true
% 151.69/152.10 % --prep_unflatten false
% 151.69/152.10 % --prep_res_sim true
% 151.69/152.10 % --prep_upred true
% 151.69/152.10 % --res_sim_input true
% 151.69/152.10 % --clause_weak_htbl true
% 151.69/152.10 % --gc_record_bc_elim false
% 151.69/152.10 % --symbol_type_check false
% 151.69/152.10 % --clausify_out false
% 151.69/152.10 % --large_theory_mode false
% 151.69/152.10 % --prep_sem_filter none
% 151.69/152.10 % --prep_sem_filter_out false
% 151.69/152.10 % --preprocessed_out false
% 151.69/152.10 % --sub_typing false
% 151.69/152.10 % --brand_transform false
% 151.69/152.10 % --pure_diseq_elim true
% 151.69/152.10 % --min_unsat_core false
% 151.69/152.11 % --pred_elim true
% 151.69/152.11 % --add_important_lit false
% 151.69/152.11 % --soft_assumptions false
% 151.69/152.11 % --reset_solvers false
% 151.69/152.11 % --bc_imp_inh []
% 151.69/152.11 % --conj_cone_tolerance 1.5
% 151.69/152.11 % --prolific_symb_bound 500
% 151.69/152.11 % --lt_threshold 2000
% 151.69/152.11
% 151.69/152.11 % ------ SAT Options
% 151.69/152.11
% 151.69/152.11 % --sat_mode false
% 151.69/152.11 % --sat_fm_restart_options ""
% 151.69/152.11 % --sat_gr_def false
% 151.69/152.11 % --sat_epr_types true
% 151.69/152.11 % --sat_non_cyclic_types false
% 151.69/152.11 % --sat_finite_models false
% 151.69/152.11 % --sat_fm_lemmas false
% 151.69/152.11 % --sat_fm_prep false
% 151.69/152.11 % --sat_fm_uc_incr true
% 151.69/152.11 % --sat_out_model small
% 151.69/152.11 % --sat_out_clauses false
% 151.69/152.11
% 151.69/152.11 % ------ QBF Options
% 151.69/152.11
% 151.69/152.11 % --qbf_mode false
% 151.69/152.11 % --qbf_elim_univ true
% 151.69/152.11 % --qbf_sk_in true
% 151.69/152.11 % --qbf_pred_elim true
% 151.69/152.11 % --qbf_split 32
% 151.69/152.11
% 151.69/152.11 % ------ BMC1 Options
% 151.69/152.11
% 151.69/152.11 % --bmc1_incremental false
% 151.69/152.11 % --bmc1_axioms reachable_all
% 151.69/152.11 % --bmc1_min_bound 0
% 151.69/152.11 % --bmc1_max_bound -1
% 151.69/152.11 % --bmc1_max_bound_default -1
% 151.69/152.11 % --bmc1_symbol_reachability true
% 151.69/152.11 % --bmc1_property_lemmas false
% 151.69/152.11 % --bmc1_k_induction false
% 151.69/152.11 % --bmc1_non_equiv_states false
% 151.69/152.11 % --bmc1_deadlock false
% 151.69/152.11 % --bmc1_ucm false
% 151.69/152.11 % --bmc1_add_unsat_core none
% 151.69/152.11 % --bmc1_unsat_core_children false
% 151.69/152.11 % --bmc1_unsat_core_extrapolate_axioms false
% 151.69/152.11 % --bmc1_out_stat full
% 151.69/152.11 % --bmc1_ground_init false
% 151.69/152.11 % --bmc1_pre_inst_next_state false
% 151.69/152.11 % --bmc1_pre_inst_state false
% 151.69/152.11 % --bmc1_pre_inst_reach_state false
% 151.69/152.11 % --bmc1_out_unsat_core false
% 151.69/152.11 % --bmc1_aig_witness_out false
% 151.69/152.11 % --bmc1_verbose false
% 151.69/152.11 % --bmc1_dump_clauses_tptp false
% 151.69/152.11 % --bmc1_dump_unsat_core_tptp false
% 151.69/152.11 % --bmc1_dump_file -
% 151.69/152.11 % --bmc1_ucm_expand_uc_limit 128
% 151.69/152.11 % --bmc1_ucm_n_expand_iterations 6
% 151.69/152.11 % --bmc1_ucm_extend_mode 1
% 151.69/152.11 % --bmc1_ucm_init_mode 2
% 151.69/152.11 % --bmc1_ucm_cone_mode none
% 151.69/152.11 % --bmc1_ucm_reduced_relation_type 0
% 151.69/152.11 % --bmc1_ucm_relax_model 4
% 151.69/152.11 % --bmc1_ucm_full_tr_after_sat true
% 151.69/152.11 % --bmc1_ucm_expand_neg_assumptions false
% 151.69/152.11 % --bmc1_ucm_layered_model none
% 151.69/152.11 % --bmc1_ucm_max_lemma_size 10
% 151.69/152.11
% 151.69/152.11 % ------ AIG Options
% 151.69/152.11
% 151.69/152.11 % --aig_mode false
% 151.69/152.11
% 151.69/152.11 % ------ Instantiation Options
% 151.69/152.11
% 151.69/152.11 % --instantiation_flag true
% 151.69/152.11 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 151.69/152.11 % --inst_solver_per_active 750
% 151.69/152.11 % --inst_solver_calls_frac 0.5
% 151.69/152.11 % --inst_passive_queue_type priority_queues
% 151.69/152.11 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 151.69/152.11 % --inst_passive_queues_freq [25;2]
% 151.69/152.11 % --inst_dismatching true
% 151.69/152.11 % --inst_eager_unprocessed_to_passive true
% 151.69/152.11 % --inst_prop_sim_given true
% 151.69/152.11 % --inst_prop_sim_new false
% 151.69/152.11 % --inst_orphan_elimination true
% 151.69/152.11 % --inst_learning_loop_flag true
% 151.69/152.11 % --inst_learning_start 3000
% 151.69/152.11 % --inst_learning_factor 2
% 151.69/152.11 % --inst_start_prop_sim_after_learn 3
% 151.69/152.11 % --inst_sel_renew solver
% 151.69/152.11 % --inst_lit_activity_flag true
% 151.69/152.11 % --inst_out_proof true
% 151.69/152.11
% 151.69/152.11 % ------ Resolution Options
% 151.69/152.11
% 151.69/152.11 % --resolution_flag true
% 151.69/152.11 % --res_lit_sel kbo_max
% 151.69/152.11 % --res_to_prop_solver none
% 151.69/152.11 % --res_prop_simpl_new false
% 151.69/152.11 % --res_prop_simpl_given false
% 151.69/152.11 % --res_passive_queue_type priority_queues
% 151.69/152.11 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 151.69/152.11 % --res_passive_queues_freq [15;5]
% 151.69/152.11 % --res_forward_subs full
% 151.69/152.11 % --res_backward_subs full
% 151.69/152.11 % --res_forward_subs_resolution true
% 151.69/152.11 % --res_backward_subs_resolution true
% 151.69/152.11 % --res_orphan_elimination false
% 151.69/152.11 % --res_time_limit 1000.
% 151.69/152.11 % --res_out_proof true
% 151.69/152.11 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0cf017.s
% 151.69/152.11 % --modulo true
% 151.69/152.11
% 151.69/152.11 % ------ Combination Options
% 151.69/152.11
% 151.69/152.11 % --comb_res_mult 1000
% 151.69/152.11 % --comb_inst_mult 300
% 151.69/152.11 % ------
% 151.69/152.11
% 151.69/152.11
% 151.69/152.11
% 151.69/152.11 % ------ Proving...
% 151.69/152.11 %
% 151.69/152.11
% 151.69/152.11
% 151.69/152.11 % Resolution empty clause
% 151.69/152.11
% 151.69/152.11 % ------ Statistics
% 151.69/152.11
% 151.69/152.11 % ------ General
% 151.69/152.11
% 151.69/152.11 % num_of_input_clauses: 848
% 151.69/152.11 % num_of_input_neg_conjectures: 3
% 151.69/152.11 % num_of_splits: 0
% 151.69/152.11 % num_of_split_atoms: 0
% 151.69/152.11 % num_of_sem_filtered_clauses: 0
% 151.69/152.11 % num_of_subtypes: 0
% 151.69/152.11 % monotx_restored_types: 0
% 151.69/152.11 % sat_num_of_epr_types: 0
% 151.69/152.11 % sat_num_of_non_cyclic_types: 0
% 151.69/152.11 % sat_guarded_non_collapsed_types: 0
% 151.69/152.11 % is_epr: 0
% 151.69/152.11 % is_horn: 0
% 151.69/152.11 % has_eq: 1
% 151.69/152.11 % num_pure_diseq_elim: 0
% 151.69/152.11 % simp_replaced_by: 0
% 151.69/152.11 % res_preprocessed: 6
% 151.69/152.11 % prep_upred: 0
% 151.69/152.11 % prep_unflattend: 0
% 151.69/152.11 % pred_elim_cands: 0
% 151.69/152.11 % pred_elim: 0
% 151.69/152.11 % pred_elim_cl: 0
% 151.69/152.11 % pred_elim_cycles: 0
% 151.69/152.11 % forced_gc_time: 0
% 151.69/152.11 % gc_basic_clause_elim: 0
% 151.69/152.11 % parsing_time: 0.022
% 151.69/152.11 % sem_filter_time: 0.
% 151.69/152.11 % pred_elim_time: 0.
% 151.69/152.11 % out_proof_time: 0.
% 151.69/152.11 % monotx_time: 0.
% 151.69/152.11 % subtype_inf_time: 0.
% 151.69/152.11 % unif_index_cands_time: 0.
% 151.69/152.11 % unif_index_add_time: 0.
% 151.69/152.11 % total_time: 1.559
% 151.69/152.11 % num_of_symbols: 82
% 151.69/152.11 % num_of_terms: 1683
% 151.69/152.11
% 151.69/152.11 % ------ Propositional Solver
% 151.69/152.11
% 151.69/152.11 % prop_solver_calls: 1
% 151.69/152.11 % prop_fast_solver_calls: 9
% 151.69/152.11 % prop_num_of_clauses: 804
% 151.69/152.11 % prop_preprocess_simplified: 2546
% 151.69/152.11 % prop_fo_subsumed: 0
% 151.69/152.11 % prop_solver_time: 0.
% 151.69/152.11 % prop_fast_solver_time: 0.
% 151.69/152.11 % prop_unsat_core_time: 0.
% 151.69/152.11
% 151.69/152.11 % ------ QBF
% 151.69/152.11
% 151.69/152.11 % qbf_q_res: 0
% 151.69/152.11 % qbf_num_tautologies: 0
% 151.69/152.11 % qbf_prep_cycles: 0
% 151.69/152.11
% 151.69/152.11 % ------ BMC1
% 151.69/152.11
% 151.69/152.11 % bmc1_current_bound: -1
% 151.69/152.11 % bmc1_last_solved_bound: -1
% 151.69/152.11 % bmc1_unsat_core_size: -1
% 151.69/152.11 % bmc1_unsat_core_parents_size: -1
% 151.69/152.11 % bmc1_merge_next_fun: 0
% 151.69/152.11 % bmc1_unsat_core_clauses_time: 0.
% 151.69/152.11
% 151.69/152.11 % ------ Instantiation
% 151.69/152.11
% 151.69/152.11 % inst_num_of_clauses: 745
% 151.69/152.11 % inst_num_in_passive: 0
% 151.69/152.11 % inst_num_in_active: 0
% 151.69/152.11 % inst_num_in_unprocessed: 848
% 151.69/152.11 % inst_num_of_loops: 0
% 151.69/152.11 % inst_num_of_learning_restarts: 0
% 151.69/152.11 % inst_num_moves_active_passive: 0
% 151.69/152.11 % inst_lit_activity: 0
% 151.69/152.11 % inst_lit_activity_moves: 0
% 151.69/152.11 % inst_num_tautologies: 0
% 151.69/152.11 % inst_num_prop_implied: 0
% 151.69/152.11 % inst_num_existing_simplified: 0
% 151.69/152.11 % inst_num_eq_res_simplified: 0
% 151.69/152.11 % inst_num_child_elim: 0
% 151.69/152.11 % inst_num_of_dismatching_blockings: 0
% 151.69/152.11 % inst_num_of_non_proper_insts: 0
% 151.69/152.11 % inst_num_of_duplicates: 0
% 151.69/152.11 % inst_inst_num_from_inst_to_res: 0
% 151.69/152.11 % inst_dismatching_checking_time: 0.
% 151.69/152.11
% 151.69/152.11 % ------ Resolution
% 151.69/152.11
% 151.69/152.11 % res_num_of_clauses: 804
% 151.69/152.11 % res_num_in_passive: 4
% 151.69/152.11 % res_num_in_active: 319
% 151.69/152.11 % res_num_of_loops: 2
% 151.69/152.11 % res_forward_subset_subsumed: 483
% 151.69/152.11 % res_backward_subset_subsumed: 0
% 151.69/152.11 % res_forward_subsumed: 0
% 151.69/152.11 % res_backward_subsumed: 0
% 151.69/152.11 % res_forward_subsumption_resolution: 1
% 151.69/152.11 % res_backward_subsumption_resolution: 0
% 151.69/152.11 % res_clause_to_clause_subsumption: 1
% 151.69/152.11 % res_orphan_elimination: 0
% 151.69/152.11 % res_tautology_del: 0
% 151.69/152.11 % res_num_eq_res_simplified: 0
% 151.69/152.11 % res_num_sel_changes: 0
% 151.69/152.11 % res_moves_from_active_to_pass: 0
% 151.69/152.11
% 151.69/152.11 % Status Unsatisfiable
% 151.69/152.11 % SZS status Unsatisfiable
% 151.69/152.11 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------