%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : ANA020-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 10:08:49 EDT 2023

% Result   : Unsatisfiable 86.96s 21.50s
% Output   : Refutation 87.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      : 1158
% Syntax   : Number of formulae    : 2223 ( 457 unt;  94 typ;   0 def)
%            Number of atoms       : 5609 (1104 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 25424 (3230   ~;3480   |;   0   &;18714   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  140 ( 140   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   96 (  94 usr;  14 con; 0-3 aty)
%            Number of variables   : 4064 (   0   ^;4064   !;   0   ?;4064   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_f_type,type,
    v_f: $i > $i ).

thf(c_0_type,type,
    c_0: $i ).

thf(c_less_type,type,
    c_less: $i > $i > $i > $o ).

thf(v_c_type,type,
    v_c: $i ).

thf(t_a_type,type,
    t_a: $i ).

thf(c_lessequals_type,type,
    c_lessequals: $i > $i > $i > $o ).

thf(c_HOL_Oabs_type,type,
    c_HOL_Oabs: $i > $i > $i ).

thf(c_Suc_type,type,
    c_Suc: $i > $i ).

thf(c_times_type,type,
    c_times: $i > $i > $i > $i ).

thf(v_h_type,type,
    v_h: $i > $i ).

thf(v_x_type,type,
    v_x: $i ).

thf(class_Ring__and__Field_Oordered__idom_type,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

thf(c_Divides_Oop_Amod_type,type,
    c_Divides_Oop_Amod: $i > $i > $i > $i ).

thf(c_Numeral_Onumber__of_type,type,
    c_Numeral_Onumber__of: $i > $i > $i ).

thf(c_Numeral_OBit_type,type,
    c_Numeral_OBit: $i > $i > $i ).

thf(c_Numeral_OPls_type,type,
    c_Numeral_OPls: $i ).

thf(c_Numeral_Obit_OB1_type,type,
    c_Numeral_Obit_OB1: $i ).

thf(c_Numeral_Obit_OB0_type,type,
    c_Numeral_Obit_OB0: $i ).

thf(tc_IntDef_Oint_type,type,
    tc_IntDef_Oint: $i ).

thf(c_1_type,type,
    c_1: $i ).

thf(class_Numeral_Onumber__ring_type,type,
    class_Numeral_Onumber__ring: $i > $o ).

thf(c_IntDef_Oiszero_type,type,
    c_IntDef_Oiszero: $i > $i > $o ).

thf(c_Numeral_Obin__add_type,type,
    c_Numeral_Obin__add: $i > $i > $i ).

thf(c_Numeral_Obin__minus_type,type,
    c_Numeral_Obin__minus: $i > $i ).

thf(c_IntDef_Oneg_type,type,
    c_IntDef_Oneg: $i > $i > $o ).

thf(tc_nat_type,type,
    tc_nat: $i ).

thf(c_plus_type,type,
    c_plus: $i > $i > $i > $i ).

thf(c_div_type,type,
    c_div: $i > $i > $i > $i ).

thf(c_Numeral_Obin__succ_type,type,
    c_Numeral_Obin__succ: $i > $i ).

thf(class_Ring__and__Field_Odivision__by__zero_type,type,
    class_Ring__and__Field_Odivision__by__zero: $i > $o ).

thf(class_Ring__and__Field_Oordered__field_type,type,
    class_Ring__and__Field_Oordered__field: $i > $o ).

thf(c_divide_type,type,
    c_divide: $i > $i > $i > $i ).

thf(class_Power_Orecpower_type,type,
    class_Power_Orecpower: $i > $o ).

thf(c_Nat_Opower_type,type,
    c_Nat_Opower: $i > $i > $i > $i ).

thf(c_minus_type,type,
    c_minus: $i > $i > $i > $i ).

thf(c_Numeral_OMin_type,type,
    c_Numeral_OMin: $i ).

thf(class_Numeral_Onumber_type,type,
    class_Numeral_Onumber: $i > $o ).

thf(c_Numeral_Obin__mult_type,type,
    c_Numeral_Obin__mult: $i > $i > $i ).

thf(c_Parity_Oeven_type,type,
    c_Parity_Oeven: $i > $i > $o ).

thf(c_Divides_Oop_Advd_type,type,
    c_Divides_Oop_Advd: $i > $i > $i > $o ).

thf(class_OrderedGroup_Olordered__ab__group__abs_type,type,
    class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).

thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

thf(class_Ring__and__Field_Ofield_type,type,
    class_Ring__and__Field_Ofield: $i > $o ).

thf(c_IntDef_Oint_type,type,
    c_IntDef_Oint: $i > $i ).

thf(c_uminus_type,type,
    c_uminus: $i > $i > $i ).

thf(class_OrderedGroup_Olordered__ab__group_type,type,
    class_OrderedGroup_Olordered__ab__group: $i > $o ).

thf(c_LOrder_Omeet_type,type,
    c_LOrder_Omeet: $i > $i > $i > $i ).

thf(c_LOrder_Ojoin_type,type,
    c_LOrder_Ojoin: $i > $i > $i > $i ).

thf(class_LOrder_Ojoin__semilorder_type,type,
    class_LOrder_Ojoin__semilorder: $i > $o ).

thf(class_Ring__and__Field_Oring_type,type,
    class_Ring__and__Field_Oring: $i > $o ).

thf(class_Ring__and__Field_Oordered__semidom_type,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

thf(class_Ring__and__Field_Oaxclass__0__neq__1_type,type,
    class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).

thf(c_List_Olist_OCons_type,type,
    c_List_Olist_OCons: $i > $i > $i > $i ).

thf(c_HOL_Oinverse_type,type,
    c_HOL_Oinverse: $i > $i > $i ).

thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

thf(c_IntDef_Onat_type,type,
    c_IntDef_Onat: $i > $i ).

thf(c_NatArith_Oof__nat_type,type,
    c_NatArith_Oof__nat: $i > $i > $i ).

thf(class_LOrder_Omeet__semilorder_type,type,
    class_LOrder_Omeet__semilorder: $i > $o ).

thf(c_List_Odrop_type,type,
    c_List_Odrop: $i > $i > $i > $i ).

thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

thf(class_Ring__and__Field_Osemiring__0__cancel_type,type,
    class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).

thf(class_Ring__and__Field_Opordered__comm__semiring_type,type,
    class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).

thf(class_Orderings_Oorder_type,type,
    class_Orderings_Oorder: $i > $o ).

thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_type,type,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).

thf(class_OrderedGroup_Olordered__ab__group__meet_type,type,
    class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).

thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

thf(c_List_Oreplicate_type,type,
    c_List_Oreplicate: $i > $i > $i > $i ).

thf(class_HOL_Ominus_type,type,
    class_HOL_Ominus: $i > $o ).

thf(c_Nat_Osize_type,type,
    c_Nat_Osize: $i > $i > $i ).

thf(tc_List_Olist_type,type,
    tc_List_Olist: $i > $i ).

thf(class_OrderedGroup_Omonoid__mult_type,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

thf(class_OrderedGroup_Olordered__ab__group__join_type,type,
    class_OrderedGroup_Olordered__ab__group__join: $i > $o ).

thf(class_Ring__and__Field_Opordered__semiring_type,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

thf(class_LOrder_Olorder_type,type,
    class_LOrder_Olorder: $i > $o ).

thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

thf(tc_set_type,type,
    tc_set: $i > $i ).

thf(class_Ring__and__Field_Oaxclass__no__zero__divisors_type,type,
    class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).

thf(c_IntDef_Oof__int_type,type,
    c_IntDef_Oof__int: $i > $i > $i ).

thf(class_Ring__and__Field_Oaxclass__abs__if_type,type,
    class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).

thf(c_Binomial_Obinomial_type,type,
    c_Binomial_Obinomial: $i > $i > $i ).

thf(c_emptyset_type,type,
    c_emptyset: $i ).

thf(c_SetInterval_OatLeastLessThan_type,type,
    c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).

thf(c_List_Ochar_OChar_type,type,
    c_List_Ochar_OChar: $i > $i > $i ).

thf(c_OrderedGroup_Onprt_type,type,
    c_OrderedGroup_Onprt: $i > $i > $i ).

thf(c_SetInterval_OatLeastAtMost_type,type,
    c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).

thf(c_OrderedGroup_Opprt_type,type,
    c_OrderedGroup_Opprt: $i > $i > $i ).

thf(c_SetInterval_OgreaterThanAtMost_type,type,
    c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).

thf(c_SetInterval_OatLeast_type,type,
    c_SetInterval_OatLeast: $i > $i > $i ).

thf(c_SetInterval_OatMost_type,type,
    c_SetInterval_OatMost: $i > $i > $i ).

thf(c_Main_Omod__eq__0D__dest__1_type,type,
    c_Main_Omod__eq__0D__dest__1: $i > $i > $i ).

thf(c_Main_Ozmod__eq__0D__dest__1_type,type,
    c_Main_Ozmod__eq__0D__dest__1: $i > $i > $i ).

thf(c_List_Olexn_type,type,
    c_List_Olexn: $i > $i > $i > $i ).

thf(tc_List_Ochar_type,type,
    tc_List_Ochar: $i ).

thf(618,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).

thf(2452,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(452,axiom,
    c_lessequals @ ( c_IntDef_Oint @ c_0 ) @ c_0 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).

thf(2094,plain,
    c_lessequals @ ( c_IntDef_Oint @ c_0 ) @ c_0 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(549,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_NatArith_Oof__nat @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = ( c_Numeral_Onumber__of @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).

thf(2295,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_NatArith_Oof__nat @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = ( c_Numeral_Onumber__of @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(309,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).

thf(1767,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(1061,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_less @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).

thf(3434,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_less @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(340,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).

thf(1840,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(565,axiom,
    ! [A: $i] :
      ( ( c_div @ c_0 @ A @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).

thf(2331,plain,
    ! [A: $i] :
      ( ( c_div @ c_0 @ A @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(331,axiom,
    ! [B: $i,A: $i] :
      ( ( c_plus @ ( c_Suc @ A ) @ B @ tc_nat )
      = ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).

thf(1818,plain,
    ! [B: $i,A: $i] :
      ( ( c_plus @ ( c_Suc @ A ) @ B @ tc_nat )
      = ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(882,axiom,
    ! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).

thf(3021,plain,
    ! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(108,axiom,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).

thf(1322,plain,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(262,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ ( c_divide @ C @ D @ A ) @ A )
        = ( c_divide @ ( c_times @ B @ D @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__divide__eq__right_0) ).

thf(1665,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ ( c_divide @ C @ D @ A ) @ A )
        = ( c_divide @ ( c_times @ B @ D @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(356,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).

thf(1879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ B @ A )
       != ( c_HOL_Oinverse @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__eq__iff__eq_0) ).

thf(1337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ B @ A )
       != ( c_HOL_Oinverse @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(286,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ ( c_times @ B @ C @ A ) @ A )
        = ( c_times @ ( c_HOL_Oinverse @ B @ A ) @ ( c_HOL_Oinverse @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__mult__distrib_0) ).

thf(1718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ ( c_times @ B @ C @ A ) @ A )
        = ( c_times @ ( c_HOL_Oinverse @ B @ A ) @ ( c_HOL_Oinverse @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(689,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).

thf(2612,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(174,axiom,
    ( ( c_Numeral_Obin__minus @ c_Numeral_OPls )
    = c_Numeral_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Pls_0) ).

thf(1469,plain,
    ( ( c_Numeral_Obin__minus @ c_Numeral_OPls )
    = c_Numeral_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(749,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_11) ).

thf(2744,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(817,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Ofield @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).

thf(2889,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Ofield @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(333,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_plus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
        = ( c_minus @ ( c_plus @ C @ B @ tc_nat ) @ A @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).

thf(1823,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_plus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
        = ( c_minus @ ( c_plus @ C @ B @ tc_nat ) @ A @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(54,axiom,
    ( ( c_Numeral_Obin__minus @ c_Numeral_OMin )
    = ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Min_0) ).

thf(1190,plain,
    ( ( c_Numeral_Obin__minus @ c_Numeral_OMin )
    = ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(567,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_IntDef_Oint )
      | ( c_less @ A @ ( c_plus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).

thf(2336,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_IntDef_Oint )
      | ( c_less @ A @ ( c_plus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(876,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_HOL_Oinverse @ B @ A ) @ c_0 @ A )
      | ( c_less @ B @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__negative__iff__negative_0) ).

thf(3008,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_HOL_Oinverse @ B @ A ) @ c_0 @ A )
      | ( c_less @ B @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(423,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).

thf(2031,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(408,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_lessequals @ C @ B @ A )
      | ( c_lessequals @ ( c_divide @ C @ B @ A ) @ c_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__eq__1__pos_1) ).

thf(1995,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_lessequals @ C @ B @ A )
      | ( c_lessequals @ ( c_divide @ C @ B @ A ) @ c_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(533,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__minus1__right_0) ).

thf(2263,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).

thf(1559,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( c_Numeral_Obin__succ @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) )
      = ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).

thf(1105,plain,
    ! [A: $i] :
      ( ( c_Numeral_Obin__succ @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) )
      = ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(811,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_div @ A @ B @ tc_nat ) @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).

thf(2876,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_div @ A @ B @ tc_nat ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(73,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1_0) ).

thf(1237,plain,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(623,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ c_0 @ C @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_7) ).

thf(2463,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ c_0 @ C @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(365,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ c_0 @ B @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__0__iff_1) ).

thf(1899,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ c_0 @ B @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(769,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ c_0 @ tc_IntDef_Oint )
      | ( c_less @ A @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).

thf(2787,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ c_0 @ tc_IntDef_Oint )
      | ( c_less @ A @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(680,axiom,
    class_Numeral_Onumber @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).

thf(2595,plain,
    class_Numeral_Onumber @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(639,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ A @ c_1 @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).

thf(2499,plain,
    ! [A: $i] :
      ( ~ ( c_less @ A @ c_1 @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(631,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).

thf(2480,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_2) ).

thf(1083,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(403,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ ( c_times @ B @ C @ A ) @ ( c_times @ B @ D @ A ) @ A )
        = ( c_divide @ C @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if_1) ).

thf(1982,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ ( c_times @ B @ C @ A ) @ ( c_times @ B @ D @ A ) @ A )
        = ( c_divide @ C @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(390,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).

thf(1956,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(388,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Power_Orecpower @ A )
      | ~ ( c_Parity_Oeven @ B @ tc_nat )
      | ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ B @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).

thf(1950,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Power_Orecpower @ A )
      | ~ ( c_Parity_Oeven @ B @ tc_nat )
      | ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ B @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_Parity_Oeven @ B @ tc_nat )
      | ( c_Parity_Oeven @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).

thf(1549,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_Parity_Oeven @ B @ tc_nat )
      | ( c_Parity_Oeven @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(542,axiom,
    class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).

thf(2280,plain,
    class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ c_1 @ c_1 @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).

thf(1110,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ c_1 @ c_1 @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(271,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).

thf(1686,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(528,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).

thf(2250,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(300,axiom,
    ! [A: $i] :
      ( ( c_IntDef_Onat @ ( c_IntDef_Oint @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).

thf(1750,plain,
    ! [A: $i] :
      ( ( c_IntDef_Onat @ ( c_IntDef_Oint @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(62,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A )
      | ( c_lessequals @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_1) ).

thf(1211,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A )
      | ( c_lessequals @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(555,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).

thf(2309,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(2,negated_conjecture,
    c_less @ c_0 @ v_c @ t_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(1068,plain,
    c_less @ c_0 @ v_c @ t_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(196,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ~ ( c_Parity_Oeven @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_Parity_Oeven @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).

thf(1522,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ~ ( c_Parity_Oeven @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_Parity_Oeven @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(637,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).

thf(2495,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(764,axiom,
    class_LOrder_Olorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).

thf(2776,plain,
    class_LOrder_Olorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(998,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

thf(3285,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(915,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).

thf(3098,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(207,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ ( c_divide @ B @ c_0 @ A ) @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__self__left_0) ).

thf(1544,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ ( c_divide @ B @ c_0 @ A ) @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(290,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).

thf(1728,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(462,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).

thf(2114,plain,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).

thf(1692,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(159,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).

thf(1437,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(1039,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( ( c_times @ B @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).

thf(3382,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( ( c_times @ B @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(182,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_0
        = ( c_divide @ c_1 @ c_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__eq__1__divide__iff_1) ).

thf(1486,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_0
        = ( c_divide @ c_1 @ c_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_1) ).

thf(1200,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(443,axiom,
    class_Ring__and__Field_Oring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).

thf(2077,plain,
    class_Ring__and__Field_Oring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(903,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le__neg_0) ).

thf(3072,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(376,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ ( c_times @ C @ B @ A ) @ B @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if2_1) ).

thf(1924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ ( c_times @ C @ B @ A ) @ B @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(843,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ c_1 @ tc_IntDef_Oint )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).

thf(2940,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ c_1 @ tc_IntDef_Oint )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(457,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
      | ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).

thf(2104,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
      | ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(827,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__ring__strict @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).

thf(2908,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__ring__strict @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(436,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_divide @ B @ C @ A ) @ D @ A )
        = ( c_divide @ B @ ( c_times @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__divide__eq__left_0) ).

thf(2062,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_divide @ B @ C @ A ) @ D @ A )
        = ( c_divide @ B @ ( c_times @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(1037,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).

thf(3377,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(651,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_52) ).

thf(2527,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(849,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).

thf(2953,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(678,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ C @ B @ A )
      | ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).

thf(2590,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ C @ B @ A )
      | ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(143,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ ( c_minus @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).

thf(1401,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ ( c_minus @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(152,axiom,
    ( ( c_plus @ c_0 @ c_0 @ tc_nat )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).

thf(1422,plain,
    ( ( c_plus @ c_0 @ c_0 @ tc_nat )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(846,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).

thf(2947,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(219,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_less @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_6) ).

thf(1569,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_less @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(526,axiom,
    class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).

thf(2248,plain,
    class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(878,axiom,
    class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).

thf(3012,plain,
    class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(60,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).

thf(1205,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(455,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ ( c_divide @ B @ C @ A ) @ D @ A )
        = ( c_divide @ ( c_times @ B @ D @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__eq__2_0) ).

thf(2099,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ ( c_divide @ B @ C @ A ) @ D @ A )
        = ( c_divide @ ( c_times @ B @ D @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(229,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).

thf(1591,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_5) ).

thf(1971,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(202,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_0
       != ( c_NatArith_Oof__nat @ B @ A ) )
      | ( c_0 = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).

thf(1533,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_0
       != ( c_NatArith_Oof__nat @ B @ A ) )
      | ( c_0 = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(236,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).

thf(1608,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(724,axiom,
    class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).

thf(2686,plain,
    class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(931,axiom,
    c_less @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).

thf(3135,plain,
    c_less @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(747,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A )
      | ( c_lessequals @ ( c_uminus @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).

thf(2740,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A )
      | ( c_lessequals @ ( c_uminus @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(892,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).

thf(3044,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
      | ( c_Parity_Oeven @ ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).

thf(1999,plain,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
      | ( c_Parity_Oeven @ ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(616,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).

thf(2448,plain,
    class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(476,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).

thf(2141,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(111,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).

thf(1327,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(374,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ c_0 @ ( c_times @ c_0 @ B @ A ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if1_0) ).

thf(1919,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ c_0 @ ( c_times @ c_0 @ B @ A ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(1051,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ ( c_minus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).

thf(3414,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ ( c_minus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(478,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).

thf(2146,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(169,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).

thf(1458,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(671,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).

thf(2575,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(186,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ c_1 @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__eq__1__iff_1) ).

thf(1497,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ c_1 @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(280,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).

thf(1705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(318,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat )
      | ( c_less @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).

thf(1788,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat )
      | ( c_less @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(154,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).

thf(1426,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(924,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).

thf(3120,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(1058,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ( c_less @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).

thf(3429,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ( c_less @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(303,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).

thf(1756,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ C @ c_0 @ A )
      | ( c_less @ c_1 @ ( c_divide @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oless__divide__eq__1__neg_1) ).

thf(1310,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ C @ c_0 @ A )
      | ( c_less @ c_1 @ ( c_divide @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(425,axiom,
    ! [A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ ( c_Suc @ c_0 ) @ tc_nat )
      | ( A
        = ( c_Suc @ c_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).

thf(2035,plain,
    ! [A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ ( c_Suc @ c_0 ) @ tc_nat )
      | ( A
        = ( c_Suc @ c_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(1033,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olexn @ A @ c_0 @ B )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).

thf(3367,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olexn @ A @ c_0 @ B )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(609,axiom,
    ! [B: $i,A: $i] :
      ( ( c_div @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).

thf(2434,plain,
    ! [B: $i,A: $i] :
      ( ( c_div @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(735,axiom,
    ! [B: $i,A: $i] :
      ( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).

thf(2712,plain,
    ! [B: $i,A: $i] :
      ( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(629,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_lessequals @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_5) ).

thf(2476,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_lessequals @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(488,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).

thf(2168,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(82,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_3) ).

thf(1260,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ C @ A )
       != ( c_divide @ B @ D @ A ) )
      | ( C = D )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__cancel__left_0) ).

thf(1640,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ C @ A )
       != ( c_divide @ B @ D @ A ) )
      | ( C = D )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(673,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
      | ( C = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).

thf(2580,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
      | ( C = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(823,axiom,
    class_Numeral_Onumber @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).

thf(2901,plain,
    class_Numeral_Onumber @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(1011,axiom,
    ! [B: $i,A: $i] :
      ( ( c_times @ c_0 @ A @ tc_nat )
      = ( c_times @ c_0 @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_1) ).

thf(3313,plain,
    ! [B: $i,A: $i] :
      ( ( c_times @ c_0 @ A @ tc_nat )
      = ( c_times @ c_0 @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(740,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( ( c_HOL_Oabs @ ( c_uminus @ B @ A ) @ A )
        = ( c_HOL_Oabs @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).

thf(2723,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( ( c_HOL_Oabs @ ( c_uminus @ B @ A ) @ A )
        = ( c_HOL_Oabs @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(608,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_0) ).

thf(2432,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(238,axiom,
    ( ( c_IntDef_Oint @ c_1 )
    = c_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).

thf(1613,plain,
    ( ( c_IntDef_Oint @ c_1 )
    = c_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(816,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_minus @ A @ B @ ( tc_set @ C ) )
       != c_emptyset )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).

thf(2886,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_minus @ A @ B @ ( tc_set @ C ) )
       != c_emptyset )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_less @ C @ c_0 @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_2) ).

thf(2082,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_less @ C @ c_0 @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(177,axiom,
    c_Parity_Oeven @ c_0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).

thf(1475,plain,
    c_Parity_Oeven @ c_0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(647,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = c_0 )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).

thf(2516,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = c_0 )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(325,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_uminus @ B @ A ) @ C @ A )
        = ( c_uminus @ ( c_divide @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__minus__left_0) ).

thf(1803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_uminus @ B @ A ) @ C @ A )
        = ( c_uminus @ ( c_divide @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(807,axiom,
    ! [A: $i] : ( c_IntDef_Oneg @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).

thf(2869,plain,
    ! [A: $i] : ( c_IntDef_Oneg @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(851,axiom,
    ! [A: $i] :
      ( ( c_div @ A @ ( c_Suc @ c_0 ) @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).

thf(2957,plain,
    ! [A: $i] :
      ( ( c_div @ A @ ( c_Suc @ c_0 ) @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).

thf(1127,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(659,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_OrderedGroup_Opprt @ B @ A ) @ ( c_OrderedGroup_Opprt @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).

thf(2548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_OrderedGroup_Opprt @ B @ A ) @ ( c_OrderedGroup_Opprt @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(635,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_nat ) @ B @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).

thf(2491,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_nat ) @ B @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( c_plus @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
      = ( c_Suc @ ( c_Suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).

thf(1243,plain,
    ! [A: $i] :
      ( ( c_plus @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
      = ( c_Suc @ ( c_Suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(138,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_divide @ c_1 @ B @ A ) @ A )
      | ( c_less @ c_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__less__divide__1__iff_0) ).

thf(1391,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_divide @ c_1 @ B @ A ) @ A )
      | ( c_less @ c_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).

thf(1576,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(1009,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( c_less @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).

thf(3308,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( c_less @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(415,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ B @ A )
        = ( c_uminus @ ( c_divide @ c_1 @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus1__divide_0) ).

thf(2010,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ B @ A )
        = ( c_uminus @ ( c_divide @ c_1 @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(233,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ B @ A )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_0) ).

thf(1601,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ B @ A )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(136,axiom,
    ! [B: $i,A: $i] :
      ( ( c_div @ A @ ( c_Suc @ ( c_Suc @ ( c_Suc @ B ) ) ) @ tc_nat )
      = ( c_div @ A @ ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB1 ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).

thf(1386,plain,
    ! [B: $i,A: $i] :
      ( ( c_div @ A @ ( c_Suc @ ( c_Suc @ ( c_Suc @ B ) ) ) @ tc_nat )
      = ( c_div @ A @ ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB1 ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(996,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).

thf(3281,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(491,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_20) ).

thf(2173,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).

thf(1366,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(438,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).

thf(2067,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(787,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).

thf(2825,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(194,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).

thf(1518,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(84,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_1
        = ( c_Numeral_Onumber__of @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).

thf(1265,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_1
        = ( c_Numeral_Onumber__of @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(653,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ A @ tc_IntDef_Oint )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).

thf(2531,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ A @ tc_IntDef_Oint )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(596,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ c_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).

thf(2405,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ c_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_0) ).

thf(1228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_less @ C @ c_0 @ A )
      | ( c_less @ c_0 @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_3) ).

thf(1623,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_less @ C @ c_0 @ A )
      | ( c_less @ c_0 @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_minus @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).

thf(1254,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_minus @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(563,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).

thf(2328,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(404,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).

thf(1985,plain,
    ! [B: $i,A: $i] :
      ( ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(536,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_lessequals @ c_0 @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_1) ).

thf(2269,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_lessequals @ c_0 @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).

thf(1871,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(369,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( c_0
        = ( c_divide @ ( c_times @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oeq__divide__eq__number__of_4) ).

thf(1907,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( c_0
        = ( c_divide @ ( c_times @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).

thf(1323,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(539,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ ( c_Suc @ c_0 ) @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).

thf(2274,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ ( c_Suc @ c_0 ) @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(90,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_uminus @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).

thf(1279,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_uminus @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(469,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).

thf(2126,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(30,axiom,
    ( ( c_Numeral_OBit @ c_Numeral_OMin @ c_Numeral_Obit_OB1 )
    = c_Numeral_OMin ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_OMin__1__eq_0) ).

thf(1132,plain,
    ( ( c_Numeral_OBit @ c_Numeral_OMin @ c_Numeral_Obit_OB1 )
    = c_Numeral_OMin ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(708,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ~ ( c_lessequals @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_lessequals @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_5) ).

thf(2654,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ~ ( c_lessequals @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_lessequals @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(246,axiom,
    ! [B: $i,A: $i] :
      ( ( c_times @ ( c_Suc @ A ) @ B @ tc_nat )
      = ( c_plus @ B @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).

thf(1628,plain,
    ! [B: $i,A: $i] :
      ( ( c_times @ ( c_Suc @ A ) @ B @ tc_nat )
      = ( c_plus @ B @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(982,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).

thf(3248,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(1064,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).

thf(3442,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(1056,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).

thf(3425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(320,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).

thf(1792,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(156,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).

thf(1430,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(98,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_lessequals @ ( c_divide @ c_1 @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__0__1__iff_1) ).

thf(1298,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_lessequals @ ( c_divide @ c_1 @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_less @ c_0 @ C @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_2) ).

thf(1760,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_less @ c_0 @ C @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(929,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).

thf(3131,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(614,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).

thf(2444,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(349,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).

thf(1860,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_8) ).

thf(2217,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(722,axiom,
    class_LOrder_Olorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).

thf(2682,plain,
    class_LOrder_Olorder @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(926,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
      | ~ ( c_lessequals @ c_1 @ B @ tc_nat )
      | ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).

thf(3125,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
      | ~ ( c_lessequals @ c_1 @ B @ tc_nat )
      | ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(334,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).

thf(1826,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(497,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( ( c_Nat_Opower @ ( c_HOL_Oabs @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).

thf(2185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( ( c_Nat_Opower @ ( c_HOL_Oabs @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(168,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ ( c_times @ C @ B @ A ) @ ( c_times @ D @ B @ A ) @ A )
        = ( c_divide @ C @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if_1) ).

thf(1455,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ ( c_times @ C @ B @ A ) @ ( c_times @ D @ B @ A ) @ A )
        = ( c_divide @ C @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(665,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ C @ A ) @ D @ A ) @ A )
        = ( c_times @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__mult @ B @ C ) @ A ) @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).

thf(2562,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ C @ A ) @ D @ A ) @ A )
        = ( c_times @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__mult @ B @ C ) @ A ) @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(911,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( ( c_OrderedGroup_Opprt @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).

thf(3089,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( ( c_OrderedGroup_Opprt @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != ( c_plus @ C @ B @ tc_nat ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).

thf(1992,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != ( c_plus @ C @ B @ tc_nat ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(1027,axiom,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ ( c_Suc @ A ) @ A )
      = ( c_Suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).

thf(3353,plain,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ ( c_Suc @ A ) @ A )
      = ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(603,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).

thf(2420,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(375,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_NatArith_Oof__nat @ c_0 @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).

thf(1922,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_NatArith_Oof__nat @ c_0 @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(760,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Odrop @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_minus @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).

thf(2767,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Odrop @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_minus @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(584,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_minus @ A @ B @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).

thf(2373,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_minus @ A @ B @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(969,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

thf(3216,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(380,axiom,
    ! [A: $i] :
      ( ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) )
        = ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_2) ).

thf(1931,plain,
    ! [A: $i] :
      ( ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) )
        = ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(743,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).

thf(2730,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(420,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_times @ ( c_uminus @ B @ A ) @ C @ A )
        = ( c_uminus @ ( c_times @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).

thf(2024,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_times @ ( c_uminus @ B @ A ) @ C @ A )
        = ( c_uminus @ ( c_times @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(312,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).

thf(1773,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(125,axiom,
    ! [A: $i] : ( c_lessequals @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).

thf(1362,plain,
    ! [A: $i] : ( c_lessequals @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(654,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != ( c_Numeral_Onumber__of @ B @ tc_nat ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_0) ).

thf(2533,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != ( c_Numeral_Onumber__of @ B @ tc_nat ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ A ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_2) ).

thf(1100,plain,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ A ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(343,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).

thf(1847,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(789,axiom,
    class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).

thf(2829,plain,
    class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(362,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ B @ ( c_divide @ C @ D @ A ) @ A )
        = ( c_divide @ ( c_times @ B @ C @ A ) @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__eq__1_0) ).

thf(1892,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ B @ ( c_divide @ C @ D @ A ) @ A )
        = ( c_divide @ ( c_times @ B @ C @ A ) @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) @ C @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).

thf(1379,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) @ C @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(1040,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).

thf(3385,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(77,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
       != ( c_Numeral_Onumber__of @ C @ A ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).

thf(1247,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
       != ( c_Numeral_Onumber__of @ C @ A ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(661,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).

thf(2552,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ ( c_uminus @ C @ A ) @ A )
        = ( c_uminus @ ( c_divide @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__minus__right_0) ).

thf(1319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ ( c_uminus @ C @ A ) @ A )
        = ( c_uminus @ ( c_divide @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(279,axiom,
    class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).

thf(1704,plain,
    class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).

thf(1890,plain,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_minus @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).

thf(1115,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_minus @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(838,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
       != c_0 )
      | ( c_Divides_Oop_Advd @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).

thf(2929,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
       != c_0 )
      | ( c_Divides_Oop_Advd @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(551,axiom,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ A ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).

thf(2301,plain,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ A ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_minus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
        = ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).

thf(1815,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_minus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
        = ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(185,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_0
       != ( c_divide @ c_1 @ B @ A ) )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__eq__1__divide__iff_0) ).

thf(1494,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_0
       != ( c_divide @ c_1 @ B @ A ) )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(800,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ A )
      | ( ( c_Numeral_Onumber__of @ C @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).

thf(2852,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ A )
      | ( ( c_Numeral_Onumber__of @ C @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(976,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_0
        = ( c_times @ B @ c_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).

thf(3231,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_0
        = ( c_times @ B @ c_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(71,axiom,
    ( ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ tc_nat )
    = c_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__1__eq__1_0) ).

thf(1232,plain,
    ( ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ tc_nat )
    = c_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(986,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).

thf(3258,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(620,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
      | ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).

thf(2456,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
      | ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(514,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_minus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ ( tc_set @ C ) )
      = ( c_minus @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).

thf(2222,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_minus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ ( tc_set @ C ) )
      = ( c_minus @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oabs @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
      = ( c_IntDef_Oint @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).

thf(1489,plain,
    ! [A: $i] :
      ( ( c_HOL_Oabs @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
      = ( c_IntDef_Oint @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(172,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A )
      | ( c_lessequals @ c_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).

thf(1465,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A )
      | ( c_lessequals @ c_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(1059,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).

thf(3431,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(772,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_lessequals @ ( c_uminus @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).

thf(2794,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_lessequals @ ( c_uminus @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_lessequals @ c_1 @ ( c_divide @ C @ B @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ole__divide__eq__1__pos_0) ).

thf(1450,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_lessequals @ c_1 @ ( c_divide @ C @ B @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(871,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).

thf(2996,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(706,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( ( c_SetInterval_OgreaterThanAtMost @ C @ B @ A )
        = c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).

thf(2650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( ( c_SetInterval_OgreaterThanAtMost @ C @ B @ A )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(521,axiom,
    ! [A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_IntDef_Onat @ ( c_Divides_Oop_Amod @ c_1 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).

thf(2236,plain,
    ! [A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_IntDef_Onat @ ( c_Divides_Oop_Amod @ c_1 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).

thf(1334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(335,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_2) ).

thf(1828,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(547,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).

thf(2291,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(267,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).

thf(1677,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(392,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ B @ C @ tc_nat )
      | ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).

thf(1960,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ B @ C @ tc_nat )
      | ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(284,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ c_1 @ ( c_divide @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ole__divide__eq__1__pos_1) ).

thf(1714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ c_1 @ ( c_divide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(421,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).

thf(2027,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(450,axiom,
    ! [A: $i] :
      ~ ( c_IntDef_Oneg @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).

thf(2090,plain,
    ! [A: $i] :
      ~ ( c_IntDef_Oneg @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(1043,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_0
        = ( c_IntDef_Oof__int @ c_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).

thf(3393,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_0
        = ( c_IntDef_Oof__int @ c_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(819,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).

thf(2893,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(248,axiom,
    ( ( c_IntDef_Oint @ c_0 )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).

thf(1632,plain,
    ( ( c_IntDef_Oint @ c_0 )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(269,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).

thf(1682,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( c_Numeral_Obin__add @ A @ c_Numeral_OPls )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).

thf(1136,plain,
    ! [A: $i] :
      ( ( c_Numeral_Obin__add @ A @ c_Numeral_OPls )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_5) ).

thf(1858,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(350,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_3) ).

thf(1864,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ B @ C @ tc_IntDef_Oint )
      | ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).

thf(2122,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ B @ C @ tc_IntDef_Oint )
      | ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(765,axiom,
    ! [A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Suc @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__succ @ A ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).

thf(2777,plain,
    ! [A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Suc @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__succ @ A ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(940,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).

thf(3152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_uminus @ ( c_LOrder_Omeet @ B @ C @ A ) @ A )
        = ( c_LOrder_Ojoin @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).

thf(1283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_uminus @ ( c_LOrder_Omeet @ B @ C @ A ) @ A )
        = ( c_LOrder_Ojoin @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(441,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).

thf(2073,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(581,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).

thf(2367,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0) ).

thf(1215,plain,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(359,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).

thf(1886,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(322,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A )
      | ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_9) ).

thf(1796,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A )
      | ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(120,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ c_Numeral_OPls @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).

thf(1351,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ c_Numeral_OPls @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(1030,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).

thf(3361,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
        = c_0 )
      | ( ( c_times @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oeq__divide__eq__number__of_0) ).

thf(1405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
        = c_0 )
      | ( ( c_times @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(974,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).

thf(3226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(778,axiom,
    class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).

thf(2804,plain,
    class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(276,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_HOL_Oabs @ ( c_HOL_Oinverse @ B @ A ) @ A )
        = ( c_HOL_Oinverse @ ( c_HOL_Oabs @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__inverse_0) ).

thf(1697,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_HOL_Oabs @ ( c_HOL_Oinverse @ B @ A ) @ A )
        = ( c_HOL_Oinverse @ ( c_HOL_Oabs @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(967,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_0
        = ( c_times @ c_0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).

thf(3211,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_0
        = ( c_times @ c_0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(506,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).

thf(2205,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(400,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_2) ).

thf(1975,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(757,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_7) ).

thf(2762,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(692,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_LOrder_Ojoin @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).

thf(2618,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_LOrder_Ojoin @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(791,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_times @ ( c_HOL_Oinverse @ B @ A ) @ B @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).

thf(2833,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_times @ ( c_HOL_Oinverse @ B @ A ) @ B @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(543,axiom,
    ! [B: $i,A: $i] :
      ( ( c_minus @ A @ A @ ( tc_set @ B ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).

thf(2281,plain,
    ! [B: $i,A: $i] :
      ( ( c_minus @ A @ A @ ( tc_set @ B ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(499,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).

thf(2190,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(1054,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ c_1 @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).

thf(3421,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ c_1 @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(605,axiom,
    ! [A: $i] :
      ~ ( c_lessequals @ c_0 @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).

thf(2424,plain,
    ! [A: $i] :
      ~ ( c_lessequals @ c_0 @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(862,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).

thf(2979,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ( c_less @ ( c_divide @ B @ C @ A ) @ c_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__eq__1__pos_1) ).

thf(1526,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ( c_less @ ( c_divide @ B @ C @ A ) @ c_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(474,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(2137,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(523,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).

thf(2242,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(118,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_IntDef_Oint @ A )
       != ( c_IntDef_Oint @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).

thf(1345,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_IntDef_Oint @ A )
       != ( c_IntDef_Oint @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(775,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Numeral_Onumber @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).

thf(2799,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Numeral_Onumber @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
        = c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).

thf(2286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(701,axiom,
    class_HOL_Ominus @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).

thf(2639,plain,
    class_HOL_Ominus @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(955,axiom,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ c_0 @ ( c_Suc @ A ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).

thf(3184,plain,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ c_0 @ ( c_Suc @ A ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(676,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).

thf(2586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(864,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).

thf(2982,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(815,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).

thf(2884,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(256,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_divide @ c_1 @ B @ A )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__divide__eq__0__iff_0) ).

thf(1651,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_divide @ c_1 @ B @ A )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(828,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_IntDef_Oof__int @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ tc_IntDef_Oint ) @ A )
        = ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).

thf(2910,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_IntDef_Oof__int @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ tc_IntDef_Oint ) @ A )
        = ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(628,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_minus @ A @ B @ tc_nat )
       != c_0 )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).

thf(2473,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_minus @ A @ B @ tc_nat )
       != c_0 )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(101,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).

thf(1306,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(956,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odrop @ c_0 @ A @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).

thf(3186,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Odrop @ c_0 @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(465,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_32) ).

thf(2118,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(1013,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( ( c_HOL_Oabs @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_Numeral_Onumber__of @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).

thf(3318,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( ( c_HOL_Oabs @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_Numeral_Onumber__of @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(372,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).

thf(1915,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
       != c_0 )
      | ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
       != c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oneq__one__mod__two_1) ).

thf(1074,plain,
    ! [A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
       != c_0 )
      | ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
       != c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).

thf(1604,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(834,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).

thf(2922,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(1006,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).

thf(3301,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(1007,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_times @ A @ B @ tc_nat )
       != ( c_times @ C @ B @ tc_nat ) )
      | ( A = C )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).

thf(3303,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_times @ A @ B @ tc_nat )
       != ( c_times @ C @ B @ tc_nat ) )
      | ( A = C )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_lessequals @ c_1 @ ( c_divide @ C @ B @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ole__divide__eq__1__neg_0) ).

thf(1783,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_lessequals @ c_1 @ ( c_divide @ C @ B @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(746,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_LOrder_Omeet @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).

thf(2737,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_LOrder_Omeet @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(519,axiom,
    ! [B: $i,A: $i] :
      ( ( c_div @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).

thf(2232,plain,
    ! [B: $i,A: $i] :
      ( ( c_div @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(554,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_plus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_lessequals @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).

thf(2307,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_plus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_lessequals @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(6,negated_conjecture,
    class_Ring__and__Field_Oordered__idom @ t_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

thf(1067,plain,
    class_Ring__and__Field_Oordered__idom @ t_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_4) ).

thf(1736,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(693,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
       != c_0 )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_1) ).

thf(2621,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
       != c_0 )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(711,axiom,
    ! [B: $i,A: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).

thf(2660,plain,
    ! [B: $i,A: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(826,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_1 @ B @ A )
      | ( ( c_Nat_Opower @ B @ C @ A )
       != ( c_Nat_Opower @ B @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).

thf(2905,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_1 @ B @ A )
      | ( ( c_Nat_Opower @ B @ C @ A )
       != ( c_Nat_Opower @ B @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(352,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( B = c_0 )
      | ( c_1
        = ( c_divide @ B @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oeq__divide__eq__1_2) ).

thf(1868,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( B = c_0 )
      | ( c_1
        = ( c_divide @ B @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(587,axiom,
    ! [A: $i] :
      ( ( c_Nat_Opower @ A @ c_0 @ tc_nat )
      = c_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).

thf(2382,plain,
    ! [A: $i] :
      ( ( c_Nat_Opower @ A @ c_0 @ tc_nat )
      = c_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(291,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_5) ).

thf(1730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(889,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).

thf(3037,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

thf(1274,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ c_1 @ ( c_divide @ C @ B @ A ) @ A )
      | ( c_less @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oless__divide__eq__1__neg_0) ).

thf(1723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ c_1 @ ( c_divide @ C @ B @ A ) @ A )
      | ( c_less @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB1 ) )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__succ @ B ) ) @ c_Numeral_Obit_OB0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).

thf(1091,plain,
    ! [B: $i,A: $i] :
      ( ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB1 ) )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__succ @ B ) ) @ c_Numeral_Obit_OB0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(527,axiom,
    class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).

thf(2249,plain,
    class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(681,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_37) ).

thf(2596,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(26,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_less @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_1) ).

thf(1123,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_less @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(883,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_2) ).

thf(3022,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(902,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_0
        = ( c_HOL_Oabs @ c_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_1) ).

thf(3069,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_0
        = ( c_HOL_Oabs @ c_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(841,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).

thf(2937,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(686,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).

thf(2606,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(941,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le_0) ).

thf(3154,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(480,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).

thf(2150,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(866,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A )
      | ( c_lessequals @ D @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_8) ).

thf(2986,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A )
      | ( c_lessequals @ D @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(983,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).

thf(3250,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

thf(593,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_OrderedGroup_Onprt @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).

thf(2396,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_OrderedGroup_Onprt @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(1021,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ c_0 @ tc_IntDef_Oint )
      | ( c_lessequals @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).

thf(3339,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ c_0 @ tc_IntDef_Oint )
      | ( c_lessequals @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(358,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ B @ ( c_times @ B @ C @ A ) @ A )
        = ( c_divide @ c_1 @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if1_1) ).

thf(1883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ B @ ( c_times @ B @ C @ A ) @ A )
        = ( c_divide @ c_1 @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(732,axiom,
    ! [B: $i,A: $i] :
      ( ( c_minus @ A @ c_emptyset @ ( tc_set @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).

thf(2705,plain,
    ! [B: $i,A: $i] :
      ( ( c_minus @ A @ c_emptyset @ ( tc_set @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(598,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).

thf(2409,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(117,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).

thf(1343,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(664,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).

thf(2560,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(779,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).

thf(2805,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(122,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).

thf(1355,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ ( c_divide @ B @ C @ A ) @ A )
        = ( c_divide @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__divide_0) ).

thf(1580,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ ( c_divide @ B @ C @ A ) @ A )
        = ( c_divide @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_minus @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
        = ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ D ) ) @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__diff2_0) ).

thf(1174,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_minus @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
        = ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ D ) ) @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(472,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).

thf(2133,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(947,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).

thf(3166,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(991,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( ( c_OrderedGroup_Onprt @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).

thf(3269,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( ( c_OrderedGroup_Onprt @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(1004,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint )
      | ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).

thf(3297,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint )
      | ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(504,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_5) ).

thf(2200,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(494,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_lessequals @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_0) ).

thf(2179,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_lessequals @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(42,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != ( c_Numeral_Onumber__of @ B @ tc_nat ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_2) ).

thf(1159,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != ( c_Numeral_Onumber__of @ B @ tc_nat ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(895,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).

thf(3050,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(571,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_minus @ C @ D @ A ) @ A )
        = ( c_minus @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).

thf(2344,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_minus @ C @ D @ A ) @ A )
        = ( c_minus @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(91,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ c_0 @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_2) ).

thf(1281,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ c_0 @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(761,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).

thf(2769,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(707,axiom,
    class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).

thf(2653,plain,
    class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ c_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).

thf(1938,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ c_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(755,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).

thf(2758,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(810,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_OrderedGroup_Opprt @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).

thf(2873,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_OrderedGroup_Opprt @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(696,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_times @ ( c_minus @ B @ C @ A ) @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
        = ( c_minus @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).

thf(2628,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_times @ ( c_minus @ B @ C @ A ) @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
        = ( c_minus @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(716,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).

thf(2670,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(666,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
      | ( c_less @ B @ C @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).

thf(2565,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
      | ( c_less @ B @ C @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(962,axiom,
    ! [A: $i] :
      ( ( c_times @ A @ c_0 @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).

thf(3198,plain,
    ! [A: $i] :
      ( ( c_times @ A @ c_0 @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(713,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).

thf(2663,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_less @ C @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_1) ).

thf(1555,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_less @ C @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(785,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
       != c_0 )
      | ( c_Divides_Oop_Advd @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).

thf(2820,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
       != c_0 )
      | ( c_Divides_Oop_Advd @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(360,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).

thf(1888,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_less @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_7) ).

thf(1296,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_less @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(338,axiom,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).

thf(1836,plain,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(495,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_50) ).

thf(2181,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(562,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).

thf(2327,plain,
    class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(510,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A )
      | ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).

thf(2213,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A )
      | ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).

thf(1195,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(509,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_49) ).

thf(2211,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(249,axiom,
    ! [A: $i] :
      ( ~ ( c_lessequals @ c_0 @ A @ tc_IntDef_Oint )
      | ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).

thf(1634,plain,
    ! [A: $i] :
      ( ~ ( c_lessequals @ c_0 @ A @ tc_IntDef_Oint )
      | ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(517,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).

thf(2228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(461,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_21) ).

thf(2112,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_0) ).

thf(1291,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(887,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).

thf(3033,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(296,axiom,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ~ ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).

thf(1740,plain,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ~ ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(370,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ ( c_Suc @ ( c_Suc @ ( c_Suc @ B ) ) ) @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB1 ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).

thf(1910,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ ( c_Suc @ ( c_Suc @ ( c_Suc @ B ) ) ) @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB1 ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_plus @ ( c_Numeral_Onumber__of @ C @ A ) @ D @ A ) @ A )
        = ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ C ) @ A ) @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).

thf(1234,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_plus @ ( c_Numeral_Onumber__of @ C @ A ) @ D @ A ) @ A )
        = ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ C ) @ A ) @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(306,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_less @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_0) ).

thf(1762,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_less @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(776,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).

thf(2801,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(821,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_LOrder_Omeet @ B @ ( c_uminus @ B @ A ) @ A )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).

thf(2895,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_LOrder_Omeet @ B @ ( c_uminus @ B @ A ) @ A )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(794,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_IntDef_Oint )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).

thf(2841,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_IntDef_Oint )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).

thf(1587,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_divide @ C @ B @ A ) @ c_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__eq__1__neg_1) ).

thf(1540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_divide @ C @ B @ A ) @ c_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(906,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).

thf(3078,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(978,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_Suc @ ( c_minus @ A @ ( c_Suc @ c_0 ) @ tc_nat ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).

thf(3237,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_Suc @ ( c_minus @ A @ ( c_Suc @ c_0 ) @ tc_nat ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( c_Numeral_Obin__add @ c_Numeral_OPls @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).

thf(1118,plain,
    ! [A: $i] :
      ( ( c_Numeral_Obin__add @ c_Numeral_OPls @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_1 @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).

thf(1360,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_1 @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(525,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_LOrder_Ojoin @ B @ ( c_uminus @ B @ A ) @ A )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).

thf(2245,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_LOrder_Ojoin @ B @ ( c_uminus @ B @ A ) @ A )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(382,axiom,
    ! [B: $i,A: $i] :
      ( ( c_div @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      = ( c_div @ ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB1 ) @ tc_nat ) @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).

thf(1936,plain,
    ! [B: $i,A: $i] :
      ( ( c_div @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      = ( c_div @ ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB1 ) @ tc_nat ) @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(484,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_times @ B @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ A )
        = ( c_uminus @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).

thf(2157,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_times @ B @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ A )
        = ( c_uminus @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(35,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_1) ).

thf(1143,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(463,axiom,
    class_HOL_Ominus @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).

thf(2115,plain,
    class_HOL_Ominus @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(345,axiom,
    ! [A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).

thf(1851,plain,
    ! [A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(925,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( ( c_OrderedGroup_Onprt @ B @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).

thf(3122,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( ( c_OrderedGroup_Onprt @ B @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(868,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

thf(2990,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(321,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_lessequals @ c_0 @ ( c_divide @ c_1 @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__divide__1__iff_1) ).

thf(1794,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_lessequals @ c_0 @ ( c_divide @ c_1 @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(389,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_plus @ A @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).

thf(1953,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_plus @ A @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(578,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ B @ c_0 @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).

thf(2359,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ B @ c_0 @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(859,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_18) ).

thf(2973,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(970,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint )
      | ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).

thf(3218,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint )
      | ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(347,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A )
      | ( c_less @ c_0 @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).

thf(1856,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A )
      | ( c_less @ c_0 @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(15,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ c_0 @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ohalf__gt__zero_0) ).

thf(1096,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ c_0 @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(644,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_1) ).

thf(2509,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(917,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ c_0 @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le__neg_1) ).

thf(3102,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ c_0 @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_6) ).

thf(1672,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(741,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).

thf(2726,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(697,axiom,
    ! [A: $i] :
      ( ( c_div @ A @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = ( c_uminus @ A @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).

thf(2631,plain,
    ! [A: $i] :
      ( ( c_div @ A @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = ( c_uminus @ A @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(33,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_5) ).

thf(1138,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(802,axiom,
    class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).

thf(2858,plain,
    class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(1063,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ~ ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).

thf(3440,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ~ ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(965,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ c_0 @ B @ A )
        = ( c_times @ c_0 @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_1) ).

thf(3205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ c_0 @ B @ A )
        = ( c_times @ c_0 @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(899,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).

thf(3060,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(951,axiom,
    ! [A: $i] :
      ( ( c_less @ c_0 @ A @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).

thf(3176,plain,
    ! [A: $i] :
      ( ( c_less @ c_0 @ A @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(881,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).

thf(3018,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ ( c_plus @ A @ B @ tc_nat ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).

thf(1397,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ ( c_plus @ A @ B @ tc_nat ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(218,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).

thf(1567,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(622,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).

thf(2460,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ C @ A )
       != ( c_divide @ D @ C @ A ) )
      | ( B = D )
      | ( C = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__cancel__right_0) ).

thf(1329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ C @ A )
       != ( c_divide @ D @ C @ A ) )
      | ( B = D )
      | ( C = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(1016,axiom,
    ! [A: $i] :
      ( ( c_times @ c_0 @ A @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).

thf(3326,plain,
    ! [A: $i] :
      ( ( c_times @ c_0 @ A @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(936,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).

thf(3143,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(1048,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).

thf(3407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(913,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).

thf(3094,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(806,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).

thf(2868,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(445,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).

thf(2080,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(328,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( B = c_Numeral_Obit_OB0 )
      | ( ( c_div @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ C @ B ) @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = ( c_div @ ( c_plus @ ( c_Numeral_Onumber__of @ C @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_2) ).

thf(1810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( B = c_Numeral_Obit_OB0 )
      | ( ( c_div @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ C @ B ) @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = ( c_div @ ( c_plus @ ( c_Numeral_Onumber__of @ C @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(935,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ~ ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).

thf(3141,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ~ ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(812,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

thf(2877,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(394,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_less @ ( c_divide @ c_1 @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__0__1__iff_1) ).

thf(1964,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_less @ ( c_divide @ c_1 @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_1
       != ( c_divide @ B @ C @ A ) )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oeq__divide__eq__1_1) ).

thf(1942,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_1
       != ( c_divide @ B @ C @ A ) )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) @ B @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).

thf(1659,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) @ B @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(873,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).

thf(3000,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(561,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ochar_OChar @ A @ B )
       != ( c_List_Ochar_OChar @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).

thf(2323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ochar_OChar @ A @ B )
       != ( c_List_Ochar_OChar @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(952,axiom,
    ( ( c_Suc @ c_0 )
    = ( c_times @ c_1 @ c_1 @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).

thf(3179,plain,
    ( ( c_Suc @ c_0 )
    = ( c_times @ c_1 @ c_1 @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(790,axiom,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_0
        = ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).

thf(2830,plain,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_0
        = ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat ) @ tc_nat )
      | ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__gr__0_0) ).

thf(1182,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat ) @ tc_nat )
      | ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(153,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).

thf(1424,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(557,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).

thf(2312,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(877,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
      = ( c_List_Oreplicate @ ( c_minus @ B @ A @ tc_nat ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).

thf(3010,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
      = ( c_List_Oreplicate @ ( c_minus @ B @ A @ tc_nat ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(149,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ c_0 @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__self__if_0) ).

thf(1414,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ c_0 @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(502,axiom,
    ! [A: $i] :
      ( ( c_div @ A @ c_1 @ tc_IntDef_Oint )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).

thf(2196,plain,
    ! [A: $i] :
      ( ( c_div @ A @ c_1 @ tc_IntDef_Oint )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(341,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_times @ ( c_divide @ C @ B @ A ) @ B @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__self__left_1) ).

thf(1842,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_times @ ( c_divide @ C @ B @ A ) @ B @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(277,axiom,
    ! [A: $i] :
      ( ( c_IntDef_Onat @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).

thf(1700,plain,
    ! [A: $i] :
      ( ( c_IntDef_Onat @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(690,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ~ ( c_less @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less_0) ).

thf(2613,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ~ ( c_less @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(960,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_less @ c_0 @ A @ tc_nat )
      | ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).

thf(3194,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_less @ c_0 @ A @ tc_nat )
      | ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(573,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).

thf(2349,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(459,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

thf(2108,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(426,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ c_0 @ A @ tc_IntDef_Oint )
      | ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ A ) )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).

thf(2038,plain,
    ! [A: $i] :
      ( ( c_lessequals @ c_0 @ A @ tc_IntDef_Oint )
      | ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ A ) )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(163,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).

thf(1446,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(1003,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_0) ).

thf(3294,plain,
    ! [A: $i] :
      ( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(40,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ B ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_4) ).

thf(1155,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ B ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(980,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_IntDef_Oof__int @ B @ A )
       != ( c_IntDef_Oof__int @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).

thf(3242,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_IntDef_Oof__int @ B @ A )
       != ( c_IntDef_Oof__int @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(856,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).

thf(2968,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(83,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Numeral_Obin__mult @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) @ B )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__mult @ A @ B ) @ c_Numeral_Obit_OB0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).

thf(1263,plain,
    ! [B: $i,A: $i] :
      ( ( c_Numeral_Obin__mult @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) @ B )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__mult @ A @ B ) @ c_Numeral_Obit_OB0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(839,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).

thf(2932,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(655,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
        = c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).

thf(2536,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(589,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ~ ( c_less @ c_1 @ B @ tc_nat )
      | ( c_less @ ( c_div @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).

thf(2387,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ~ ( c_less @ c_1 @ B @ tc_nat )
      | ( c_less @ ( c_div @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(524,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).

thf(2243,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(624,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
      | ( c_less @ C @ ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).

thf(2465,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
      | ( c_less @ C @ ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(387,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( B = c_0 )
      | ( ( c_divide @ B @ B @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__eq__1_2) ).

thf(1947,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( B = c_0 )
      | ( ( c_divide @ B @ B @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(782,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ B @ ( c_uminus @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).

thf(2813,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ B @ ( c_uminus @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(922,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).

thf(3115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(900,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
       != ( c_times @ B @ C @ A ) )
      | ( B = c_0 )
      | ( C = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_0) ).

thf(3064,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
       != ( c_times @ B @ C @ A ) )
      | ( B = c_0 )
      | ( C = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(754,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_lessequals @ c_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_0) ).

thf(2756,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_lessequals @ c_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(38,axiom,
    ! [A: $i] :
      ( ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__minus @ A ) @ c_Numeral_Obit_OB0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).

thf(1150,plain,
    ! [A: $i] :
      ( ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__minus @ A ) @ c_Numeral_Obit_OB0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(179,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_NatArith_Oof__nat @ B @ A )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_0) ).

thf(1478,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_NatArith_Oof__nat @ B @ A )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(648,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_uminus @ A @ tc_IntDef_Oint ) @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = ( c_uminus @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).

thf(2519,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_uminus @ A @ tc_IntDef_Oint ) @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = ( c_uminus @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(200,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).

thf(1530,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(792,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_less @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).

thf(2836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_less @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_less @ C @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_1) ).

thf(1382,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_less @ C @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(796,axiom,
    ! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ A @ c_0 @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_2) ).

thf(2845,plain,
    ! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ A @ c_0 @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(682,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_less @ c_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__positive__iff__positive_0) ).

thf(2598,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_less @ c_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).

thf(1668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(399,axiom,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).

thf(1974,plain,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(576,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ B @ C @ tc_nat )
      | ~ ( c_less @ c_1 @ D @ A )
      | ( c_less @ ( c_Nat_Opower @ D @ B @ A ) @ ( c_Nat_Opower @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).

thf(2355,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ B @ C @ tc_nat )
      | ~ ( c_less @ c_1 @ D @ A )
      | ( c_less @ ( c_Nat_Opower @ D @ B @ A ) @ ( c_Nat_Opower @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(55,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).

thf(1192,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(642,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_45) ).

thf(2505,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(1042,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( c_times @ B @ C @ A )
       != c_0 )
      | ( C = c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).

thf(3390,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( c_times @ B @ C @ A )
       != c_0 )
      | ( C = c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(972,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).

thf(3222,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(638,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_less @ ( c_HOL_Oinverse @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__negative__iff__negative_1) ).

thf(2497,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_less @ ( c_HOL_Oinverse @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(1049,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_less @ c_0 @ A @ tc_nat )
      | ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).

thf(3409,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_less @ c_0 @ A @ tc_nat )
      | ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(804,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_minus @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ C @ tc_nat )
        = ( c_minus @ ( c_Suc @ B ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).

thf(2862,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_minus @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ C @ tc_nat )
        = ( c_minus @ ( c_Suc @ B ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(432,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).

thf(2052,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(632,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_NatArith_Oof__nat @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).

thf(2482,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_NatArith_Oof__nat @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(729,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).

thf(2697,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(904,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ~ ( c_lessequals @ c_0 @ C @ A )
      | ( c_lessequals @ c_0 @ ( c_times @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).

thf(3074,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ~ ( c_lessequals @ c_0 @ C @ A )
      | ( c_lessequals @ c_0 @ ( c_times @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(875,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_IntDef_Oint @ A )
       != ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).

thf(3005,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_IntDef_Oint @ A )
       != ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(908,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_less @ c_0 @ ( c_HOL_Oabs @ c_0 @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).

thf(3083,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_less @ c_0 @ ( c_HOL_Oabs @ c_0 @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(945,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).

thf(3162,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(139,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).

thf(1393,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(245,axiom,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).

thf(1627,plain,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(583,axiom,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_IntDef_Onat @ ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).

thf(2370,plain,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_IntDef_Onat @ ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(938,axiom,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ A @ ( c_Suc @ c_0 ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).

thf(3147,plain,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ A @ ( c_Suc @ c_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(836,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).

thf(2926,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(59,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
       != c_1 )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).

thf(1202,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
       != c_1 )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(731,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ c_1 @ B @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).

thf(2702,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ c_1 @ B @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(46,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Numeral_Obin__mult @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB1 ) @ B )
      = ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ ( c_Numeral_Obin__mult @ A @ B ) @ c_Numeral_Obit_OB0 ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).

thf(1170,plain,
    ! [B: $i,A: $i] :
      ( ( c_Numeral_Obin__mult @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB1 ) @ B )
      = ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ ( c_Numeral_Obin__mult @ A @ B ) @ c_Numeral_Obit_OB0 ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(595,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ A @ tc_nat ) @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).

thf(2402,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ A @ tc_nat ) @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(193,axiom,
    ! [A: $i] :
      ( ( ( c_IntDef_Oint @ A )
       != c_0 )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).

thf(1515,plain,
    ! [A: $i] :
      ( ( ( c_IntDef_Oint @ A )
       != c_0 )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(704,axiom,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Suc @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).

thf(2645,plain,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Suc @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ( c_div @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_0) ).

thf(1185,plain,
    ! [B: $i,A: $i] :
      ( ( c_div @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(568,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).

thf(2338,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(652,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ D @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_4) ).

thf(2529,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ D @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ C @ c_0 @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_2) ).

thf(1732,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ C @ c_0 @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(699,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).

thf(2634,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(751,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
      | ( ( c_Numeral_Onumber__of @ C @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).

thf(2749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
      | ( ( c_Numeral_Onumber__of @ C @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(158,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_times @ B @ ( c_divide @ C @ B @ A ) @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__self__right_1) ).

thf(1434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_times @ B @ ( c_divide @ C @ B @ A ) @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(428,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ B @ C @ tc_nat )
      | ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).

thf(2043,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ B @ C @ tc_nat )
      | ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(995,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).

thf(3279,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(434,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ~ ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ B @ A )
      | ( c_less @ C @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_8) ).

thf(2057,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ~ ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ B @ A )
      | ( c_less @ C @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_4) ).

thf(1712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(1008,axiom,
    ( ( c_times @ c_1 @ c_1 @ tc_nat )
    = ( c_Suc @ c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).

thf(3306,plain,
    ( ( c_times @ c_1 @ c_1 @ tc_nat )
    = ( c_Suc @ c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(854,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_uminus @ A @ ( tc_set @ B ) )
       != ( c_uminus @ C @ ( tc_set @ B ) ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).

thf(2963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_uminus @ A @ ( tc_set @ B ) )
       != ( c_uminus @ C @ ( tc_set @ B ) ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_0) ).

thf(1286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(1014,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).

thf(3321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = c_0 )
      | ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oneq__one__mod__two_0) ).

thf(1187,plain,
    ! [A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = c_0 )
      | ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(830,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Omeet__semilorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).

thf(2915,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Omeet__semilorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(612,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ A ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).

thf(2440,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ A ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(261,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_Parity_Oeven @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).

thf(1663,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_Parity_Oeven @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(958,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
      | ( c_less @ B @ c_0 @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).

thf(3190,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
      | ( c_less @ B @ c_0 @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ c_0 @ C @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_1) ).

thf(1895,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ c_0 @ C @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(45,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).

thf(1167,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(255,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
       != c_0 )
      | ( ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__eq__eq__number__of_1) ).

thf(1648,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
       != c_0 )
      | ( ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(411,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).

thf(2001,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(191,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ c_1 @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__1_0) ).

thf(1510,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ c_1 @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(302,axiom,
    ! [A: $i] :
      ( ( c_IntDef_Oint @ ( c_Suc @ A ) )
      = ( c_plus @ c_1 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).

thf(1754,plain,
    ! [A: $i] :
      ( ( c_IntDef_Oint @ ( c_Suc @ A ) )
      = ( c_plus @ c_1 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(825,axiom,
    ! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).

thf(2904,plain,
    ! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) @ ( c_Numeral_OBit @ B @ C ) )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__add @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).

thf(1103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) @ ( c_Numeral_OBit @ B @ C ) )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__add @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(737,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).

thf(2717,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(181,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ A @ tc_nat )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).

thf(1483,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ A @ tc_nat )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(669,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ B @ A )
        = ( c_uminus @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).

thf(2570,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ B @ A )
        = ( c_uminus @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(377,axiom,
    ( ( c_IntDef_Onat @ c_1 )
    = ( c_Suc @ c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).

thf(1927,plain,
    ( ( c_IntDef_Onat @ c_1 )
    = ( c_Suc @ c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(988,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_less @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).

thf(3262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_less @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(1000,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).

thf(3289,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(684,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_IntDef_Oint )
      = ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).

thf(2602,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_IntDef_Oint )
      = ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(993,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
        = ( c_div @ B @ C @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).

thf(3274,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
        = ( c_div @ B @ C @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(943,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).

thf(3158,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(307,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_lessequals @ c_0 @ C @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_2) ).

thf(1764,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_lessequals @ c_0 @ C @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(600,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).

thf(2413,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(1029,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint )
       != c_0 )
      | ( A
        = ( c_times @ B @ ( c_Main_Ozmod__eq__0D__dest__1 @ B @ A ) @ tc_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).

thf(3358,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint )
       != c_0 )
      | ( A
        = ( c_times @ B @ ( c_Main_Ozmod__eq__0D__dest__1 @ B @ A ) @ tc_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(529,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ B @ ( c_uminus @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).

thf(2253,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ B @ ( c_uminus @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).

thf(2033,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(891,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ c_0 @ A )
      | ~ ( c_less @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less__neg_0) ).

thf(3042,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ c_0 @ A )
      | ~ ( c_less @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(675,axiom,
    class_Power_Orecpower @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).

thf(2585,plain,
    class_Power_Orecpower @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(1036,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).

thf(3375,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ B @ ( c_times @ C @ B @ A ) @ A )
        = ( c_divide @ c_1 @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if1_1) ).

thf(1595,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ B @ ( c_times @ C @ B @ A ) @ A )
        = ( c_divide @ c_1 @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(745,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).

thf(2734,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(820,axiom,
    class_Orderings_Oorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

thf(2894,plain,
    class_Orderings_Oorder @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(130,axiom,
    ! [A: $i] :
      ( ( c_Parity_Oeven @ A @ tc_nat )
      | ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).

thf(1374,plain,
    ! [A: $i] :
      ( ( c_Parity_Oeven @ A @ tc_nat )
      | ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(650,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).

thf(2524,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(1044,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).

thf(3396,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(585,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_div @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
        = ( c_plus @ ( c_div @ B @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).

thf(2376,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_div @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
        = ( c_plus @ ( c_div @ B @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(1035,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
       != ( c_times @ C @ B @ A ) )
      | ( B = c_0 )
      | ( C = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).

thf(3372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
       != ( c_times @ C @ B @ A ) )
      | ( B = c_0 )
      | ( C = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(1041,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_times @ B @ C @ A )
       != C )
      | ( C = c_0 )
      | ( B = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right2_0) ).

thf(3387,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_times @ B @ C @ A )
       != C )
      | ( C = c_0 )
      | ( B = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(337,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_Numeral_Onumber__of @ c_Numeral_OPls @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).

thf(1833,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_Numeral_Onumber__of @ c_Numeral_OPls @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(857,axiom,
    class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).

thf(2970,plain,
    class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_uminus @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_uminus @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).

thf(2188,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_uminus @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_uminus @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(378,axiom,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ A @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).

thf(1929,plain,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ A @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(869,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_times @ B @ ( c_HOL_Oinverse @ B @ A ) @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oright__inverse_0) ).

thf(2991,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_times @ B @ ( c_HOL_Oinverse @ B @ A ) @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(144,axiom,
    ( ( c_Numeral_Obin__succ @ c_Numeral_OMin )
    = c_Numeral_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Min_0) ).

thf(1403,plain,
    ( ( c_Numeral_Obin__succ @ c_Numeral_OMin )
    = c_Numeral_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(788,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_minus @ ( c_minus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
      = ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).

thf(2827,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_minus @ ( c_minus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
      = ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(852,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
      | ( c_less @ B @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).

thf(2959,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
      | ( c_less @ B @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(977,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ c_0 )
       != ( c_times @ A @ B @ tc_nat ) )
      | ( B = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).

thf(3234,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ c_0 )
       != ( c_times @ A @ B @ tc_nat ) )
      | ( B = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(430,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).

thf(2048,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(803,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_4) ).

thf(2859,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(239,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).

thf(1615,plain,
    ! [B: $i,A: $i] :
      ( ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(985,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_0
       != ( c_HOL_Oabs @ B @ A ) )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).

thf(3255,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_0
       != ( c_HOL_Oabs @ B @ A ) )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(771,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( ( c_div @ A @ A @ tc_IntDef_Oint )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).

thf(2791,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( ( c_div @ A @ A @ tc_IntDef_Oint )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(979,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
      | ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).

thf(3240,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
      | ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(770,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_56) ).

thf(2789,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(27,axiom,
    ( ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB0 )
    = c_Numeral_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_OPls__0__eq_0) ).

thf(1125,plain,
    ( ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB0 )
    = c_Numeral_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(241,axiom,
    c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_1) ).

thf(1620,plain,
    c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(634,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).

thf(2489,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(301,axiom,
    ! [A: $i] :
      ( ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) )
      = ( c_Numeral_Onumber__of @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).

thf(1752,plain,
    ! [A: $i] :
      ( ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) )
      = ( c_Numeral_Onumber__of @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(592,axiom,
    ! [B: $i,A: $i] :
      ( ( c_less @ c_0 @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).

thf(2393,plain,
    ! [B: $i,A: $i] :
      ( ( c_less @ c_0 @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(910,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( ( c_HOL_Oabs @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_0) ).

thf(3086,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( ( c_HOL_Oabs @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(997,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).

thf(3283,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(718,axiom,
    class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).

thf(2674,plain,
    class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(417,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ ( c_HOL_Oinverse @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__inverse__eq_0) ).

thf(2016,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ ( c_HOL_Oinverse @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(646,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).

thf(2514,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(137,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_times @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__eq__eq__number__of_4) ).

thf(1388,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_times @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(992,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).

thf(3272,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(195,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ c_0 @ ( c_divide @ c_1 @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__less__divide__1__iff_1) ).

thf(1520,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ c_0 @ ( c_divide @ c_1 @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(1047,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).

thf(3404,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(784,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_minus @ B @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).

thf(2817,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_minus @ B @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(728,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).

thf(2695,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( c_Numeral_Obin__succ @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB1 ) )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__succ @ A ) @ c_Numeral_Obit_OB0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).

thf(1226,plain,
    ! [A: $i] :
      ( ( c_Numeral_Obin__succ @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB1 ) )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__succ @ A ) @ c_Numeral_Obit_OB0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ ( c_divide @ C @ B @ A ) @ c_1 @ A )
      | ( c_less @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__eq__1__neg_0) ).

thf(1428,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ ( c_divide @ C @ B @ A ) @ c_1 @ A )
      | ( c_less @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(188,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_times @ B @ c_0 @ A ) @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if2_0) ).

thf(1503,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_times @ B @ c_0 @ A ) @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(422,axiom,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).

thf(2029,plain,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(104,axiom,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oint @ ( c_plus @ A @ B @ tc_nat ) )
      = ( c_plus @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).

thf(1312,plain,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oint @ ( c_plus @ A @ B @ tc_nat ) )
      = ( c_plus @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(966,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_times @ A @ B @ tc_nat )
       != ( c_Suc @ c_0 ) )
      | ( B = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).

thf(3208,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_times @ A @ B @ tc_nat )
       != ( c_Suc @ c_0 ) )
      | ( B = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ c_1 @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__power2_0) ).

thf(1107,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ c_1 @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(409,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A )
      | ( c_less @ c_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).

thf(1997,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A )
      | ( c_less @ c_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(113,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).

thf(1332,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(613,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).

thf(2442,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(1052,axiom,
    ! [A: $i] :
      ( c_0
     != ( c_Suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).

thf(3416,plain,
    ! [A: $i] :
      ( c_0
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(281,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
       != ( c_IntDef_Oint @ B ) )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).

thf(1707,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
       != ( c_IntDef_Oint @ B ) )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(548,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A )
      | ( c_less @ ( c_uminus @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).

thf(2293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A )
      | ( c_less @ ( c_uminus @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(818,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).

thf(2891,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(86,axiom,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).

thf(1271,plain,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(129,axiom,
    ! [A: $i] :
      ( ~ ( c_lessequals @ A @ c_0 @ tc_IntDef_Oint )
      | ( ( c_IntDef_Onat @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).

thf(1371,plain,
    ! [A: $i] :
      ( ~ ( c_lessequals @ A @ c_0 @ tc_IntDef_Oint )
      | ( ( c_IntDef_Onat @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(840,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).

thf(2935,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(874,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
      | ( c_1 != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__neq__zero_0) ).

thf(3002,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
      | ( c_1 != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(364,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).

thf(1897,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(663,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).

thf(2557,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(1028,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( ( c_HOL_Oabs @ B @ A )
        = ( c_uminus @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).

thf(3355,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( ( c_HOL_Oabs @ B @ A )
        = ( c_uminus @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ A @ tc_nat )
      = ( c_Suc @ ( c_Suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).

thf(1224,plain,
    ! [A: $i] :
      ( ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ A @ tc_nat )
      = ( c_Suc @ ( c_Suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(670,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oordered__idom @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).

thf(2573,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oordered__idom @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(479,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_40) ).

thf(2148,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(556,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).

thf(2311,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(649,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).

thf(2521,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(739,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_4) ).

thf(2721,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(146,axiom,
    ( ( c_IntDef_Onat @ c_0 )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).

thf(1408,plain,
    ( ( c_IntDef_Onat @ c_0 )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(630,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).

thf(2478,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(703,axiom,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = ( c_IntDef_Onat @ ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_IntDef_Oint ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).

thf(2642,plain,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = ( c_IntDef_Onat @ ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_IntDef_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(604,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

thf(2422,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(1053,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Ochar_OChar @ A @ B ) @ tc_List_Ochar )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).

thf(3419,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Ochar_OChar @ A @ B ) @ tc_List_Ochar )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(228,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_3) ).

thf(1589,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(850,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).

thf(2955,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(206,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).

thf(1542,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(464,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).

thf(2116,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(324,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_divide @ c_1 @ B @ A ) @ A )
      | ( c_lessequals @ c_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__divide__1__iff_0) ).

thf(1801,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_divide @ c_1 @ B @ A ) @ A )
      | ( c_lessequals @ c_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(437,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).

thf(2065,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(447,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).

thf(2084,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(694,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).

thf(2624,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(601,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_0) ).

thf(2415,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(636,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).

thf(2493,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(221,axiom,
    ! [A: $i] :
      ( ( c_plus @ A @ c_0 @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(1574,plain,
    ! [A: $i] :
      ( ( c_plus @ A @ c_0 @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(326,axiom,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).

thf(1806,plain,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(763,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).

thf(2774,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(999,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).

thf(3287,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ~ ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ B @ A )
      | ( c_less @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_9) ).

thf(1524,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ~ ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ B @ A )
      | ( c_less @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(119,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).

thf(1349,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(454,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).

thf(2097,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(311,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A )
      | ( c_less @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).

thf(1771,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A )
      | ( c_less @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(845,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A )
      | ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).

thf(2945,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A )
      | ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(777,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ B ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_3) ).

thf(2802,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ B ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(933,axiom,
    c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_1) ).

thf(3138,plain,
    c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(273,axiom,
    ~ ( c_Parity_Oeven @ c_1 @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).

thf(1690,plain,
    ~ ( c_Parity_Oeven @ c_1 @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(954,axiom,
    ! [A: $i] :
      ~ ( c_less @ A @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).

thf(3182,plain,
    ! [A: $i] :
      ~ ( c_less @ A @ c_0 @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_NatArith_Oof__nat @ B @ A )
       != ( c_NatArith_Oof__nat @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).

thf(1571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_NatArith_Oof__nat @ B @ A )
       != ( c_NatArith_Oof__nat @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(809,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ C @ B @ A )
      | ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).

thf(2871,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ C @ B @ A )
      | ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(131,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ c_0 @ A )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).

thf(1376,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ c_0 @ A )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_4) ).

thf(1969,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(944,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( c_lessequals @ c_0 @ ( c_OrderedGroup_Opprt @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).

thf(3160,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( c_lessequals @ c_0 @ ( c_OrderedGroup_Opprt @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(175,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_54) ).

thf(1471,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
       != c_0 )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).

thf(1080,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
       != c_0 )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(748,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_1 @ A @ tc_IntDef_Oint )
      | ( c_less @ ( c_Suc @ c_0 ) @ ( c_IntDef_Onat @ A ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).

thf(2742,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_1 @ A @ tc_IntDef_Oint )
      | ( c_less @ ( c_Suc @ c_0 ) @ ( c_IntDef_Onat @ A ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(247,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ B @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_7) ).

thf(1630,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ( c_less @ B @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(532,axiom,
    ! [B: $i,A: $i] :
      ( ( c_minus @ c_emptyset @ A @ ( tc_set @ B ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).

thf(2261,plain,
    ! [B: $i,A: $i] :
      ( ( c_minus @ c_emptyset @ A @ ( tc_set @ B ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
       != c_1 )
      | ( c_less @ c_0 @ ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__gr__0_1) ).

thf(1162,plain,
    ! [A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
       != c_1 )
      | ( c_less @ c_0 @ ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(615,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).

thf(2446,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(959,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).

thf(3192,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(768,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ c_0 @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__positive__iff__positive_1) ).

thf(2785,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ c_0 @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(688,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).

thf(2610,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(885,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).

thf(3027,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(930,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ~ ( c_less @ c_0 @ C @ tc_nat )
      | ( c_less @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).

thf(3133,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ~ ( c_less @ c_0 @ C @ tc_nat )
      | ( c_less @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(897,axiom,
    ! [B: $i,A: $i] :
      ( ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).

thf(3055,plain,
    ! [B: $i,A: $i] :
      ( ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(213,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Parity_Oeven @ A @ tc_nat )
      | ( c_Parity_Oeven @ B @ tc_nat )
      | ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).

thf(1557,plain,
    ! [B: $i,A: $i] :
      ( ( c_Parity_Oeven @ A @ tc_nat )
      | ( c_Parity_Oeven @ B @ tc_nat )
      | ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(766,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_div @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).

thf(2780,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_div @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(535,axiom,
    ! [B: $i,A: $i] :
      ( ( c_div @ ( c_uminus @ A @ tc_IntDef_Oint ) @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = ( c_div @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).

thf(2267,plain,
    ! [B: $i,A: $i] :
      ( ( c_div @ ( c_uminus @ A @ tc_IntDef_Oint ) @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = ( c_div @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(339,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).

thf(1838,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ c_0 @ C @ A )
      | ~ ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ B @ A )
      | ( c_lessequals @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_9) ).

thf(1325,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ c_0 @ C @ A )
      | ~ ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ B @ A )
      | ( c_lessequals @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(657,axiom,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_1) ).

thf(2542,plain,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_uminus @ ( c_LOrder_Ojoin @ B @ C @ A ) @ A )
        = ( c_LOrder_Omeet @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).

thf(1460,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( ( c_uminus @ ( c_LOrder_Ojoin @ B @ C @ A ) @ A )
        = ( c_LOrder_Omeet @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(546,axiom,
    ! [A: $i] :
      ( ( c_minus @ A @ A @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).

thf(2289,plain,
    ! [A: $i] :
      ( ( c_minus @ A @ A @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(96,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ c_0 @ ( c_times @ B @ c_0 @ A ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if1_0) ).

thf(1293,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ c_0 @ ( c_times @ B @ c_0 @ A ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(541,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
      | ( c_lessequals @ B @ C @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).

thf(2278,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
      | ( c_lessequals @ B @ C @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(837,axiom,
    class_LOrder_Ojoin__semilorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).

thf(2928,plain,
    class_LOrder_Ojoin__semilorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(49,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_12) ).

thf(1177,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(133,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).

thf(1381,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(734,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).

thf(2710,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ C @ tc_nat )
        = ( c_minus @ ( c_plus @ B @ C @ tc_nat ) @ A @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).

thf(1820,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ C @ tc_nat )
        = ( c_minus @ ( c_plus @ B @ C @ tc_nat ) @ A @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(672,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_lessequals @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_6) ).

thf(2578,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_lessequals @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(272,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).

thf(1688,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(442,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).

thf(2075,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_Suc @ ( c_Suc @ A ) ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__Suc__Suc_0) ).

thf(1198,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_Suc @ ( c_Suc @ A ) ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(580,axiom,
    ! [A: $i] :
      ( ( c_div @ A @ c_0 @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).

thf(2365,plain,
    ! [A: $i] :
      ( ( c_div @ A @ c_0 @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(490,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oordered__ring__strict @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_38) ).

thf(2171,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oordered__ring__strict @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(63,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_0) ).

thf(1213,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(252,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).

thf(1643,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(475,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_15) ).

thf(2139,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(582,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).

thf(2369,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(552,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).

thf(2303,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(507,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).

thf(2207,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(439,axiom,
    ! [B: $i,A: $i] :
      ( ( c_plus @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = ( c_minus @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).

thf(2069,plain,
    ! [B: $i,A: $i] :
      ( ( c_plus @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = ( c_minus @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(216,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_IntDef_Oint @ A )
       != ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) )
      | ( A
        = ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).

thf(1562,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_IntDef_Oint @ A )
       != ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) )
      | ( A
        = ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(759,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_IntDef_Oint )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).

thf(2765,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_IntDef_Oint )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(1055,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs @ c_0 @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).

thf(3423,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs @ c_0 @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(660,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_1 @ B @ A )
      | ~ ( c_less @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A )
      | ( c_less @ C @ D @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).

thf(2550,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_1 @ B @ A )
      | ~ ( c_less @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A )
      | ( c_less @ C @ D @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(76,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_0) ).

thf(1245,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(1,negated_conjecture,
    ( ( v_f @ c_0 )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1066,plain,
    ( ( v_f @ c_0 )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).

thf(1528,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(920,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).

thf(3110,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(448,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A )
      | ( c_less @ B @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).

thf(2086,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A )
      | ( c_less @ B @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB0 ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).

thf(1113,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB0 ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(774,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).

thf(2797,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(752,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ c_Numeral_OPls @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).

thf(2752,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ c_Numeral_OPls @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).

thf(1775,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(679,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
      | ( C = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).

thf(2592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
      | ( C = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(698,axiom,
    ! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).

thf(2633,plain,
    ! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(1031,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
        = ( c_div @ B @ C @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).

thf(3363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
        = ( c_div @ B @ C @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(1010,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).

thf(3310,plain,
    ! [A: $i] :
      ( ~ ( c_less @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(591,axiom,
    c_0 != c_1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).

thf(2390,plain,
    c_0 != c_1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(78,axiom,
    ( ( c_Numeral_Obin__succ @ c_Numeral_OPls )
    = ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Pls_0) ).

thf(1250,plain,
    ( ( c_Numeral_Obin__succ @ c_Numeral_OPls )
    = ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(1025,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_times @ A @ B @ tc_nat ) @ A @ tc_nat )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).

thf(3348,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_times @ A @ B @ tc_nat ) @ A @ tc_nat )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(483,axiom,
    c_less @ c_0 @ c_1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).

thf(2156,plain,
    c_less @ c_0 @ c_1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
        = ( c_divide @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__divide__divide_0) ).

thf(1694,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
        = ( c_divide @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(727,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).

thf(2693,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(865,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ A @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).

thf(2984,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ A @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(398,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).

thf(1973,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(413,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( c_1
       != ( c_divide @ B @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__eq__divide__iff_1) ).

thf(2005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( c_1
       != ( c_divide @ B @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(433,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
        = c_0 )
      | ( ( c_divide @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__eq__eq__number__of_3) ).

thf(2054,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
        = c_0 )
      | ( ( c_divide @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(522,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ A )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).

thf(2239,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ A )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(225,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).

thf(1583,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(304,axiom,
    ( ( c_uminus @ ( c_IntDef_Oint @ c_0 ) @ tc_IntDef_Oint )
    = ( c_IntDef_Oint @ c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).

thf(1758,plain,
    ( ( c_uminus @ ( c_IntDef_Oint @ c_0 ) @ tc_IntDef_Oint )
    = ( c_IntDef_Oint @ c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(61,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_0
        = ( c_Numeral_Onumber__of @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).

thf(1208,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_0
        = ( c_Numeral_Onumber__of @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(714,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_8) ).

thf(2665,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(1002,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).

thf(3293,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( c_div @ ( c_plus @ A @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).

thf(1134,plain,
    ! [A: $i] :
      ( ( c_div @ ( c_plus @ A @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(617,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_minus @ C @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ tc_nat )
        = ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ ( c_Suc @ B ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).

thf(2449,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_minus @ C @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ tc_nat )
        = ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ ( c_Suc @ B ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(116,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( ( c_HOL_Oabs @ ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) @ A )
        = ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).

thf(1340,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( ( c_HOL_Oabs @ ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) @ A )
        = ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ C @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_6) ).

thf(1958,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ C @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(210,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_lessequals @ C @ c_0 @ A )
      | ( c_lessequals @ c_0 @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_3) ).

thf(1551,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_lessequals @ C @ c_0 @ A )
      | ( c_lessequals @ c_0 @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(354,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ B @ A )
       != c_1 )
      | ( B = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__eq__1__iff_0) ).

thf(1873,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ B @ A )
       != c_1 )
      | ( B = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(1057,axiom,
    ( c_1
    = ( c_Suc @ c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).

thf(3427,plain,
    ( c_1
    = ( c_Suc @ c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).

thf(1467,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_Parity_Oeven @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(870,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).

thf(2994,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(559,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ( c_less @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less_1) ).

thf(2318,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ( c_less @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(537,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_17) ).

thf(2271,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ~ ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ B @ A )
      | ( c_less @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_8) ).

thf(1905,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ~ ( c_less @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ B @ A )
      | ( c_less @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ( c_plus @ A @ ( c_Suc @ B ) @ tc_nat )
      = ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).

thf(1420,plain,
    ! [B: $i,A: $i] :
      ( ( c_plus @ A @ ( c_Suc @ B ) @ tc_nat )
      = ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(641,axiom,
    ! [A: $i] :
      ( ( c_Nat_Opower @ A @ c_0 @ tc_IntDef_Oint )
      = c_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).

thf(2503,plain,
    ! [A: $i] :
      ( ( c_Nat_Opower @ A @ c_0 @ tc_IntDef_Oint )
      = c_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_divide @ C @ B @ A ) @ c_1 @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__eq__1__neg_0) ).

thf(1684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_divide @ C @ B @ A ) @ c_1 @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(468,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_14) ).

thf(2124,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(520,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
      | ( c_lessequals @ C @ ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).

thf(2234,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
      | ( c_lessequals @ C @ ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(406,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).

thf(1990,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(894,axiom,
    ~ ( c_less @ c_0 @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).

thf(3048,plain,
    ~ ( c_less @ c_0 @ c_0 @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(505,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).

thf(2202,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(566,axiom,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_2) ).

thf(2333,plain,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ A )
        = ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower2__eq__square__number__of_0) ).

thf(1145,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ A )
        = ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(797,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).

thf(2846,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(844,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( A
        = ( c_Suc @ ( c_minus @ A @ c_1 @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).

thf(2942,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( A
        = ( c_Suc @ ( c_minus @ A @ c_1 @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(712,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_31) ).

thf(2661,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(861,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).

thf(2977,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(500,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ c_0 @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).

thf(2192,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_less @ c_0 @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(968,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).

thf(3214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_lessequals @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(477,axiom,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_Suc @ c_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).

thf(2143,plain,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Divides_Oop_Amod @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
        = ( c_Suc @ c_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(254,axiom,
    c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_1) ).

thf(1647,plain,
    c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(720,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).

thf(2678,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB1 ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).

thf(1098,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB1 ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(814,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).

thf(2882,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(726,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_11) ).

thf(2689,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(667,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).

thf(2567,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(342,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_less @ ( c_divide @ C @ B @ A ) @ c_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__eq__1__neg_1) ).

thf(1845,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_less @ ( c_divide @ C @ B @ A ) @ c_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(208,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_minus @ B @ C @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).

thf(1547,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_minus @ B @ C @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(299,axiom,
    ( ( c_Numeral_Onumber__of @ c_Numeral_OPls @ tc_nat )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__0__eq__0_0) ).

thf(1748,plain,
    ( ( c_Numeral_Onumber__of @ c_Numeral_OPls @ tc_nat )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(323,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Power_Orecpower @ A )
      | ( c_Parity_Oeven @ B @ tc_nat )
      | ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ B @ A )
        = ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).

thf(1798,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Power_Orecpower @ A )
      | ( c_Parity_Oeven @ B @ tc_nat )
      | ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ B @ A )
        = ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(550,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_plus @ B @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) @ A @ tc_nat )
        = ( c_plus @ C @ ( c_div @ B @ A @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).

thf(2298,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_plus @ B @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) @ A @ tc_nat )
        = ( c_plus @ C @ ( c_div @ B @ A @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(1012,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
       != c_0 )
      | ( A
        = ( c_times @ B @ ( c_Main_Omod__eq__0D__dest__1 @ B @ A ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).

thf(3315,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
       != c_0 )
      | ( A
        = ( c_times @ B @ ( c_Main_Omod__eq__0D__dest__1 @ B @ A ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_divide @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) )
      | ( ( c_Numeral_Onumber__of @ C @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oeq__divide__eq__number__of_3) ).

thf(1598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_divide @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) )
      | ( ( c_Numeral_Onumber__of @ C @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(4,negated_conjecture,
    v_x = c_0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(1070,plain,
    v_x = c_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(921,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ B @ C @ A )
       != ( c_times @ D @ C @ A ) )
      | ( B = D )
      | ( C = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_0) ).

thf(3112,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ B @ C @ A )
       != ( c_times @ D @ C @ A ) )
      | ( B = D )
      | ( C = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(987,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ B @ c_0 @ tc_IntDef_Oint )
      | ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).

thf(3260,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ B @ c_0 @ tc_IntDef_Oint )
      | ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(677,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).

thf(2588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(744,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
      | ( c_less @ c_0 @ ( c_IntDef_Onat @ A ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).

thf(2732,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
      | ( c_less @ c_0 @ ( c_IntDef_Onat @ A ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(79,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB0 ) )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__add @ A @ B ) @ c_Numeral_Obit_OB1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).

thf(1252,plain,
    ! [B: $i,A: $i] :
      ( ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB0 ) )
      = ( c_Numeral_OBit @ ( c_Numeral_Obin__add @ A @ B ) @ c_Numeral_Obit_OB1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_times @ B @ ( c_uminus @ C @ A ) @ A )
        = ( c_uminus @ ( c_times @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).

thf(1368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_times @ B @ ( c_uminus @ C @ A ) @ A )
        = ( c_uminus @ ( c_times @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(975,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_times @ B @ C @ A )
       != B )
      | ( B = c_0 )
      | ( C = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).

thf(3228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_times @ B @ C @ A )
       != B )
      | ( B = c_0 )
      | ( C = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(492,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Binomial_Obinomial @ ( c_Suc @ A ) @ ( c_Suc @ B ) )
      = ( c_plus @ ( c_Binomial_Obinomial @ A @ B ) @ ( c_Binomial_Obinomial @ A @ ( c_Suc @ B ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).

thf(2175,plain,
    ! [B: $i,A: $i] :
      ( ( c_Binomial_Obinomial @ ( c_Suc @ A ) @ ( c_Suc @ B ) )
      = ( c_plus @ ( c_Binomial_Obinomial @ A @ B ) @ ( c_Binomial_Obinomial @ A @ ( c_Suc @ B ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(597,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_51) ).

thf(2407,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(898,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).

thf(3058,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ( c_div @ ( c_Suc @ ( c_Suc @ A ) ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
      = ( c_Suc @ ( c_div @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).

thf(1230,plain,
    ! [A: $i] :
      ( ( c_div @ ( c_Suc @ ( c_Suc @ A ) ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat )
      = ( c_Suc @ ( c_div @ A @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(799,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).

thf(2850,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(485,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_42) ).

thf(2160,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(668,axiom,
    class_LOrder_Omeet__semilorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).

thf(2569,plain,
    class_LOrder_Omeet__semilorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(451,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_lessequals @ C @ c_0 @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_1) ).

thf(2092,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_lessequals @ C @ c_0 @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(833,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).

thf(2920,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(1023,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).

thf(3344,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(964,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_times @ B @ A @ tc_nat ) @ A @ tc_nat )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).

thf(3202,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_times @ B @ A @ tc_nat ) @ A @ tc_nat )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_times @ B @ c_0 @ A ) @ ( c_times @ C @ c_0 @ A ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if_0) ).

thf(1785,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_times @ B @ c_0 @ A ) @ ( c_times @ C @ c_0 @ A ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(607,axiom,
    ! [A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_0) ).

thf(2429,plain,
    ! [A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).

thf(1085,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(268,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ ( c_uminus @ B @ A ) @ A )
        = ( c_uminus @ ( c_HOL_Oinverse @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__minus__eq_0) ).

thf(1679,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ ( c_uminus @ B @ A ) @ A )
        = ( c_uminus @ ( c_HOL_Oinverse @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(950,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ c_0 @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).

thf(3174,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ c_0 @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(29,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A )
      | ~ ( c_lessequals @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_0) ).

thf(1130,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A )
      | ~ ( c_lessequals @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(626,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).

thf(2468,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(709,axiom,
    ! [A: $i] :
      ( ( class_OrderedGroup_Omonoid__mult @ ( tc_set @ A ) )
      | ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_14) ).

thf(2656,plain,
    ! [A: $i] :
      ( ( class_OrderedGroup_Omonoid__mult @ ( tc_set @ A ) )
      | ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(907,axiom,
    ! [A: $i] :
      ( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).

thf(3080,plain,
    ! [A: $i] :
      ( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).

thf(1790,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(405,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ c_0 @ B @ A )
        = ( c_divide @ c_0 @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__cancel__left_1) ).

thf(1987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ c_0 @ B @ A )
        = ( c_divide @ c_0 @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(285,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
      = ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).

thf(1716,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
      = ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(515,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).

thf(2224,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(619,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_1 @ B @ A )
      | ~ ( c_lessequals @ C @ D @ tc_nat )
      | ( c_lessequals @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).

thf(2454,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_1 @ B @ A )
      | ~ ( c_lessequals @ C @ D @ tc_nat )
      | ( c_lessequals @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__semidom @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).

thf(1432,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__semidom @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(487,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__mult @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).

thf(2165,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__mult @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_5) ).

thf(1813,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(99,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_1
       != ( c_divide @ B @ c_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oeq__divide__eq__1_0) ).

thf(1300,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_1
       != ( c_divide @ B @ c_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(166,axiom,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).

thf(1452,plain,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(250,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ c_0 @ ( c_divide @ B @ c_0 @ A ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__self__right_0) ).

thf(1637,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ c_0 @ ( c_divide @ B @ c_0 @ A ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(1019,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_times @ A @ B @ tc_nat )
       != c_0 )
      | ( B = c_0 )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).

thf(3334,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_times @ A @ B @ tc_nat )
       != c_0 )
      | ( B = c_0 )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(540,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).

thf(2276,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(513,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ B @ c_1 @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).

thf(2219,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ B @ c_1 @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(402,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint )
      | ( c_less @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).

thf(1980,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint )
      | ( c_less @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(470,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_nat )
      = ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).

thf(2128,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_nat )
      = ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ C @ A )
       != c_1 )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__1__iff_1) ).

thf(1830,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ C @ A )
       != c_1 )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(927,axiom,
    ! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).

thf(3127,plain,
    ! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(204,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).

thf(1538,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(658,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
      | ( c_less @ c_0 @ c_0 @ A )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).

thf(2545,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
      | ( c_less @ c_0 @ c_0 @ A )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(295,axiom,
    ! [A: $i] :
      ( ( c_Numeral_Obin__mult @ c_Numeral_OMin @ A )
      = ( c_Numeral_Obin__minus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).

thf(1738,plain,
    ! [A: $i] :
      ( ( c_Numeral_Obin__mult @ c_Numeral_OMin @ A )
      = ( c_Numeral_Obin__minus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(65,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( c_1
       != ( c_Numeral_Onumber__of @ B @ A ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).

thf(1218,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( c_1
       != ( c_Numeral_Onumber__of @ B @ A ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(719,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_times @ c_1 @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).

thf(2675,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_times @ c_1 @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(381,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).

thf(1934,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(599,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_nat ) @ A @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).

thf(2411,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_nat ) @ A @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(793,axiom,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_0
        = ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_2) ).

thf(2838,plain,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_0
        = ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(973,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).

thf(3224,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(264,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat )
      = ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).

thf(1670,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat )
      = ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(742,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).

thf(2728,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(842,axiom,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).

thf(2939,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(1045,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_IntDef_Oof__int @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).

thf(3398,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_IntDef_Oof__int @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).

thf(308,axiom,
    c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ ( c_Suc @ c_0 ) @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_1) ).

thf(1766,plain,
    c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ ( c_Suc @ c_0 ) @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(919,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_0
       != ( c_IntDef_Oof__int @ B @ A ) )
      | ( c_0 = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).

thf(3107,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_0
       != ( c_IntDef_Oof__int @ B @ A ) )
      | ( c_0 = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(344,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).

thf(1849,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
       != c_0 )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1) ).

thf(1257,plain,
    ! [A: $i] :
      ( ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
       != c_0 )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(34,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_1) ).

thf(1141,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(606,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( ( c_List_Odrop @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_0) ).

thf(2426,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( ( c_List_Odrop @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_3) ).

thf(1536,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(278,axiom,
    ! [A: $i] :
      ~ ( c_less @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).

thf(1702,plain,
    ! [A: $i] :
      ~ ( c_less @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(586,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ c_0 @ ( c_Suc @ B ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).

thf(2379,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Nat_Opower @ c_0 @ ( c_Suc @ B ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
        = ( c_Numeral_Onumber__of @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).

thf(1221,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
        = ( c_Numeral_Onumber__of @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(860,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).

thf(2975,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_less @ c_0 @ C @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_1) ).

thf(1353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_less @ c_0 @ C @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(577,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ B ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_0) ).

thf(2357,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ B ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(795,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_48) ).

thf(2843,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(560,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Nat_Opower @ B @ C @ A )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).

thf(2320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Nat_Opower @ B @ C @ A )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(189,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).

thf(1506,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ c_Numeral_OPls ) ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(226,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).

thf(1585,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(645,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
      | ( ( c_Numeral_Onumber__of @ C @ tc_nat )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).

thf(2511,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
      | ( ( c_Numeral_Onumber__of @ C @ tc_nat )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(923,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_times @ A @ B @ tc_nat )
       != ( c_Suc @ c_0 ) )
      | ( A = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).

thf(3117,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_times @ A @ B @ tc_nat )
       != ( c_Suc @ c_0 ) )
      | ( A = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(847,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_IntDef_Onat @ A ) @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).

thf(2949,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_IntDef_Onat @ A ) @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(357,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).

thf(1881,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(780,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Nat_Opower @ B @ C @ A )
       != c_0 )
      | ( c_less @ c_0 @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).

thf(2807,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Nat_Opower @ B @ C @ A )
       != c_0 )
      | ( c_less @ c_0 @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(87,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_lessequals @ C @ B @ A )
      | ( c_lessequals @ c_1 @ ( c_divide @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ole__divide__eq__1__neg_1) ).

thf(1272,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_lessequals @ C @ B @ A )
      | ( c_lessequals @ c_1 @ ( c_divide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(942,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).

thf(3156,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(798,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).

thf(2848,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(1032,axiom,
    ! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

thf(3366,plain,
    ! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(74,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_7) ).

thf(1240,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
        = ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_times @ c_0 @ B @ A ) @ ( c_times @ c_0 @ C @ A ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if_0) ).

thf(1617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_times @ c_0 @ B @ A ) @ ( c_times @ c_0 @ C @ A ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(756,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).

thf(2760,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(1060,axiom,
    ! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).

thf(3433,plain,
    ! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(934,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ c_1 @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).

thf(3139,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ c_1 @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(621,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).

thf(2458,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(395,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).

thf(1966,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ ( c_divide @ C @ B @ A ) @ c_1 @ A )
      | ( c_less @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__eq__1__pos_0) ).

thf(1553,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ ( c_divide @ C @ B @ A ) @ c_1 @ A )
      | ( c_less @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(808,axiom,
    class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).

thf(2870,plain,
    class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(949,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( ( c_times @ c_0 @ B @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).

thf(3171,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( ( c_times @ c_0 @ B @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(511,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).

thf(2215,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(890,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_times @ B @ c_1 @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).

thf(3039,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_times @ B @ c_1 @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(805,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_uminus @ c_1 @ A )
        = ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).

thf(2865,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_uminus @ c_1 @ A )
        = ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(948,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).

thf(3168,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(384,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_plus @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).

thf(1940,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_plus @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(416,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ A )
        = ( c_uminus @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__minus1_0) ).

thf(2013,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ A )
        = ( c_uminus @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(835,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ c_0 @ A )
      | ( c_less @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less__neg_1) ).

thf(2924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ c_0 @ A )
      | ( c_less @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(695,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ ( c_OrderedGroup_Onprt @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).

thf(2626,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ ( c_OrderedGroup_Onprt @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_times @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) )
      | ( ( c_Numeral_Onumber__of @ C @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__eq__eq__number__of_0) ).

thf(1316,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_times @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) )
      | ( ( c_Numeral_Onumber__of @ C @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(1046,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_times @ A @ B @ tc_nat )
       != ( c_times @ A @ C @ tc_nat ) )
      | ( B = C )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).

thf(3401,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_times @ A @ B @ tc_nat )
       != ( c_times @ A @ C @ tc_nat ) )
      | ( B = C )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(449,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_4) ).

thf(2088,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(429,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_HOL_Oabs @ ( c_divide @ B @ C @ A ) @ A )
        = ( c_divide @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__divide_0) ).

thf(2045,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_HOL_Oabs @ ( c_divide @ B @ C @ A ) @ A )
        = ( c_divide @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(912,axiom,
    ! [B: $i,A: $i] :
      ( ( c_times @ A @ c_0 @ tc_nat )
      = ( c_times @ B @ c_0 @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_1) ).

thf(3092,plain,
    ! [B: $i,A: $i] :
      ( ( c_times @ A @ c_0 @ tc_nat )
      = ( c_times @ B @ c_0 @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(901,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).

thf(3067,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_0) ).

thf(1180,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(41,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_0) ).

thf(1157,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(444,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ~ ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat )
      | ( c_Parity_Oeven @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).

thf(2078,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ~ ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat )
      | ( c_Parity_Oeven @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(957,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_lessequals @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).

thf(3188,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_lessequals @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(501,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).

thf(2194,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(572,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ C ) @ A ) @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).

thf(2347,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ C ) @ A ) @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(257,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_times @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
        = ( c_times @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).

thf(1654,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_times @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
        = ( c_times @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(148,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ c_1 @ ( c_divide @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oless__divide__eq__1__pos_1) ).

thf(1412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ c_1 @ ( c_divide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(315,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_0) ).

thf(1781,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_less @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(508,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ C ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).

thf(2209,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ C ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).

thf(1448,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(1024,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).

thf(3346,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(460,axiom,
    ! [A: $i] :
      ( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_set @ A ) )
      | ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_15) ).

thf(2110,plain,
    ! [A: $i] :
      ( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_set @ A ) )
      | ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(553,axiom,
    ! [A: $i] :
      ( ( c_minus @ A @ c_0 @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).

thf(2305,plain,
    ! [A: $i] :
      ( ( c_minus @ A @ c_0 @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(832,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).

thf(2919,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(570,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).

thf(2342,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(516,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).

thf(2226,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_5) ).

thf(1453,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(351,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).

thf(1866,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(440,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ c_1 @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).

thf(2071,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ c_1 @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(710,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).

thf(2658,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(293,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).

thf(1734,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(327,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != ( c_plus @ A @ C @ tc_nat ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).

thf(1807,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != ( c_plus @ A @ C @ tc_nat ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ c_0 @ A )
        = ( c_divide @ C @ c_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__cancel__right_1) ).

thf(1276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ c_0 @ A )
        = ( c_divide @ C @ c_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(253,axiom,
    c_Parity_Oeven @ c_0 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).

thf(1646,plain,
    c_Parity_Oeven @ c_0 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(733,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
      | ( A = c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).

thf(2707,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
      | ( A = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(538,axiom,
    class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).

thf(2273,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(662,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).

thf(2554,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).

thf(1508,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(180,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).

thf(1481,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(918,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_times @ B @ c_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).

thf(3104,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_times @ B @ c_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(298,axiom,
    ! [A: $i] :
      ( ~ ( c_lessequals @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).

thf(1745,plain,
    ! [A: $i] :
      ( ~ ( c_lessequals @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(858,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ ( c_Suc @ c_0 ) @ ( c_IntDef_Onat @ A ) @ tc_nat )
      | ( c_less @ c_1 @ A @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).

thf(2971,plain,
    ! [A: $i] :
      ( ~ ( c_less @ ( c_Suc @ c_0 ) @ ( c_IntDef_Onat @ A ) @ tc_nat )
      | ( c_less @ c_1 @ A @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(346,axiom,
    ! [A: $i] :
      ( ( c_NatArith_Oof__nat @ A @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).

thf(1854,plain,
    ! [A: $i] :
      ( ( c_NatArith_Oof__nat @ A @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(687,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ B @ C @ tc_IntDef_Oint )
      | ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).

thf(2608,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ B @ C @ tc_IntDef_Oint )
      | ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(758,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(2764,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(471,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_1) ).

thf(2130,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(984,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ B @ c_0 @ A )
        = ( c_times @ C @ c_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_1) ).

thf(3252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ B @ c_0 @ A )
        = ( c_times @ C @ c_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(481,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_plus @ B @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) @ A @ tc_nat )
        = ( c_plus @ C @ ( c_div @ B @ A @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).

thf(2152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ ( c_plus @ B @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) @ A @ tc_nat )
        = ( c_plus @ C @ ( c_div @ B @ A @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(909,axiom,
    c_lessequals @ c_0 @ c_0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).

thf(3085,plain,
    c_lessequals @ c_0 @ c_0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(867,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).

thf(2988,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_minus @ B @ C @ A ) @ c_0 @ A )
      | ( c_less @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).

thf(1721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_minus @ B @ C @ A ) @ c_0 @ A )
      | ( c_less @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(544,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_times @ ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A )
        = ( c_times @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ B ) @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).

thf(2283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_times @ ( c_uminus @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A )
        = ( c_times @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__minus @ B ) @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(590,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).

thf(2389,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).

thf(1476,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(266,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_NatArith_Oof__nat @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_1) ).

thf(1674,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_NatArith_Oof__nat @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(801,axiom,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = ( c_IntDef_Onat @ ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).

thf(2855,plain,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = ( c_IntDef_Onat @ ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(367,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).

thf(1903,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(473,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).

thf(2135,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(1034,axiom,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).

thf(3369,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(786,axiom,
    ! [A: $i] :
      ~ ( c_less @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(2823,plain,
    ! [A: $i] :
      ~ ( c_less @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(971,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ~ ( c_less @ c_0 @ C @ tc_nat )
      | ( c_less @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).

thf(3220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ~ ( c_less @ c_0 @ C @ tc_nat )
      | ( c_less @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(1018,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( ( c_HOL_Oabs @ ( c_HOL_Oabs @ B @ A ) @ A )
        = ( c_HOL_Oabs @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).

thf(3331,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( ( c_HOL_Oabs @ ( c_HOL_Oabs @ B @ A ) @ A )
        = ( c_HOL_Oabs @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(932,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
      | ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).

thf(3136,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
      | ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(184,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_0
        = ( c_NatArith_Oof__nat @ c_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_1) ).

thf(1491,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_0
        = ( c_NatArith_Oof__nat @ c_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(773,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).

thf(2796,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(990,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).

thf(3267,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ c_1 @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__0__1__iff_0) ).

thf(1661,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ c_1 @ B @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(453,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).

thf(2095,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(518,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ c_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).

thf(2230,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ c_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(558,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Odrop @ ( c_minus @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ c_1 @ tc_nat ) @ C @ D ) )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_1) ).

thf(2315,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Odrop @ ( c_minus @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ c_1 @ tc_nat ) @ C @ D ) )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(831,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).

thf(2917,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(418,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_less @ c_0 @ c_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).

thf(2019,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_less @ c_0 @ c_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(953,axiom,
    ! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(3181,plain,
    ! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(588,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
       != c_0 )
      | ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_0) ).

thf(2384,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
       != c_0 )
      | ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(594,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_divide @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oinverse__eq__divide__number__of_0) ).

thf(2399,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_divide @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(427,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_less @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_1) ).

thf(2041,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_less @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(705,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).

thf(2648,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(314,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).

thf(1777,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(160,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ~ ( c_Parity_Oeven @ B @ tc_nat )
      | ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).

thf(1440,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_nat )
      | ~ ( c_Parity_Oeven @ B @ tc_nat )
      | ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(939,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_IntDef_Oof__int @ B @ A )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).

thf(3149,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_IntDef_Oof__int @ B @ A )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(564,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).

thf(2330,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_0) ).

thf(1308,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(503,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_1 @ B @ A )
      | ~ ( c_lessequals @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A )
      | ( c_lessequals @ C @ D @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).

thf(2198,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_less @ c_1 @ B @ A )
      | ~ ( c_lessequals @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A )
      | ( c_lessequals @ C @ D @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).

thf(1077,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) ) ) @ A ) @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(579,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).

thf(2362,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(486,axiom,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).

thf(2162,plain,
    ! [A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(721,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_lessequals @ C @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_6) ).

thf(2680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_lessequals @ C @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(496,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_53) ).

thf(2183,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(1026,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).

thf(3351,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(192,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_3) ).

thf(1513,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ B @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(824,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ D @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_1) ).

thf(2902,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ D @ ( c_times @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(466,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_IntDef_Oint )
      | ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).

thf(2120,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_IntDef_Oint )
      | ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
      | ( c_less @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).

thf(1444,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_less @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
      | ( c_less @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(161,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_less @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_3) ).

thf(1442,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ C @ A ) @ c_0 @ A )
      | ( c_less @ ( c_divide @ D @ ( c_Numeral_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(531,axiom,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__mult @ A @ B ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).

thf(2258,plain,
    ! [B: $i,A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_times @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__mult @ A @ B ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ C @ c_0 @ A )
      | ( c_lessequals @ c_0 @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_3) ).

thf(2102,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ c_0 @ A )
      | ( c_lessequals @ C @ c_0 @ A )
      | ( c_lessequals @ c_0 @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(723,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( ( c_Nat_Opower @ c_0 @ B @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).

thf(2683,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( ( c_Nat_Opower @ c_0 @ B @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(289,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__0__iff_2) ).

thf(1725,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(223,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ c_1 @ B @ A ) @ c_0 @ A )
      | ( c_less @ B @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__0__1__iff_0) ).

thf(1578,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_divide @ c_1 @ B @ A ) @ c_0 @ A )
      | ( c_less @ B @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(1001,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).

thf(3291,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(738,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_1) ).

thf(2719,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(989,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_times @ c_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).

thf(3264,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_times @ c_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(916,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_less @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).

thf(3100,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_less @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(848,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).

thf(2951,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(355,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_divide @ B @ c_0 @ A )
       != c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__eq__1_0) ).

thf(1876,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_divide @ B @ c_0 @ A )
       != c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(431,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ B @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_2) ).

thf(2050,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ B @ c_0 @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(946,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
      | ( c_lessequals @ c_0 @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).

thf(3164,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
      | ( c_lessequals @ c_0 @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat )
      = ( c_minus @ A @ ( c_plus @ B @ C @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).

thf(2003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat )
      = ( c_minus @ A @ ( c_plus @ B @ C @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(1038,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( ( c_HOL_Oabs @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).

thf(3379,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( ( c_HOL_Oabs @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(482,axiom,
    class_Numeral_Onumber__ring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).

thf(2155,plain,
    class_Numeral_Onumber__ring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(530,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_div @ A @ B @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).

thf(2255,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_div @ A @ B @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_less @ C @ c_0 @ A )
      | ( c_less @ c_0 @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_3) ).

thf(1395,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_less @ C @ c_0 @ A )
      | ( c_less @ c_0 @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oreplicate @ ( c_Suc @ A ) @ B @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).

thf(1625,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oreplicate @ ( c_Suc @ A ) @ B @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(230,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ c_0 @ c_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).

thf(1593,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ c_0 @ c_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(685,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).

thf(2604,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(783,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).

thf(2815,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(414,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_5) ).

thf(2008,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ c_0 @ A )
      | ~ ( c_less @ C @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ A )
      | ( ( c_LOrder_Ojoin @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).

thf(1303,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ A )
      | ( ( c_LOrder_Ojoin @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(1020,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).

thf(3337,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB0 ) @ A ) @ A )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).

thf(1148,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ c_Numeral_Obit_OB0 ) @ A ) @ A )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(880,axiom,
    ! [A: $i] :
      ( ( c_0
       != ( c_Numeral_Onumber__of @ A @ tc_nat ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_0) ).

thf(3015,plain,
    ! [A: $i] :
      ( ( c_0
       != ( c_Numeral_Onumber__of @ A @ tc_nat ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(1017,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ c_0 )
       != ( c_times @ A @ B @ tc_nat ) )
      | ( A = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).

thf(3328,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ c_0 )
       != ( c_times @ A @ B @ tc_nat ) )
      | ( A = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(258,axiom,
    ! [A: $i] :
      ( ( c_plus @ c_0 @ A @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).

thf(1657,plain,
    ! [A: $i] :
      ( ( c_plus @ c_0 @ A @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(994,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
      | ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).

thf(3277,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
      | ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(750,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(2746,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(215,axiom,
    ! [A: $i] : ( c_Divides_Oop_Advd @ c_1 @ A @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).

thf(1561,plain,
    ! [A: $i] : ( c_Divides_Oop_Advd @ c_1 @ A @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(886,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).

thf(3030,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(176,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).

thf(1473,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(5,negated_conjecture,
    ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ v_x ) @ t_a ) @ t_a ) @ t_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(1065,plain,
    ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ v_x ) @ t_a ) @ t_a ) @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(893,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs @ c_1 @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).

thf(3045,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs @ c_1 @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(767,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).

thf(2783,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(297,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_times @ c_0 @ B @ A ) @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if2_0) ).

thf(1742,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ ( c_times @ c_0 @ B @ A ) @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(937,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).

thf(3145,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(700,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_0) ).

thf(2636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_divide @ B @ C @ A )
       != c_1 )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__eq__1_1) ).

thf(1363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_divide @ B @ C @ A )
       != c_1 )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(105,axiom,
    ! [B: $i,A: $i] :
      ( ( c_times @ A @ ( c_Suc @ B ) @ tc_nat )
      = ( c_plus @ A @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).

thf(1314,plain,
    ! [B: $i,A: $i] :
      ( ( c_times @ A @ ( c_Suc @ B ) @ tc_nat )
      = ( c_plus @ A @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_1) ).

thf(1172,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ B @ ( c_Numeral_Obin__minus @ C ) ) @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(147,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).

thf(1410,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(602,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_div @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).

thf(2417,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_div @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(853,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).

thf(2961,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
      | ~ ( c_less @ c_0 @ B @ tc_nat )
      | ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ ( c_times @ B @ C @ A ) @ B @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if2_1) ).

thf(1288,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_divide @ ( c_times @ B @ C @ A ) @ B @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A )
      | ( c_lessequals @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_9) ).

thf(1710,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ C @ A )
      | ( c_lessequals @ B @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(829,axiom,
    ! [A: $i] :
      ( ( c_div @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
      = ( c_IntDef_Onat @ ( c_div @ c_1 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).

thf(2913,plain,
    ! [A: $i] :
      ( ( c_div @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
      = ( c_IntDef_Onat @ ( c_div @ c_1 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(1015,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).

thf(3323,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(736,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
      | ( c_0 != c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) ).

thf(2714,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
      | ( c_0 != c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(961,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le_1) ).

thf(3196,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_0 @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse @ C @ A ) @ ( c_HOL_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(569,axiom,
    ! [A: $i] :
      ( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_set @ A ) )
      | ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_13) ).

thf(2340,plain,
    ! [A: $i] :
      ( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_set @ A ) )
      | ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(715,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).

thf(2668,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(44,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_1) ).

thf(1165,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(419,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ C @ A )
       != c_0 )
      | ( C = c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__0__iff_0) ).

thf(2021,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_divide @ B @ C @ A )
       != c_0 )
      | ( C = c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(237,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_divide @ c_1 @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__divide__eq__0__iff_1) ).

thf(1610,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_divide @ c_1 @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(640,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).

thf(2502,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(781,axiom,
    ! [A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
        = ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).

thf(2810,plain,
    ! [A: $i] :
      ( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
        = ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(884,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).

thf(3025,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(39,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( c_0
       != ( c_Numeral_Onumber__of @ B @ A ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).

thf(1152,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( c_0
       != ( c_Numeral_Onumber__of @ B @ A ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ c_Numeral_OPls @ ( c_Numeral_Obin__minus @ B ) ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(201,axiom,
    ! [A: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).

thf(1532,plain,
    ! [A: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(534,axiom,
    ! [A: $i] :
      ( ( c_minus @ c_0 @ A @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).

thf(2265,plain,
    ! [A: $i] :
      ( ( c_minus @ c_0 @ A @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(625,axiom,
    class_Power_Orecpower @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).

thf(2467,plain,
    class_Power_Orecpower @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(643,axiom,
    ! [B: $i,A: $i] :
      ( ( c_minus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      = ( c_minus @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).

thf(2507,plain,
    ! [B: $i,A: $i] :
      ( ( c_minus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      = ( c_minus @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(656,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( ( c_minus @ A @ B @ ( tc_set @ C ) )
        = c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).

thf(2539,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( ( c_minus @ A @ B @ ( tc_set @ C ) )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(725,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).

thf(2687,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(730,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs @ ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ B @ A ) @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).

thf(2699,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs @ ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ B @ A ) @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_minus @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).

thf(1120,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( ( c_minus @ c_1 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
        = ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ ( c_Numeral_Obin__minus @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(1022,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ A ) @ B @ A ) @ A )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).

thf(3341,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ A ) @ B @ A ) @ A )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_9) ).

thf(1093,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ~ ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ ( c_Numeral_Obin__add @ A @ ( c_Numeral_Obin__minus @ B ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ A @ tc_nat )
        = ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(379,axiom,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).

thf(1930,plain,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(575,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
      | ( c_less @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).

thf(2353,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
      | ( c_less @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(928,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( ( c_OrderedGroup_Opprt @ B @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).

thf(3128,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ~ ( c_lessequals @ B @ c_0 @ A )
      | ( ( c_OrderedGroup_Opprt @ B @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(401,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_LOrder_Omeet__semilorder @ A )
      | ( ( c_LOrder_Omeet @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).

thf(1977,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_LOrder_Omeet__semilorder @ A )
      | ( ( c_LOrder_Omeet @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(855,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_11) ).

thf(2966,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(85,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2_0) ).

thf(1268,plain,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(683,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).

thf(2600,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(822,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
       != c_0 )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).

thf(2898,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
       != c_0 )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      = ( c_Divides_Oop_Amod @ ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB1 ) @ tc_nat ) @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).

thf(1384,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
      = ( c_Divides_Oop_Amod @ ( c_plus @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ ( c_Numeral_OBit @ c_Numeral_OPls @ c_Numeral_Obit_OB1 ) @ c_Numeral_Obit_OB1 ) @ tc_nat ) @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(1050,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ B @ C @ A )
       != ( c_times @ B @ D @ A ) )
      | ( C = D )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_0) ).

thf(3411,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_times @ B @ C @ A )
       != ( c_times @ B @ D @ A ) )
      | ( C = D )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(633,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ochar_OChar @ A @ B )
       != ( c_List_Ochar_OChar @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).

thf(2485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ochar_OChar @ A @ B )
       != ( c_List_Ochar_OChar @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(123,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_1) ).

thf(1357,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(674,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A )
      | ( c_lessequals @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_8) ).

thf(2583,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A )
      | ~ ( c_lessequals @ C @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_times @ D @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ C @ A )
      | ( c_lessequals @ ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(187,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
       != ( c_IntDef_Oint @ B ) )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).

thf(1500,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
       != ( c_IntDef_Oint @ B ) )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(981,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( ( c_HOL_Oabs @ B @ A )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).

thf(3245,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( ( c_HOL_Oabs @ B @ A )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(905,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).

thf(3076,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(366,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).

thf(1902,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(142,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_1 @ ( c_divide @ C @ B @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oless__divide__eq__1__pos_0) ).

thf(1399,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_less @ c_1 @ ( c_divide @ C @ B @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(242,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oordered__semidom @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_60) ).

thf(1621,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oordered__semidom @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(879,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_8) ).

thf(3013,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(235,axiom,
    ! [A: $i] :
      ( ( c_Numeral_Obin__mult @ c_Numeral_OPls @ A )
      = c_Numeral_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).

thf(1606,plain,
    ! [A: $i] :
      ( ( c_Numeral_Obin__mult @ c_Numeral_OPls @ A )
      = c_Numeral_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(753,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).

thf(2754,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(1062,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( ( c_HOL_Oabs @ c_0 @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).

thf(3437,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( ( c_HOL_Oabs @ c_0 @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_less @ C @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_4) ).

thf(1962,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ B @ ( c_times @ C @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_less @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A )
      | ( c_less @ C @ ( c_divide @ B @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(914,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).

thf(3096,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ B @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ D @ A ) @ C @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ D @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(610,axiom,
    ! [A: $i] :
      ( ( c_div @ c_0 @ A @ tc_IntDef_Oint )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).

thf(2436,plain,
    ! [A: $i] :
      ( ( c_div @ c_0 @ A @ tc_IntDef_Oint )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(435,axiom,
    ! [A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).

thf(2059,plain,
    ! [A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(611,axiom,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ A @ A )
      = c_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).

thf(2438,plain,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ A @ A )
      = c_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(896,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).

thf(3052,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(963,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).

thf(3200,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_less @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ ( c_times @ ( c_Numeral_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_lessequals @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(458,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).

thf(2106,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(627,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).

thf(2470,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(3,negated_conjecture,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ A ) ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ A ) ) @ t_a ) @ t_a ) @ t_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(1069,plain,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ A ) ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ A ) ) @ t_a ) @ t_a ) @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(493,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).

thf(2177,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ c_Numeral_OMin @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(717,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).

thf(2672,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(813,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
       != ( c_Numeral_Onumber__of @ A @ tc_nat ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_1) ).

thf(2879,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_Numeral_Onumber__of @ B @ tc_nat )
       != ( c_Numeral_Onumber__of @ A @ tc_nat ) )
      | ( c_IntDef_Oiszero @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(702,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_IntDef_Oint )
      | ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
      | ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).

thf(2640,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_IntDef_Oint )
      | ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
      | ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(386,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).

thf(1945,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(1005,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).

thf(3299,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(171,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_4) ).

thf(1463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ C @ A ) @ A )
      | ( c_lessequals @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ C @ A ) @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(872,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).

thf(2998,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(217,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).

thf(1565,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(691,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ A @ A @ tc_nat )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).

thf(2615,plain,
    ! [A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( ( c_div @ A @ A @ tc_nat )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(310,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_lessequals @ ( c_divide @ C @ B @ A ) @ c_1 @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__eq__1__pos_0) ).

thf(1769,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ B @ A )
      | ~ ( c_lessequals @ ( c_divide @ C @ B @ A ) @ c_1 @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(373,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_0) ).

thf(1917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( c_less @ c_0 @ ( c_divide @ ( c_Numeral_Onumber__of @ B @ A ) @ C @ A ) @ A )
      | ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ A ) @ A )
      | ( c_less @ ( c_Numeral_Onumber__of @ B @ A ) @ c_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(489,axiom,
    class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).

thf(2170,plain,
    class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(574,axiom,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ A @ c_0 )
      = c_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).

thf(2351,plain,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ A @ c_0 )
      = c_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(12,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_div @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ C ) @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = ( c_div @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_1) ).

thf(1088,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( ( c_div @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ B @ C ) @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ ( c_Numeral_OBit @ A @ c_Numeral_Obit_OB0 ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = ( c_div @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(371,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).

thf(1912,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(863,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).

thf(2980,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(888,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).

thf(3035,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(150,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
       != c_0 )
      | ( c_0
        = ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oeq__divide__eq__number__of_2) ).

thf(1417,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Numeral_Onumber @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Numeral_Onumber__of @ B @ A )
       != c_0 )
      | ( c_0
        = ( c_divide @ C @ ( c_Numeral_Onumber__of @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(762,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_div @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
        = ( c_plus @ ( c_div @ B @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).

thf(2771,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_div @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
        = ( c_plus @ ( c_div @ B @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(41931,plain,
    $false,
    inference(cvc4,[status(thm)],[2452,2094,2295,1767,3434,1840,2331,1818,3021,1322,1665,1879,1337,1718,2612,1469,2744,2889,1823,1190,2336,3008,2031,1995,2263,1559,1105,2876,1237,2463,1899,2787,2595,2499,2480,1083,1982,1956,1950,1549,2280,1110,1686,2250,1750,1211,2309,1068,1522,2495,2776,3285,3098,1544,1728,2114,1692,1437,3382,1486,1200,2077,3072,1924,2940,2104,2908,2062,3377,2527,2953,2590,1401,1422,2947,1569,2248,3012,1205,2099,1591,1971,1533,1608,2686,3135,2740,3044,1999,2448,2141,1327,1919,3414,2146,1458,2575,1497,1705,1788,1426,3120,3429,1756,1310,2035,3367,2434,2712,2476,2168,1260,1640,2580,2901,3313,2723,2432,1613,2886,2082,1475,2516,1803,2869,2957,1127,2548,2491,1243,1391,1576,3308,2010,1601,1386,3281,2173,1366,2067,2825,1518,1265,2531,2405,1228,1623,1254,2328,1985,2269,1871,1907,1323,2274,1279,2126,1132,2654,1628,3248,3442,3425,1792,1430,1298,1760,3131,2444,1860,2217,2682,3125,1826,2185,1455,2562,3089,1992,3353,2420,1922,2767,2373,3216,1931,2730,2024,1773,1362,2533,1100,1847,2829,1892,1379,3385,1247,2552,1319,1704,1890,1115,2929,2301,1815,1494,2852,3231,1232,3258,2456,2222,1489,1465,3431,2794,1450,2996,2650,2236,1334,1828,2291,1677,1960,1714,2027,2090,3393,2893,1632,1682,1136,1858,1864,2122,2777,3152,1283,2073,2367,1215,1886,1796,1351,3361,1405,3226,2804,1697,3211,2205,1975,2762,2618,2833,2281,2190,3421,2424,2979,1526,2137,2242,1345,2799,2286,2639,3184,2586,2982,2884,1651,2910,2473,1306,3186,2118,3318,1915,1074,1604,2922,3301,3303,1783,2737,2232,2307,1067,1736,2621,2660,2905,1868,2382,1730,3037,1274,1723,1091,2249,2596,1123,3022,3069,2937,2606,3154,2150,2986,3250,2396,3339,1883,2705,2409,1343,2560,2805,1355,1580,1174,2133,3166,3269,3297,2200,2179,1159,3050,2344,1281,2769,2653,1938,2758,2873,2628,2670,2565,3198,2663,1555,2820,1888,1296,1836,2181,2327,2213,1195,2211,1634,2228,2112,1291,3033,1740,1910,1234,1762,2801,2895,2841,1587,1540,3078,3237,1118,1360,2245,1936,2157,1143,2115,1851,3122,2990,1794,1953,2359,2973,3218,1856,1096,2509,3102,1672,2726,2631,1138,2858,3440,3205,3060,3176,3018,1397,1567,2460,1329,3326,3143,3407,3094,2868,2080,1810,3141,2877,1964,1942,1659,3000,2323,3179,2830,1182,1424,2312,3010,1414,2196,1842,1700,2613,3194,2349,2108,2038,1446,3294,1155,3242,2968,1263,2932,2536,2387,2243,2465,1947,2813,3115,3064,2756,1150,1478,2519,1530,2836,1382,2845,2598,1668,1974,2355,1192,2505,3390,3222,2497,3409,2862,2052,2482,2697,3074,3005,3083,3162,1393,1627,2370,3147,2926,1202,2702,1170,2402,1515,2645,1185,2338,2529,1732,2634,2749,1434,2043,3279,2057,1712,3306,2963,1286,3321,1187,2915,2440,1663,3190,1895,1167,1648,2001,1510,1754,2904,1103,2717,1483,2570,1927,3262,3289,2602,3274,3158,1764,2413,3358,2253,2033,3042,2585,3375,1595,2734,2894,1374,2524,3396,2376,3372,3387,1833,2970,2188,1929,2991,1403,2827,2959,3234,2048,2859,1615,3255,2791,3240,2789,1125,1620,2489,1752,2393,3086,3283,2674,2016,2514,1388,3272,1520,3404,2817,2695,1226,1428,1503,2029,1312,3208,1107,1997,1332,2442,3416,1707,2293,2891,1271,1371,2935,3002,1897,2557,3355,1224,2573,2148,2311,2521,2721,1408,2478,2642,2422,3419,1589,2955,1542,2116,1801,2065,2084,2624,2415,2493,1574,1806,2774,3287,1524,1349,2097,1771,2945,2802,3138,1690,3182,1571,2871,1376,1969,3160,1471,1080,2742,1630,2261,1162,2446,3192,2785,2610,3027,3133,3055,1557,2780,2267,1838,1325,2542,1460,2289,1293,2278,2928,1177,1381,2710,1820,2578,1688,2075,1198,2365,2171,1213,1643,2139,2369,2303,2207,2069,1562,2765,3423,2550,1245,1066,1528,3110,2086,1113,2797,2752,1775,2592,2633,3363,3310,2390,1250,3348,2156,1694,2693,2984,1973,2005,2054,2239,1583,1758,1208,2665,3293,1134,2449,1340,1958,1551,1873,3427,1467,2994,2318,2271,1905,1420,2503,1684,2124,2234,1990,3048,2202,2333,1145,2846,2942,2661,2977,2192,3214,2143,1647,2678,1098,2882,2689,2567,1845,1547,1748,1798,2298,3315,1598,1070,3112,3260,2588,2732,1252,1368,3228,2175,2407,3058,1230,2850,2160,2569,2092,2920,3344,3202,1785,2429,1085,1679,3174,1130,2468,2656,3080,1790,1987,1716,2224,2454,1432,2165,1813,1300,1452,1637,3334,2276,2219,1980,2128,1830,3127,1538,2545,1738,1218,2675,1934,2411,2838,3224,1670,2728,2939,3398,1766,3107,1849,1257,1141,2426,1536,1702,2379,1221,2975,1353,2357,2843,2320,1506,1585,2511,3117,2949,1881,2807,1272,3156,2848,3366,1240,1617,2760,3433,3139,2458,1966,1553,2870,3171,2215,3039,2865,3168,1940,2013,2924,2626,1316,3401,2088,2045,3092,3067,1180,1157,2078,3188,2194,2347,1654,1412,1781,2209,1448,3346,2110,2305,2919,2342,2226,1453,1866,2071,2658,1734,1807,1276,1646,2707,2273,2554,1508,1481,3104,1745,2971,1854,2608,2764,2130,3252,2152,3085,2988,1721,2283,2389,1476,1674,2855,1903,2135,3369,2823,3220,3331,3136,1491,2796,3267,1661,2095,2230,2315,2917,2019,3181,2384,2399,2041,2648,1777,1440,3149,2330,1308,2198,1077,2362,2162,2680,2183,3351,1513,2902,2120,1444,1442,2258,2102,2683,1725,1578,3291,2719,3264,3100,2951,1876,2050,3164,2003,3379,2155,2255,1395,1625,1593,2604,2815,2008,1303,3337,1148,3015,3328,1657,3277,2746,1561,3030,1473,1065,3045,2783,1742,3145,2636,1363,1314,1172,1410,2417,2961,1288,1710,2913,3323,2714,3196,2340,2668,1165,2021,1610,2502,2810,3025,1152,1532,2265,2467,2507,2539,2687,2699,1120,3341,1093,1930,2353,3128,1977,2966,1268,2600,2898,1384,3411,2485,1357,2583,1500,3245,3076,1902,1399,1621,3013,1606,2754,3437,1962,3096,2436,2059,2438,3052,3200,2106,2470,1069,2177,2672,2879,2640,1945,3299,1463,2998,1565,2615,1769,1917,2170,2351,1088,1912,2980,3035,1417,2771]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : ANA020-1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n012.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 17:50:02 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.94/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.32/1.24  % [INFO] 	 Parsing done (377ms). 
% 2.32/1.25  % [INFO] 	 Running in sequential loop mode. 
% 2.85/1.48  % [INFO] 	 eprover registered as external prover. 
% 2.85/1.48  % [INFO] 	 cvc4 registered as external prover. 
% 2.85/1.48  % [INFO] 	 Scanning for conjecture ... 
% 3.46/1.66  % [INFO] 	 Found a conjecture and 2785 axioms. Running axiom selection ... 
% 4.32/1.90  % [INFO] 	 Axiom selection finished. Selected 1058 axioms (removed 1727 axioms). 
% 5.19/2.10  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.35/2.12  % [INFO] 	 Type checking passed. 
% 5.35/2.12  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 86.96/21.49  % External prover 'cvc4' found a proof!
% 86.96/21.49  % [INFO] 	 Killing All external provers ... 
% 86.96/21.49  % Time passed: 20979ms (effective reasoning time: 20243ms)
% 86.96/21.49  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 86.96/21.50  % Axioms used in derivation (1058): cls_NatSimprocs_Omult__less__cancel__right__number__of_3, cls_IntDef_Ozero__less__int__conv_0, cls_Nat_Onot__gr0_0, cls_OrderedGroup_Ojoin__0__eq__0_1, cls_Divides_Odiv__mult__self1_0, cls_Ring__and__Field_Omult__divide__cancel__right__if_0, cls_Ring__and__Field_Odivide__le__eq__1__neg_0, cls_Set_OCompl__subset__Compl__iff_1, cls_Power_Opower__0__Suc_0, cls_NatBin_Oeq__nat__number__of_7, cls_NatArith_Oadd__diff__assoc2_0, clsrel_Ring__and__Field_Oordered__field_0, clsrel_Ring__and__Field_Oordered__field_37, clsrel_Ring__and__Field_Opordered__semiring_10, clsarity_IntDef__Oint_34, cls_Parity_Oneq__one__mod__two_0, cls_Parity_Opower__less__zero__eq__number__of_0, cls_Ring__and__Field_Odivide__less__0__1__iff_0, cls_IntDiv_Ozdiv__zadd__self1_0, clsrel_Ring__and__Field_Oordered__idom_3, cls_NatBin_Odvd__eq__mod__eq__0__number__of_1, cls_NatBin_Oeq__nat__number__of_11, cls_IntDiv_Ozdvd__0__right_0, cls_Parity_Opower__le__zero__eq__number__of_1, clsrel_Ring__and__Field_Opordered__cancel__semiring_11, cls_IntArith_Oarith__special__8_0, cls_Nat_Onot__less0_0, cls_Ring__and__Field_Oinverse__less__iff__less_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_NatSimprocs_Ozero__le__divide__iff__number__of_4, cls_NatSimprocs_Ozero__less__divide__iff__number__of_4, cls_OrderedGroup_Oneg__less__iff__less_1, cls_Nat_Oone__eq__mult__iff_0, cls_List_Odrop__replicate_0, cls_IntArith_Oarith__special__7_0, cls_NatArith_Oof__nat__0__le__iff_0, cls_IntDef_Oof__int__le__iff_0, clsrel_OrderedGroup_Olordered__ab__group__abs_3, cls_NatBin_OSuc__pred_H_0, cls_Ring__and__Field_Ozero__eq__1__divide__iff_1, cls_NatSimprocs_Omult__less__cancel__left__number__of_5, cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0, cls_Power_Onat__zero__less__power__iff_2, clsrel_Ring__and__Field_Oordered__field_54, clsrel_Ring__and__Field_Oordered__field_48, cls_OrderedGroup_Odiff__le__0__iff__le_0, cls_Parity_Oeven__nat__power_2, cls_IntDef_Oint__eq__0__conv_1, cls_Parity_Oeven__sum_2, cls_OrderedGroup_Oneg__le__iff__le_0, cls_NatSimprocs_Oless__divide__eq__number__of_9, clsrel_Ring__and__Field_Oordered__semidom_2, cls_Nat_Onat__add__left__cancel__less_1, cls_IntDef_Ozless__nat__conj_1, cls_NatBin_Onat__numeral__0__eq__0_0, cls_NatBin_Opower__nat__number__of__number__of_1, cls_Parity_Opower__eq__0__iff__number__of_2, cls_IntDef_Ozless__int_0, cls_NatSimprocs_Odivide__le__eq__number__of_8, cls_Ring__and__Field_Oone__divide__eq__0__iff_0, cls_Divides_Omod__eq__0D__dest_0, cls_IntDiv_Ozmod__self_0, cls_NatSimprocs_Odivide__le__0__iff__number__of_4, cls_Ring__and__Field_Oeq__divide__eq__1_0, cls_Ring__and__Field_Oinverse__negative__iff__negative_0, cls_Nat_Onat__add__right__cancel_0, cls_Parity_Ozero__less__power__eq__number__of_4, cls_IntDef_Oof__int__0__le__iff_0, clsarity_IntDef__Oint_46, clsrel_Ring__and__Field_Ofield_8, cls_Ring__and__Field_Odivide__minus__left_0, cls_Parity_Oeven__difference_2, clsarity_IntDef__Oint_52, cls_IntDiv_Ozminus__dvd__iff_1, clsarity_IntDef__Oint_24, cls_NatSimprocs_Omult__less__cancel__left__number__of_2, cls_NatSimprocs_Oeq__divide__eq__number__of_2, clsrel_Ring__and__Field_Oordered__ring__strict_26, cls_NatSimprocs_Ole__divide__eq__number__of_7, cls_OrderedGroup_Oneg__0__less__iff__less_0, cls_IntDef_Oint__nat__eq_0, cls_Set_ODiff__cancel_0, clsrel_Ring__and__Field_Oordered__idom_12, cls_Numeral_Obin__minus__0_0, cls_NatSimprocs_Ohalf__gt__zero_0, cls_Nat_Omult__le__cancel1_1, clsrel_OrderedGroup_Opordered__ab__group__add_1, cls_Parity_Oeven__nat__product_1, cls_Numeral_Onumeral__1__eq__1_0, cls_IntDiv_Ozmod__zmult__self1_0, cls_IntDef_Oof__int__0__less__iff_0, cls_NatSimprocs_Ole__divide__eq__number__of_8, cls_Nat_Oop_A_K_Omult__Suc_0, cls_Numeral_Obin__rel__simps__11_0, cls_NatSimprocs_Odivide__less__0__iff__number__of_3, cls_Binomial_Obinomial__Suc__n_0, cls_Ring__and__Field_Odivide__eq__eq__1_1, cls_NatArith_Oof__nat__0__eq__iff_1, cls_NatSimprocs_Odivide__less__eq__number__of_6, cls_Nat_Oless__one_1, clsrel_Power_Orecpower_21, clsrel_Numeral_Onumber__ring_16, cls_Parity_Oeven__nat__product_2, cls_NatSimprocs_Odivide__le__0__iff__number__of_0, cls_Divides_Odvd__refl_0, cls_NatSimprocs_Odivide__minus1_0, cls_IntDiv_Ozdiv__1_0, cls_OrderedGroup_Oneg__0__le__iff__le_1, clsrel_Ring__and__Field_Oordered__semidom_28, cls_Nat_Odiff__is__0__eq_0, cls_NatSimprocs_Ozero__less__divide__iff__number__of_0, clsrel_Ring__and__Field_Oordered__semidom_34, cls_OrderedGroup_Opprt__eq__id_0, cls_Parity_Oeven__nat__sum_1, cls_Ring__and__Field_Oinverse__eq__1__iff_1, cls_Numeral_OPls__0__eq_0, cls_OrderedGroup_Oneg__le__0__iff__le_1, cls_Nat_OSuc__Suc__eq_0, cls_IntArith_Oarith__special__11_1, cls_Nat_Oop_A_K_Omult__0_0, cls_Power_Ozero__less__power__abs__iff_2, cls_IntDiv_Ozdiv__zminus__zminus_0, clsrel_Ring__and__Field_Ofield_5, cls_Orderings_Oorder__less__irrefl_0, cls_Parity_Ozero__less__power__eq__number__of_1, cls_IntDef_Oint__Suc_0, cls_IntDiv_Ozero__less__zpower__abs__iff_2, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_NatArith_Oof__nat__less__iff_0, cls_Ring__and__Field_Oinverse__less__iff__less__neg_1, cls_NatSimprocs_Odivide__eq__eq__number__of_1, cls_Ring__and__Field_Ole__divide__eq__1__neg_0, clsarity_nat_40, clsrel_Ring__and__Field_Ofield_32, cls_Numeral_Ominus__number__of__mult_0, cls_OrderedGroup_Oabs__ge__zero_0, cls_Ring__and__Field_Oinverse__positive__iff__positive_0, cls_Numeral_Obin__succ__Pls_0, clsrel_Ring__and__Field_Oordered__ring__strict_22, cls_NatSimprocs_Ozero__less__divide__iff__number__of_5, cls_OrderedGroup_Oabs__not__less__zero_0, clsrel_Ring__and__Field_Oordered__ring__strict_33, cls_IntDef_Onegative__eq__positive_0, cls_OrderedGroup_Ozero__less__abs__iff_0, cls_List_Olist_Oinject_1, cls_NatBin_Oless__0__number__of_1, cls_NatSimprocs_Omult__less__cancel__right__number__of_2, cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0, cls_Numeral_Obin__minus__Min_0, cls_Nat_Odiff__0__eq__0_0, cls_Ring__and__Field_Ominus__mult__minus_0, clsrel_Ring__and__Field_Oordered__idom_17, cls_IntDef_Oneg__zminus__int_0, cls_Divides_Odiv__less_0, clsrel_Ring__and__Field_Oordered__field_21, cls_Divides_Odiv__1_0, clsrel_OrderedGroup_Olordered__ab__group__join_0, cls_NatSimprocs_Odivide__le__eq__number__of_5, cls_NatBin_Oint__nat__number__of_1, cls_LOrder_Omeet__idempotent_0, clsrel_Ring__and__Field_Oordered__idom_56, cls_OrderedGroup_Oabs__0__eq_0, clsarity_IntDef__Oint_56, cls_IntArith_Oarith__special__10_0, cls_NatBin_Opower__nat__number__of__number__of_0, cls_Ring__and__Field_Odivide__le__0__1__iff_0, cls_IntDef_Oint__less__0__conv_0, cls_OrderedGroup_Onprt__mono_0, cls_OrderedGroup_Oabs__add__abs_0, cls_Nat_Oless__irrefl_0, cls_Set_ODiff__idemp_0, cls_Nat_Odiff__le__self_0, cls_Nat_Oadd__is__0_0, clsarity_set_2, clsarity_nat_3, cls_IntDiv_ODIVISION__BY__ZERO_0, clsrel_Numeral_Onumber__ring_12, cls_NatSimprocs_Oless__divide__eq__number__of_6, cls_Ring__and__Field_Omult__divide__cancel__left__if1_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1, cls_NatSimprocs_Omult__le__cancel__left__number__of_3, cls_NatBin_Oeq__0__number__of_1, cls_NatArith_Oof__nat__less__0__iff_0, cls_OrderedGroup_Oneg__meet__eq__join_0, clsarity_IntDef__Oint_60, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, cls_NatSimprocs_Odivide__less__0__iff__number__of_0, cls_IntDiv_Ozmod__zmult__self2_0, cls_Ring__and__Field_Omult__cancel__left1_2, cls_Numeral_Oadd__number__of__left_0, cls_List_Olength__drop_0, cls_Numeral_Obin__rel__simps__8_0, cls_IntDef_Ozero__less__int__conv_1, cls_NatBin_OSuc__nat__number__of_0, cls_Numeral_Obin__rel__simps__9_0, cls_Power_Opower_Osimps__2_0, cls_Divides_Omod__add__self1_0, cls_Parity_Opower__0__left__number__of_1, cls_Power_Opower__one__right_0, cls_NatSimprocs_Oinverse__eq__divide__number__of_0, cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0, cls_IntDef_Oof__int__less__iff_0, clsarity_nat_29, cls_IntDef_Onat__le__0_0, cls_IntDiv_Odvd__zminus__iff_0, cls_NatSimprocs_Odivide__less__eq__number__of_3, cls_OrderedGroup_Odiff__le__0__iff__le_1, cls_Nat_Ozero__less__diff_1, clsrel_Numeral_Onumber__ring_23, cls_Numeral_Obin__rel__simps__2_0, clsrel_Ring__and__Field_Oaxclass__abs__if_0, cls_Nat_Omult__less__cancel2_1, cls_List_Odrop__Cons__number__of_1, cls_NatSimprocs_Omult__le__cancel__right__number__of_3, clsarity_IntDef__Oint_0, cls_IntArith_Oof__int__m1_0, cls_Numeral_Omult__minus1__right_0, cls_Numeral_Obin__succ__1_0, cls_Set_OpsubsetI_0, cls_Set_Osubset__refl_0, cls_NatBin_Oeq__nat__number__of_6, cls_List_Olist_Osize__2_0, cls_NatArith_Odiff__diff__right_0, cls_Ring__and__Field_Odivide__cancel__right_1, cls_Divides_Odiv__mult__self__is__m_0, cls_NatBin_Oless__nat__number__of_2, cls_Parity_Oeven__power_2, cls_Nat_Omult__0__right_0, cls_Set_OCompl__eq__Compl__iff_0, clsrel_OrderedGroup_Opordered__ab__group__add_10, cls_IntDiv_Omod__div__trivial_0, cls_IntDiv_Ozdvd__0__left_1, cls_LOrder_Ojoin__idempotent_0, cls_Nat_Onat__add__left__cancel__le_0, clsrel_Ring__and__Field_Oordered__field_38, cls_Ring__and__Field_Omult__cancel__right1_2, cls_Power_Opower__eq__0__iff_2, cls_Ring__and__Field_Omult__divide__cancel__left__if2_1, cls_List_Odrop__Suc__Cons_0, cls_Ring__and__Field_Ofield__mult__cancel__left_1, cls_Ring__and__Field_Oinverse__eq__iff__eq_0, cls_NatSimprocs_Ole__divide__eq__number__of_0, cls_List_Olength__replicate_0, cls_Ring__and__Field_Odivide__divide__eq__left_0, cls_Ring__and__Field_Otimes__divide__self__left_1, clsrel_Ring__and__Field_Oordered__field_50, cls_OrderedGroup_Omeet__0__eq__0_0, cls_NatBin_Oless__0__number__of_0, cls_NatSimprocs_Ole__divide__eq__number__of_3, cls_NatBin_Odiv__nat__number__of_0, cls_NatSimprocs_Odivide__le__eq__number__of_3, cls_Nat_Omult__eq__1__iff_0, cls_IntDef_Onot__neg__int_0, cls_Nat_Oadd__gr__0_2, cls_IntDiv_Ozdvd__refl_0, cls_NatBin_Oeq__number__of__0_2, cls_NatArith_Oof__nat__le__iff_0, cls_NatSimprocs_Odivide__le__eq__number__of_4, cls_IntArith_Oarith__special__5_0, cls_Divides_Odiv__less__dividend_0, cls_NatSimprocs_Oless__divide__eq__number__of_2, cls_List_Ochar_Oinject_0, cls_NatSimprocs_Omod2__Suc__Suc_0, cls_Ring__and__Field_Oinverse__minus__eq_0, cls_Divides_Odvd__1__iff__1_0, cls_IntArith_Oarith__special__12_1, cls_Nat_Omult__less__cancel1_1, clsrel_OrderedGroup_Olordered__ab__group__abs_0, cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0, cls_Nat_Onat__add__left__cancel__less_0, clsrel_Numeral_Onumber__ring_5, cls_Parity_Oneg__one__even__power_0, cls_Ring__and__Field_Ominus__divide__divide_0, cls_NatBin_Odiv__nat__number__of_1, cls_NatBin_Oeq__nat__number__of_4, cls_OrderedGroup_Oabs__eq__0_0, clsarity_nat_36, cls_IntDef_Ozero__less__nat__eq_1, cls_IntArith_Oint__eq__iff__number__of_1, clsrel_Ring__and__Field_Oordered__idom_55, clsrel_Ring__and__Field_Oordered__ring__strict_19, cls_IntArith_Oarith__special__17_0, clsrel_Ring__and__Field_Ofield_17, clsrel_Ring__and__Field_Oordered__field_8, cls_IntArith_Oarith__special__9_1, cls_Power_Opower__strict__increasing__iff_0, cls_Power_Ozero__le__power__abs_0, cls_Ring__and__Field_Omult__divide__cancel__right__if2_1, cls_Ring__and__Field_Odivide__cancel__left_1, cls_SetInterval_OatLeastAtMost__empty_0, cls_Power_Opower__increasing__iff_1, cls_NatSimprocs_Ole__divide__eq__number__of_4, cls_Nat_Odiff__Suc__Suc_0, cls_Nat_Omult__eq__1__iff_2, cls_Nat_Omult__le__cancel1_0, clsarity_IntDef__Oint_59, cls_IntDiv_Ozdiv__number__of__BIT_2, clsrel_Ring__and__Field_Oordered__field_49, cls_IntDef_Oof__int__le__0__iff_1, cls_Ring__and__Field_Otimes__divide__eq__2_0, cls_Nat_Oless__one_0, cls_IntDiv_Omod__mod__trivial_0, clsrel_Ring__and__Field_Oordered__semidom_35, clsarity_IntDef__Oint_47, cls_IntDef_Oint__nat__eq_1, cls_Ring__and__Field_Oinverse__positive__iff__positive_1, clsarity_IntDef__Oint_48, cls_List_Odrop__Cons__number__of_0, cls_Ring__and__Field_Odivide__less__eq__1__neg_1, cls_Ring__and__Field_Omult__divide__cancel__right__if1_0, clsarity_IntDef__Oint_19, cls_Set_Osubset__empty_0, cls_Parity_Oeven__neg_0, clsrel_OrderedGroup_Olordered__ab__group_6, cls_Parity_Ozero__less__power__nat__eq__number__of_1, cls_NatSimprocs_Oless__minus__iff__number__of_1, clsarity_IntDef__Oint_58, cls_Ring__and__Field_Oinverse__negative__iff__negative_1, cls_Ring__and__Field_Odivide__eq__0__iff_1, cls_Divides_Omod__le__divisor_0, cls_Nat_Omult__less__cancel2_0, cls_IntDiv_Opower_Osimps__2_0, cls_Parity_Oeven__nat__power_0, cls_Parity_Ozero__less__power__nat__eq__number__of_0, cls_Ring__and__Field_Omult__divide__cancel__left__if2_0, clsrel_Ring__and__Field_Oordered__idom_51, cls_Ring__and__Field_Odivide__divide__eq__right_0, cls_IntDiv_Ozdiv__minus1__right_0, cls_Power_Onat__one__le__power_0, clsrel_OrderedGroup_Olordered__ab__group__abs_14, cls_NatSimprocs_Ominus__less__iff__number__of_1, cls_NatSimprocs_Omult__less__cancel__left__number__of_1, cls_Nat_Ole__add__diff__inverse2_0, cls_IntArith_Oarith__special__7_1, cls_Parity_Ozero__le__power__eq__number__of_1, cls_IntDef_Onegative__eq__positive_2, clsrel_Ring__and__Field_Oordered__field_60, clsrel_Ring__and__Field_Oordered__idom_38, cls_IntArith_Oarith__special__4_0, cls_IntArith_Oarith__special__10_1, clsrel_Ring__and__Field_Oordered__idom_52, cls_Divides_Odvd__0__left__iff_0, clsrel_Ring__and__Field_Oordered__field_53, clsrel_Ring__and__Field_Ofield_3, cls_Numeral_Obin__rel__simps__13_1, clsrel_OrderedGroup_Olordered__ab__group_0, cls_Parity_Oeven__product_0, cls_NatSimprocs_Omult__le__cancel__left__number__of_0, cls_Parity_Opower__le__zero__eq__number__of_5, cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_1, clsrel_Ring__and__Field_Oordered__idom_36, cls_Divides_Omod__mult__self1_0, cls_Numeral_Obin__add__Pls__right_0, cls_Ring__and__Field_Odivide__le__0__1__iff_1, cls_NatSimprocs_Omult__le__cancel__left__number__of_5, clsrel_Ring__and__Field_Oordered__idom_42, cls_Power_Ozero__less__power__abs__iff_0, cls_OrderedGroup_Ozero__le__pprt_0, cls_NatSimprocs_Odivide__le__0__iff__number__of_5, clsrel_OrderedGroup_Olordered__ab__group__join_17, cls_Nat_Oadd__is__0_1, cls_OrderedGroup_Oneg__0__less__iff__less_1, cls_Ring__and__Field_Ozero__le__divide__1__iff_0, cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0, cls_Parity_Oeven__sum_0, clsrel_Ring__and__Field_Opordered__comm__semiring_13, cls_Parity_Opower__eq__0__iff__number__of_1, cls_Parity_Oeven__nat__power_1, cls_OrderedGroup_Ojoin__0__eq__0_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_Power_Orecpower__class_Oaxioms__1_0, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0, cls_Ring__and__Field_Onot__one__le__zero_0, cls_IntDef_Oof__int__less__iff_1, cls_NatArith_Oof__nat__le__0__iff_1, cls_NatSimprocs_Odivide__less__eq__number__of_4, cls_Ring__and__Field_Odivide__le__eq__1__pos_0, cls_NatSimprocs_Omult__less__cancel__right__number__of_5, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0, cls_IntArith_Oarith__special__15_1, cls_NatBin_Oless__nat__number__of_4, cls_IntDef_Oof__int__0__le__iff_1, clsrel_Numeral_Onumber__ring_17, cls_NatArith_Oof__nat__0__less__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_36, cls_Ring__and__Field_Oinverse__le__iff__le__neg_1, cls_NatSimprocs_Oeq__divide__eq__number__of_0, cls_NatBin_Odvd__eq__mod__eq__0__number__of_0, cls_Parity_Oeven__difference_1, cls_Parity_Opower__le__zero__eq__number__of_0, cls_Set_OCompl__subset__Compl__iff_0, cls_Nat_Omult__le__cancel2_2, cls_NatSimprocs_Ozero__le__divide__iff__number__of_2, clsrel_Ring__and__Field_Oordered__idom_47, clsarity_nat_38, cls_Nat_Omult__cancel1_1, cls_OrderedGroup_Onprt__le__zero_0, cls_SetInterval_OatLeast__subset__iff_0, cls_NatBin_Oadd__nat__number__of_2, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, cls_Nat_Onat__0__less__mult__iff_0, cls_Ring__and__Field_Odivide__eq__eq__1_0, clsrel_OrderedGroup_Olordered__ab__group_17, cls_NatSimprocs_Odivide__less__eq__number__of_7, cls_Power_Ozero__less__power__abs__iff_1, cls_NatSimprocs_Omult__le__cancel__right__number__of_0, cls_NatBin_Oone__power2_0, cls_IntDef_Oof__int__eq__iff_0, clsrel_Ring__and__Field_Oordered__field_46, cls_NatArith_Oof__nat__le__0__iff_0, cls_NatSimprocs_Omod2__gr__0_1, clsrel_Ring__and__Field_Oordered__ring__strict_16, cls_Ring__and__Field_Omult__cancel__right1_1, cls_Divides_Odiv__mult__self1__is__m_0, cls_Divides_Onat__mod__div__trivial_0, cls_NatSimprocs_Ozero__le__divide__iff__number__of_5, cls_IntDiv_Ozero__less__zpower__abs__iff_1, cls_IntDiv_Odvd__zminus__iff_1, cls_NatBin_Oeq__0__number__of_2, clsrel_Ring__and__Field_Oordered__idom_18, cls_IntDef_Oof__int__0__eq__iff_0, cls_Divides_Odiv__mult__mult2_0, cls_Nat_Ole__0__eq_0, cls_Power_Opower__inject__exp_0, cls_NatArith_Odiff__less_0, cls_Divides_ODIVISION__BY__ZERO__DIV_0, cls_Numeral_Onumeral__0__eq__0_0, clsrel_Ring__and__Field_Opordered__comm__semiring_2, cls_IntDiv_Ozdvd__triv__right_0, cls_NatBin_Omod__nat__number__of_1, cls_NatSimprocs_Omult__less__cancel__right__number__of_1, cls_Ring__and__Field_Oinverse__le__iff__le_1, cls_Nat_Ozero__less__diff_0, cls_OrderedGroup_Oneg__le__iff__le_1, cls_Set_Oempty__subsetI_0, cls_Parity_Oeven__sum_3, cls_Numeral_OMin__1__eq_0, cls_Numeral_Obin__succ__Min_0, clsarity_IntDef__Oint_31, cls_Nat_OSuc__le__mono_0, cls_IntDef_Oabs__int__eq_0, cls_Parity_Opower__le__zero__eq__number__of_4, cls_IntArith_Oarith__special__6_1, cls_Divides_Omod__add__self2_0, cls_Numeral_Obin__arith__extra__simps__2_0, cls_Divides_Odvd__0__left__iff_1, cls_Parity_Ozero__less__power__eq__number__of_3, cls_List_Odrop__0_0, cls_Ring__and__Field_Omult__eq__0__iff_0, cls_NatSimprocs_Oless__divide__eq__number__of_1, cls_IntDiv_Ozdiv__zero_0, cls_IntDiv_Opos__mod__sign_0, cls_NatBin_Oeq__nat__number__of_0, clsrel_Ring__and__Field_Oordered__field_20, cls_Parity_Oeven__nat__sum_0, cls_Power_Opower_Osimps__1_0, cls_NatBin_Oof__nat__number__of__eq_0, cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_1, cls_Power_Opower__eq__0__iff_0, cls_Nat_Oone__le__mult__iff_1, clsrel_Ring__and__Field_Oordered__idom_11, cls_Ring__and__Field_Odivide__eq__0__iff_2, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_Ring__and__Field_Omult__cancel__left1_1, cls_List_Olist_Oinject_0, clsrel_OrderedGroup_Olordered__ab__group__meet_6, cls_NatSimprocs_Oadd__2__eq__Suc_H_0, cls_Nat_OSuc__less__eq_1, cls_IntArith_Oarith__special__14_0, clsrel_OrderedGroup_Olordered__ab__group__meet_17, clsrel_Ring__and__Field_Oordered__field_42, cls_Set_Oempty__Diff_0, clsarity_nat_37, cls_NatSimprocs_Odivide__eq__eq__number__of_3, clsrel_Ring__and__Field_Opordered__cancel__semiring_15, cls_IntArith_Oarith__special__9_0, cls_IntDef_Oint__int__eq_0, clsrel_LOrder_Olorder_0, cls_Divides_Omod__mult__self1__is__0_0, cls_Orderings_Oorder__less__imp__le_0, cls_Parity_Opower__0__left__number__of_0, cls_Nat_Onat__add__left__cancel__le_1, cls_Numeral_Obin__rel__simps__13_0, cls_IntDiv_Ozdvd__triv__left_0, cls_Nat_Ozero__less__Suc_0, cls_Nat_Odiff__self__eq__0_0, cls_Parity_Oeven__nat__zero_0, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1, cls_NatSimprocs_Odivide__less__0__iff__number__of_1, cls_Divides_Omod__less__divisor_0, cls_Nat_Omult__cancel2_0, cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0, clsarity_set_14, cls_Nat_Omult__less__cancel1_0, cls_Ring__and__Field_Ozero__le__one_0, cls_Set_Osubset__antisym_0, cls_IntArith_Oarith__special__8_1, clsrel_Ring__and__Field_Oordered__semidom_12, cls_Ring__and__Field_Omult__cancel__left2_0, cls_Parity_Oeven__power_1, cls_Power_Opower__strict__increasing__iff_1, cls_NatSimprocs_Oless__divide__eq__number__of_5, cls_IntDef_Ozless__nat__conj_2, cls_Numeral_Obin__add__BIT__10_0, cls_NatBin_Oint__nat__number__of_0, cls_NatSimprocs_Odivide__le__eq__number__of_9, cls_IntDiv_Ozdvd__1__left_0, clsrel_Numeral_Onumber__ring_30, clsarity_IntDef__Oint_37, cls_Ring__and__Field_Omult__divide__cancel__right__if2_0, cls_Ring__and__Field_Ole__divide__eq__1__pos_0, cls_Ring__and__Field_Oone__eq__divide__iff_1, clsarity_nat_6, cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_0, cls_NatSimprocs_Oright__diff__distrib__number__of_0, clsarity_nat_43, cls_IntDef_Onegative__eq__positive_1, clsrel_Ring__and__Field_Oordered__field_31, cls_IntDiv_Ozdiv__number__of__BIT_0, cls_NatSimprocs_Odivide__le__0__iff__number__of_2, cls_NatBin_Oeq__nat__number__of_10, cls_Divides_Omod__1_0, cls_Numeral_Obin__arith__extra__simps__4_0, clsrel_OrderedGroup_Olordered__ab__group__abs_16, clsrel_Power_Orecpower_3, cls_Set_Osubset__empty_1, clsrel_OrderedGroup_Olordered__ab__group__abs_15, cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_0, cls_Numeral_Obin__add__Pls_0, cls_Ring__and__Field_Oinverse__less__iff__less__neg_0, cls_Ring__and__Field_Odivide__eq__0__iff_0, clsrel_OrderedGroup_Olordered__ab__group__meet_15, cls_IntDiv_Ozmod__zero_0, cls_NatSimprocs_Omod2__gr__0_0, cls_Nat_OSuc__diff__diff_0, cls_OrderedGroup_Opprt__0_0, cls_Ring__and__Field_Ozero__le__divide__1__iff_1, cls_Nat_Omult__cancel2_1, cls_IntArith_Oone__less__nat__eq_1, cls_Finite__Set_Oof__nat__id_0, cls_NatBin_Oeq__nat__number__of_5, cls_NatBin_Omod__nat__number__of_2, clsarity_IntDef__Oint_18, clsrel_OrderedGroup_Olordered__ab__group__join_8, cls_IntArith_Oint__eq__iff__number__of_0, cls_Nat_Onat__0__less__mult__iff_1, cls_NatSimprocs_Ole__divide__eq__number__of_1, cls_Ring__and__Field_Otimes__divide__eq__1_0, cls_NatSimprocs_Ominus__less__iff__number__of_0, clsarity_nat_34, cls_Parity_Ozero__less__power__nat__eq__number__of_2, cls_Ring__and__Field_Oabs__divide_0, clsrel_Ring__and__Field_Oordered__idom_46, cls_NatSimprocs_Odivide__le__eq__number__of_2, cls_Ring__and__Field_Ozero__less__divide__1__iff_1, cls_Binomial_Obinomial__n__n_0, clsrel_Ring__and__Field_Oordered__semidom_38, cls_Ring__and__Field_Oless__divide__eq__1__neg_0, clsarity_nat_45, cls_NatSimprocs_Odiv__Suc__eq__div__add3_0, cls_IntDiv_Ozdiv__number__of__BIT_1, cls_Nat_OSuc__le__mono_1, clsrel_Ring__and__Field_Oordered__ring__strict_35, cls_Ring__and__Field_Omult__minus__left_0, cls_NatSimprocs_Omult__le__cancel__right__number__of_5, cls_NatBin_Omult__nat__number__of_0, cls_IntDef_Oof__int__less__0__iff_0, cls_OrderedGroup_Opprt__eq__0_0, cls_NatBin_Onat__number__of_0, cls_SetInterval_OatLeastLessThan__empty_0, cls_NatBin_Oless__nat__number__of_3, clsrel_Ring__and__Field_Oordered__semidom_36, cls_Divides_Omod__mult__self2_0, cls_Numeral_Obin__add__BIT__11_0, cls_OrderedGroup_Oabs__of__nonpos_0, cls_NatArith_Odiff__Suc__diff__eq2_0, cls_Binomial_Obinomial__Suc__Suc_0, cls_Ring__and__Field_Oless__divide__eq__1__pos_1, clsarity_nat_17, cls_NatSimprocs_Odivide__less__0__iff__number__of_5, cls_Ring__and__Field_Omult__divide__cancel__left__if1_1, cls_Ring__and__Field_Odivide__cancel__left_0, cls_NatSimprocs_Odivide__less__eq__number__of_0, cls_Numeral_Obin__rel__simps__4_0, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1, cls_NatSimprocs_Oeq__divide__eq__number__of_4, cls_IntDiv_Ozdiv__zmult__self1_0, cls_NatSimprocs_Omult__le__cancel__right__number__of_2, cls_Divides_Odvd__triv__right_0, cls_Ring__and__Field_Oinverse__divide_0, clsrel_Ring__and__Field_Oordered__field_56, cls_NatSimprocs_Ozero__less__divide__iff__number__of_2, cls_Numeral_Obin__arith__extra__simps__5_0, cls_IntArith_Ozle__add1__eq__le_1, cls_NatArith_Oof__nat__0__less__iff_0, cls_NatBin_Oadd__nat__number__of_1, cls_OrderedGroup_Opprt__mono_0, cls_IntDef_Onat__int_0, cls_OrderedGroup_Odiff__less__0__iff__less_0, cls_Ring__and__Field_Oright__inverse_0, cls_NatSimprocs_Odivide__less__eq__number__of_5, clsarity_IntDef__Oint_54, clsrel_Ring__and__Field_Oordered__field_58, clsrel_LOrder_Ojoin__semilorder_1, cls_Nat_Odiff__is__0__eq_H_0, clsarity_IntDef__Oint_40, cls_Ring__and__Field_Ole__divide__eq__1__pos_1, cls_Ring__and__Field_Odivide__less__eq__1__neg_0, clsrel_Numeral_Onumber__ring_22, cls_List_Oreplicate_Oreplicate__Suc_0, cls_Parity_Oeven__nat__Suc_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, cls_Nat_Oadd__gr__0_0, cls_IntArith_Ozabs__less__one__iff_0, cls_Parity_Oneg__one__odd__power_0, clsrel_Ring__and__Field_Oordered__idom_53, cls_OrderedGroup_Odiff__less__0__iff__less_1, clsrel_OrderedGroup_Olordered__ab__group__join_16, cls_NatBin_Oone__mod__nat__number__of_0, cls_Ring__and__Field_Oeq__divide__eq__1_2, clsrel_Ring__and__Field_Oordered__idom_35, clsarity_nat_23, cls_OrderedGroup_Onprt__eq__id_0, cls_IntArith_Oarith__special__13_0, cls_Nat_Oless__Suc0_0, cls_NatBin_Oeq__nat__number__of_9, cls_IntDef_Oint__1_0, cls_NatSimprocs_Ozero__le__divide__iff__number__of_1, cls_NatArith_Oof__nat__eq__0__iff_0, cls_Divides_Odvd__triv__left_0, cls_NatSimprocs_Ole__divide__eq__number__of_5, cls_OrderedGroup_Oabs__minus__cancel_0, cls_NatBin_Oof__nat__number__of__eq_1, cls_IntArith_Oarith__special__16_1, cls_Numeral_Obin__rel__simps__6_1, cls_Nat_Oop_A_N_Odiff__0_0, cls_Parity_Opower__less__zero__eq__number__of_2, cls_OrderedGroup_Onprt__eq__0_0, cls_Parity_Oeven__difference_0, cls_Ring__and__Field_Odivide__1_0, cls_Parity_Opower__le__zero__eq__number__of_3, cls_Numeral_Obin__rel__simps__7_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_IntArith_Ozle__diff1__eq_0, cls_Numeral_Obin__arith__extra__simps__3_0, cls_NatBin_Onat__numeral__1__eq__1_0, clsrel_LOrder_Olorder_2, cls_Nat_Onot__add__less1_0, cls_Parity_Oodd__one_0, cls_Divides_Odvd__0__right_0, cls_IntDef_Onot__zle__0__negative_0, cls_OrderedGroup_Ozero__less__abs__iff_1, cls_SetInterval_OatLeast__subset__iff_1, clsrel_Ring__and__Field_Oordered__field_52, clsrel_OrderedGroup_Olordered__ab__group__abs_1, clsrel_Ring__and__Field_Oordered__ring__strict_24, cls_NatArith_Odiff__diff__cancel_0, cls_NatSimprocs_Omult__le__cancel__left__number__of_1, cls_Nat_Oadd__is__0_2, cls_OrderedGroup_Oabs__eq__0_1, cls_Ring__and__Field_Omult__cancel__left1_0, cls_Numeral_Oadd__number__of__diff2_0, clsrel_Ring__and__Field_Oordered__field_34, cls_NatBin_Omod__nat__number__of_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2, cls_NatSimprocs_Odivide__less__eq__number__of_9, cls_Parity_Oeven__nat__sum_2, cls_NatBin_Opower2__eq__square__number__of_0, clsrel_OrderedGroup_Olordered__ab__group_15, cls_NatSimprocs_Omult__le__cancel__left__number__of_4, clsrel_Ring__and__Field_Oordered__idom_41, cls_Ring__and__Field_Otimes__divide__self__right_1, cls_IntDef_Onot__int__zless__negative_0, clsrel_Ring__and__Field_Oordered__ring__strict_28, cls_Ring__and__Field_Onot__one__less__zero_0, cls_NatBin_Oeq__number__of__0_0, cls_Parity_Oeven__product_1, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0, clsrel_Power_Orecpower_15, clsrel_OrderedGroup_Olordered__ab__group__meet_18, clsrel_OrderedGroup_Olordered__ab__group_16, cls_Nat_Omult__cancel1_0, cls_Parity_Ozero__less__power__eq__number__of_2, cls_NatSimprocs_Oless__divide__eq__number__of_0, clsrel_Ring__and__Field_Oordered__field_14, clsarity_IntDef__Oint_32, cls_IntDiv_Ozmod__zadd__self2_0, cls_NatSimprocs_Ole__minus__iff__number__of_1, cls_Parity_Oeven__power_0, cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_0, cls_List_Onot__Cons__self_0, cls_Ring__and__Field_Omult__divide__cancel__left__if_1, clsarity_IntDef__Oint_22, cls_IntArith_Oarith__special__14_1, clsrel_Ring__and__Field_Oring_12, cls_Nat_Omult__le__cancel2_1, clsrel_Ring__and__Field_Oordered__field_47, cls_Nat_Oone__eq__mult__iff_2, cls_Ring__and__Field_Oless__divide__eq__1__pos_0, cls_Nat_Odiff__Suc__less_0, cls_Numeral_Obin__rel__simps__4_1, cls_NatSimprocs_Odivide__le__eq__number__of_7, cls_NatBin_Oless__nat__number__of_0, cls_OrderedGroup_Oabs__le__zero__iff_0, cls_Ring__and__Field_Oone__neq__zero_0, clsrel_OrderedGroup_Olordered__ab__group__join_2, cls_Nat_OOne__nat__def_0, cls_IntDiv_Oneg__mod__bound_0, cls_OrderedGroup_Oneg__less__0__iff__less_1, clsrel_Ring__and__Field_Oordered__ring__strict_3, cls_Nat_Oadd__0__right_0, cls_Nat_Ole__add__diff__inverse_0, cls_NatSimprocs_Odivide__less__0__iff__number__of_2, cls_Ring__and__Field_Omult__zero__right_0, clsarity_nat_5, cls_IntArith_Oarith__special__3_0, cls_Binomial_Obinomial__n__0_0, cls_Numeral_Obin__arith__extra__simps__6_1, cls_Nat_Onot__gr0_1, cls_Numeral_Obin__rel__simps__6_0, cls_Set_ODiff__eq__empty__iff_1, cls_Nat_Onot__add__less2_0, cls_Power_Onat__zero__less__power__iff_1, cls_NatSimprocs_Oless__divide__eq__number__of_4, cls_IntArith_Oarith__special__2_0, cls_NatBin_Oeq__nat__number__of_1, cls_NatBin_Ozero__power2_0, cls_Ring__and__Field_Oabs__inverse_0, cls_Ring__and__Field_Ofield__class_Oaxioms__1_0, cls_Set_ODiff__eq__empty__iff_0, cls_Set_OpsubsetE_0, cls_IntDiv_Oneg__mod__sign_0, clsrel_Ring__and__Field_Oordered__field_45, clsrel_Ring__and__Field_Oordered__idom_8, cls_Nat_Oadd__Suc__right_0, cls_IntDiv_Ozero__less__zpower__abs__iff_0, cls_NatArith_Oof__nat__eq__0__iff_1, clsarity_IntDef__Oint_43, clsrel_Ring__and__Field_Oordered__semidom_11, cls_NatSimprocs_Odivide__eq__eq__number__of_4, clsrel_Ring__and__Field_Oordered__semidom_26, cls_IntDef_Ozless__int_1, cls_Set_ODiff__empty_0, clsrel_Ring__and__Field_Oordered__idom_40, cls_Numeral_Obin__rel__simps__12_0, cls_Numeral_Obin__rel__simps__1_1, clsrel_Ring__and__Field_Opordered__comm__semiring_15, clsrel_Ring__and__Field_Oordered__semidom_32, cls_NatArith_Oof__nat__eq__iff_0, cls_Ring__and__Field_Oabs__one_0, cls_Ring__and__Field_Oinverse__le__iff__le_0, cls_Ring__and__Field_Ole__divide__eq__1__neg_1, clsarity_nat_9, cls_Ring__and__Field_Omult__cancel__right2_0, cls_IntDiv_Ozmod__eq__0D__dest_0, clsarity_set_13, cls_Numeral_Obit_Odistinct__1_0, cls_Numeral_Obin__mult__Pls_0, cls_Numeral_Obin__mult__0_0, cls_Numeral_Omult__minus1_0, cls_NatSimprocs_Oless__minus__iff__number__of_0, cls_IntArith_Oarith__special__15_0, cls_Ring__and__Field_Odivide__minus__right_0, cls_Ring__and__Field_Ofield__mult__cancel__right_0, cls_IntDef_Oof__int__eq__0__iff_0, cls_NatSimprocs_Ozero__less__divide__iff__number__of_3, cls_NatSimprocs_Omult__less__cancel__right__number__of_0, clsrel_Ring__and__Field_Oordered__ring__strict_0, cls_NatArith_Odiff__Suc__diff__eq1_0, cls_Numeral_Obin__mult__1_0, cls_Nat_Oone__le__mult__iff_0, cls_Ring__and__Field_Ofield__mult__cancel__right_1, cls_Ring__and__Field_Otimes__divide__self__left_0, clsrel_OrderedGroup_Olordered__ab__group_8, clsrel_Ring__and__Field_Oordered__semidom_5, cls_Parity_Oneq__one__mod__two_1, cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_1, cls_IntArith_Oarith__special__13_1, cls_Parity_Opower__le__zero__eq__number__of_2, cls_NatSimprocs_Odivide__less__eq__number__of_1, cls_Numeral_Omult__number__of__left_0, cls_Divides_Omod__less_0, cls_Parity_Oeven__zero_0, cls_IntArith_Ozabs__less__one__iff_1, cls_NatSimprocs_Oless__divide__eq__number__of_8, cls_Parity_Oeven__sum_1, cls_OrderedGroup_Oneg__less__iff__less_0, clsarity_nat_46, cls_Nat_Odiff__diff__left_0, cls_Ring__and__Field_Omult__nonneg__nonneg_0, cls_Parity_Ozero__less__power__eq__number__of_5, cls_IntDef_Ozero__zle__int_0, cls_NatArith_Oadd__diff__assoc_0, cls_IntArith_Oarith__special__1_0, clsarity_IntDef__Oint_33, clsrel_Ring__and__Field_Oordered__semidom_6, cls_Parity_Ozero__le__power__eq__number__of_0, cls_Ring__and__Field_Omult__divide__cancel__left__if_0, clsrel_Ring__and__Field_Ofield_11, clsrel_Ring__and__Field_Oordered__ring__strict_34, cls_Parity_Opower__less__zero__eq__number__of_1, cls_Binomial_Obinomial__1_0, cls_Ring__and__Field_Odivide__less__0__1__iff_1, cls_Ring__and__Field_Odivide__less__eq__1__pos_1, cls_Ring__and__Field_Oinverse__mult__distrib_0, cls_Numeral_Obin__arith__extra__simps__1_0, clsrel_Ring__and__Field_Oordered__idom_44, cls_IntArith_Onat__1_0, cls_IntDef_Oof__int__le__iff_1, cls_Divides_Odiv__mult__mult1_0, cls_OrderedGroup_Oabs__0__eq_1, cls_Ring__and__Field_Oinverse__eq__1__iff_0, cls_IntDiv_Ozmod__minus1__right_0, cls_NatSimprocs_Oeq__divide__eq__number__of_3, cls_IntDef_Oof__int__0__less__iff_1, cls_Orderings_Oorder__class_Oaxioms__1_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_0, cls_Ring__and__Field_Omult__divide__cancel__right__if_1, cls_OrderedGroup_Onprt__0_0, clsrel_OrderedGroup_Olordered__ab__group__meet_16, cls_NatSimprocs_Odivide__le__0__iff__number__of_1, cls_Power_Opower__eq__0__iff_1, cls_NatSimprocs_Ozero__le__divide__iff__number__of_3, cls_IntDiv_Ozdiv__zadd__self2_0, clsrel_Ring__and__Field_Oordered__ring__strict_20, cls_NatBin_Omult__nat__number__of_1, cls_Divides_Omod__self_0, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_Power_Orecpower_9, cls_NatSimprocs_Ole__divide__eq__number__of_6, clsrel_Ring__and__Field_Oordered__ring__strict_18, clsrel_OrderedGroup_Olordered__ab__group_2, cls_IntDef_Oof__int__less__0__iff_1, cls_IntDef_Ozle__int_1, cls_Divides_Odiv__mult__self2_0, clsrel_Ring__and__Field_Oordered__ring__strict_23, cls_NatSimprocs_Omult__less__cancel__left__number__of_4, cls_Divides_Odiv__0_0, cls_NatSimprocs_Ozero__less__divide__iff__number__of_1, clsrel_Ring__and__Field_Oordered__ring__strict_29, cls_IntDef_Oof__int__le__0__iff_0, cls_Nat_OSuc__not__Zero_0, cls_NatSimprocs_Omult__less__cancel__right__number__of_4, clsrel_OrderedGroup_Opordered__ab__group__add_13, cls_Nat_Omult__less__cancel1_2, clsrel_OrderedGroup_Olordered__ab__group__abs_17, cls_Nat_Oless__Suc0_1, cls_IntDef_Oint__eq__0__conv_0, cls_IntDiv_Ozero__le__zpower__abs_0, cls_IntDiv_Ozdiv__self_0, cls_Divides_Odvd__1__left_0, cls_NatSimprocs_Odivide__le__eq__number__of_1, cls_SetInterval_OatMost__subset__iff_0, cls_Numeral_Obin__rel__simps__3_0, clsrel_Ring__and__Field_Oordered__semidom_29, cls_NatBin_Oeq__nat__number__of_2, cls_Parity_Oeven__nat__Suc_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1, cls_NatSimprocs_Odivide__less__0__iff__number__of_4, cls_IntArith_Oarith__special__6_0, cls_Ring__and__Field_Odivide__eq__eq__1_2, clsrel_Ring__and__Field_Oordered__field_6, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0, cls_NatSimprocs_Omult__less__cancel__left__number__of_3, cls_NatSimprocs_Ozero__le__divide__iff__number__of_0, cls_NatSimprocs_Omod__Suc__eq__mod__add3_0, cls_Divides_ODIVISION__BY__ZERO__MOD_0, cls_Nat_Onat__add__left__cancel_0, cls_IntDef_Oof__int__0__eq__iff_1, cls_Nat_Onat__0__less__mult__iff_2, clsarity_IntDef__Oint_39, cls_IntDef_Onegative__zle_0, clsarity_nat_13, cls_Ring__and__Field_Oeq__divide__eq__1_1, cls_Ring__and__Field_Odivide__le__eq__1__pos_1, cls_Ring__and__Field_Omult__zero__left_0, cls_Ring__and__Field_Omult__divide__cancel__right__if1_1, cls_NatArith_Oof__nat__less__iff_1, clsrel_OrderedGroup_Olordered__ab__group__abs_7, clsrel_Numeral_Onumber__ring_21, cls_NatSimprocs_Oadd__2__eq__Suc_0, cls_NatSimprocs_Oadd__self__div__2_0, cls_IntDiv_Ozdiv__zmult__self2_0, cls_Divides_Onat__mod__mod__trivial_0, cls_Ring__and__Field_Omult__cancel__right1_0, cls_Nat_Oone__le__mult__iff_2, cls_Numeral_Obin__add__BIT__0_0, clsarity_IntDef__Oint_41, cls_Numeral_Obin__minus__Pls_0, cls_NatSimprocs_Odivide__le__0__iff__number__of_3, cls_Power_Opower__one_0, cls_Parity_Oeven__nat__product_0, cls_IntArith_Ozle__add1__eq__le_0, clsarity_nat_24, cls_IntArith_Oarith__special__16_0, cls_NatBin_OSuc__nat__number__of_1, cls_OrderedGroup_Oneg__le__0__iff__le_0, clsrel_Ring__and__Field_Oordered__idom_34, cls_NatBin_Oeq__nat__number__of_8, cls_NatSimprocs_Ole__divide__eq__number__of_2, cls_NatSimprocs_Omult__less__cancel__left__number__of_0, cls_Parity_Ozero__less__power__eq__number__of_0, cls_NatSimprocs_Omult__le__cancel__right__number__of_1, clsrel_Ring__and__Field_Oordered__field_51, cls_Ring__and__Field_Oless__divide__eq__1__neg_1, cls_NatBin_Oone__mod__nat__number__of_1, clsrel_OrderedGroup_Olordered__ab__group__join_15, cls_NatSimprocs_Ominus__le__iff__number__of_0, cls_List_Olexn_Osimps__1_0, clsrel_LOrder_Omeet__semilorder_1, clsarity_set_0, clsarity_IntDef__Oint_51, cls_IntArith_Ozle__diff1__eq_1, clsrel_OrderedGroup_Ocomm__monoid__mult_1, clsrel_OrderedGroup_Olordered__ab__group__meet_0, cls_IntDiv_Ozminus__dvd__iff_0, cls_Ring__and__Field_Oinverse__less__iff__less_1, cls_Nat_Ole0_0, cls_Nat_OSuc__less__eq_0, cls_Parity_Oeven__nat__sum_3, cls_Parity_Opower__eq__0__iff__number__of_0, cls_NatSimprocs_Odiv2__Suc__Suc_0, clsarity_nat_4, cls_OrderedGroup_Oneg__0__le__iff__le_0, cls_Ring__and__Field_Odivide__less__eq__1__pos_0, cls_NatBin_Oone__div__nat__number__of_0, clsarity_IntDef__Oint_23, clsrel_OrderedGroup_Olordered__ab__group__meet_8, cls_NatSimprocs_Odivide__less__eq__number__of_2, clsarity_IntDef__Oint_63, cls_IntDiv_Opower_Osimps__1_0, cls_IntDef_Oint__0__neq__1_0, cls_NatSimprocs_Oless__divide__eq__number__of_7, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0, cls_IntArith_Oone__less__nat__eq_0, cls_NatSimprocs_Odivide__eq__eq__number__of_0, cls_NatBin_Oadd__nat__number__of_0, cls_IntDef_Ozless__nat__conj_0, cls_Nat_Oop_A_L_Oadd__0_0, cls_Numeral_Obin__succ__0_0, cls_Ring__and__Field_Odivide__le__eq__1__neg_1, cls_Parity_Oeven__difference_3, clsrel_Ring__and__Field_Oordered__semidom_30, cls_IntDiv_Opos__mod__bound_0, cls_Ring__and__Field_Odivide__self__if_0, clsrel_OrderedGroup_Ocomm__monoid__mult_4, cls_Nat_Oadd__gr__0_1, cls_Ring__and__Field_Oinverse__le__iff__le__neg_0, cls_Set_Onot__psubset__empty_0, cls_Numeral_Obin__arith__extra__simps__6_0, cls_Numeral_Obin__rel__simps__1_0, cls_NatSimprocs_Ominus__le__iff__number__of_1, cls_NatSimprocs_Odivide__less__eq__number__of_8, cls_NatArith_Oof__nat__0__eq__iff_0, cls_IntArith_Oabs__minus__one_0, clsarity_IntDef__Oint_50, cls_Ring__and__Field_Odivide__cancel__right_0, cls_Nat_Omult__le__cancel1_2, cls_NatSimprocs_Ole__minus__iff__number__of_0, cls_NatSimprocs_Ominus1__divide_0, clsrel_Power_Orecpower_16, cls_IntDef_Ozero__less__nat__eq_0, cls_OrderedGroup_Oneg__less__0__iff__less_0, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, cls_SetInterval_OgreaterThanAtMost__empty_0, cls_NatBin_Oeq__nat__number__of_3, cls_Nat_Ole__0__eq_1, cls_IntArith_Oint__eq__iff__number__of_2, clsrel_Ring__and__Field_Oordered__field_40, cls_List_Ochar_Oinject_1, cls_NatSimprocs_Omult__le__cancel__left__number__of_2, cls_OrderedGroup_Oabs__of__nonneg_0, clsrel_Ring__and__Field_Oordered__field_15, cls_Numeral_Obin__rel__simps__5_0, cls_Power_Opower__increasing__iff_0, cls_NatSimprocs_Ole__divide__eq__number__of_9, cls_Divides_Odiv__le__dividend_0, cls_Numeral_Obin__rel__simps__12_1, cls_Parity_Oeven__product_2, cls_Nat_Oop_A_L_Oadd__Suc_0, cls_Ring__and__Field_Oinverse__inverse__eq_0, clsrel_Ring__and__Field_Ofield_18, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1, cls_Set_OpsubsetE_1, cls_Nat_Omult__le__cancel2_0, cls_NatSimprocs_Oleft__diff__distrib__number__of_0, clsarity_IntDef__Oint_55, cls_NatSimprocs_Odivide__le__eq__number__of_0, clsrel_OrderedGroup_Olordered__ab__group__meet_2, cls_IntDiv_Ozmod__zminus__zminus_0, cls_Nat_OZero__not__Suc_0, cls_Divides_Omod__mult__self__is__0_0, cls_SetInterval_OatMost__subset__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_2, cls_Nat_OlessI_0, cls_IntDef_Oof__int__eq__0__iff_1, cls_OrderedGroup_Oabs__idempotent_0, cls_Set_Odouble__complement_0, cls_Divides_Odiv__self_0, cls_NatBin_Oless__nat__number__of_1, cls_NatSimprocs_Odivide__le__eq__number__of_6, cls_OrderedGroup_Oabs__le__zero__iff_1, cls_Ring__and__Field_Ozero__less__divide__1__iff_0, cls_Ring__and__Field_Ozero__eq__1__divide__iff_0, cls_NatSimprocs_Oless__divide__eq__number__of_3, cls_Nat_Omult__less__cancel2_2, cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0, cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1, cls_Nat_OSuc__pred_0, cls_IntArith_Oabs__power__minus__one_0, clsrel_Ring__and__Field_Oordered__ring__strict_30, cls_Ring__and__Field_Odivide__eq__1__iff_1, cls_IntDef_Onat__zero_0, cls_IntDiv_Ozdvd__0__left_0, cls_Nat_Omult__eq__1__iff_1, cls_NatBin_Oeq__nat__number__of_12, cls_NatBin_Oeq__number__of__0_1, cls_NatSimprocs_Omult__le__cancel__right__number__of_4, cls_Divides_Omod__0_0, cls_Nat_Omult__Suc__right_0, cls_Ring__and__Field_Ofield__mult__cancel__left_0, cls_Ring__and__Field_Omult__minus__right_0, cls_IntDef_Oint__le__0__conv_0, cls_Nat_Oone__eq__mult__iff_1, cls_List_Ochar_Osize_0, clsrel_Ring__and__Field_Ofield_12, cls_NatArith_Oof__nat__le__iff_1, cls_OrderedGroup_Omeet__0__eq__0_1, cls_Numeral_Obit_Odistinct__2_0, cls_OrderedGroup_Oneg__join__eq__meet_0, cls_IntDef_Onat__zminus__int_0, cls_Nat_Omult__is__0_0, cls_IntDiv_Ozmod__zadd__self1_0, cls_Ring__and__Field_Otimes__divide__self__right_0, cls_Parity_Ozero__le__power__eq__number__of_2, cls_IntDef_Oint__le__0__conv_1, cls_IntArith_Oarith__special__17_1, cls_Parity_Opower__even__abs__number__of_0, clsrel_Ring__and__Field_Oordered__field_11, cls_Parity_Oeven__neg_1, cls_IntDef_Onegative__zless_0, cls_Numeral_Obin__mult__Min_0, cls_NatBin_Oeq__0__number__of_0, cls_Power_Onat__zero__less__power__iff_0, clsrel_OrderedGroup_Olordered__ab__group__join_18, cls_IntArith_Oarith__special__12_0, clsrel_Ring__and__Field_Oring_7, cls_IntDiv_Ozmod__1_0, cls_Divides_Odvd__1__iff__1_1, cls_IntArith_Oarith__special__11_0, cls_Ring__and__Field_Oone__divide__eq__0__iff_1, cls_Binomial_Obinomial__0__Suc_0, cls_IntDef_Ozle__int_0, clsarity_IntDef__Oint_9, clsarity_set_15, cls_List_Odrop__drop_0
% 86.96/21.50  % No. of inferences in proof: 2129
% 86.96/21.50  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20979 ms resp. 20243 ms w/o parsing
% 87.50/21.74  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 87.50/21.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------